Author(s) Oelmann, Harlan Daryl. Title Monterey ... · This document was downloaded on January 03,...
339
This document was downloaded on January 03, 2015 at 08:40:18 Author(s) Oelmann, Harlan Daryl. Title Fleet multi-channel broadcast traffic intensity study. Publisher Monterey, California. Naval Postgraduate School Issue Date 1972 URL http://hdl.handle.net/10945/16148
Transcript of Author(s) Oelmann, Harlan Daryl. Title Monterey ... · This document was downloaded on January 03,...
This document was downloaded on January 03, 2015 at 08:40:18
Author(s) Oelmann, Harlan Daryl.
Title Fleet multi-channel broadcast traffic intensity study.
Publisher Monterey, California. Naval Postgraduate School
Issue Date 1972
URL http://hdl.handle.net/10945/16148
HMHB
FLEET MULTI-CHANNEL BROADCASTTRAFFIC INTENSITY STUDY
Harlan Daryl Oe lmann
NAVAL POSTGRADUATE SCHOOL
Monterey, California
THESISFLEET MULTI:-CHANNEL BROADCAST
TRAFFIC INTENSITY
by
STUDY
Harlan Daryl Oelmann
Thesis Advisor: K. T. Marshall
June 1972
TU8515Appswvud ^on. puhLLc k.qJLqjx&<l; di^thJJovJtion. untimit&d.
r.')
Fleet Multi-Channel Broadcas
Traffic Intensity Study
by
Harlan Daryl^OelmannLieutenant Commander, United States Navy
B.S., Iowa State University, 1359
Submitted in partial fulfillment of therequirements for the degree of
MASTER OF SCIENCE IN OPERATIONS RESEARCH
from the
NAVAL POSTGRADUATE SCHOOLJune 1972
ABSTRACT
This thesis contains the analysis of data of message
traffic loads on the Naval Communications Fleet Multi-
channel Broadcast System and results of a simulation model
of the system under various channel alignments. Distri-
butions of interarrival times, message lengtlis and requests
for screens and reruns are determined from the data. These
distributions are used in a simulation model of the Broad-
cast System. The model is used to compare the average
delays caused by backlogs of messages when two channels
devoted to a given ship-type are a) used in series with the
second channel used to rebroadcast messages from the first
channel after a one hour delay, and b) both channels are
used in parallel to transmit first-run messages. The
results of the simulation show that backlogs are reduced
considerably by running the two channels in parallel at
all times.
TABLE OF CONTENTS
I. THE PROBLEM 11
A. THE QUESTION AS POSED FOR SOLUTION 11
B. TYPES OF CHANNEL PAIR OPERATION 12
1. Situation 1 12
2. Situation 2 13
C. DISCUSSION OF THE PROBLEM 14
II. THE APPROACH TO THE PROBLEM AND ITS SOLUTION 18
A. THE DECISION VARIABLE 18
B. MODELING THE PROBLEM 20
C. REQUIRED DATA 22
D. SUMMARY OF RESULTS 22
III. DATA COLLECTION AND ANALYSIS 2 4
A. FIRST RUN MESSAGE INTERARRIVALTIMES ANALYSIS 24
1. Source of Data 24
2. Analysis Results 24
B. MESSAGE LENGTH ANALYSIS 31
1. Source of Data 31
2. Analysis of Message Lengths 32
3. Analysis Results 33
C. SCREEN REQUEST AND FEEDBACK LOOP ANALYSIS 42
1. Reason for Analysis 42
2. Source of Data 43
3. Number of Subscribers that CopyRebroadcast Channel 43
4. Analysis of the Causes of Rerur s 44
a. Results of the Statistical andRegression Analysis 47
5. Analysis of Time Delays in theFeedback Loop 62
a. Interorigination and InterarrivalDistribution Analysis Results 63
b. Transmission Delay DistributionAnalysis Results 64
c. Service Desk Delay Distrib itionAnalysis Results 64
d. Reruns per Screen Request Distri-bution Analysis Results 65
IV. THE MODEL 71
A. GENERAL DESCRIPTION 71
B. MODEL CAPABILITIES 71
C. DESCRIPTION OF THE MESSAGE FLOWIN THE MODEL 73
D. THE MODEL AND THE REBROADCASTCHANNEL SIMULATION 82
E. VERIFICATION OF THE MODEL 84
F. MODEL SIMULATION RUNS AND RESULTS 89
1. Description of the Simulation Runs 89
2. The Results of the Simulation Runs 9 3
V. CONCLUSIONS 101
APPENDIX A: ORIGIN OF THE STUDY 102
APPENDIX B: PROBLEM BACKGROUND 103
APPENDIX C: GOODNESS OF FIT DATA ANALYSIS COMPUTERPROGRAM 114
APPENDIX D: TABLES OF CHANNEL SERVICE STATISTICSFOR MAY-JUNE 144
SIMULATION MODEL COMPUTER PROGRAM 14 8
LIST OF REFERENCES 161
INITIAL DISTRIBUTION LIST 163
DD FORM 1473 165
LIST OF TABLES
I. Broadcast Speed of Service Criteria — 19
II. Goodness of Fit Results for InterarrivalTimes 26
III. Goodness of Fit Results for MessageLengths 35
IV. Number of Subscribers Using the RebroadcastChannel — 44
V. FASW (Channel 1) Aug-Sep Service Statistics 49
VI. FALD (Channel 3) Aug-Sep Service Statistics 52
VII. FNSC (Channel 5) Aug-Sep Service Statistics 55
VIII. FRTT (Single Non-FMUL Channel) Aug-SepService Statistics < 57
IX. XRTT (Dedicated Exercise Channel) Aug-SepService Statistics 59
X. Goodness of Fit Results for Feedback LoopDistributions 66
XI. Model Parameters Held Constant 85
XII. FASW 13-16 Sep Observed Traffic Loads 86
XIII. Model Verification Results 90
XIV. Model Simulation Results for 13-16 SepFASW Traffic Loads 94
XV. Model Simulation Results for High TrafficLoads 96
XVI. Speed of Service Criteria 106
XVII. FMUL-Broadcast Channel Alignment 10 8
XVIII. FASW May-June Service Statistics 144
XIX. FALD May-June Service Statistics 145
XX. FNSC May-June Service Statistics 146
XXI. FRTT May-June Service Statistics 147
6
LIST OF FIGURES
1. Types of Channel Pair Operations 15
2. Log of the Tail Distribution for InterarrivalTimes, 5 MAR., All Precedences 27
3. CDFs for Interarrival Times, 5 MAR., AllPrecedences 28
4. Log of the Tail Distribution for InterarrivalTimes, 6 MAR., All Precedences 29
5. CDFs for Interarrival Times, 6 MAR., AllPrecedences 30
6. Log of the Tail Distribution for FASW MessageLengths, All Precedences 36
7. CDFs for FASW Message Lengths, All Precedences 37
8. Log of the Tail Distribution for FNSC MessageLengths, All Precedences 38
9. CDFs for FNSC Message Lengths, All Precedences 39
10. Log of the Tail Distribution for World WideMessage Lengths, All Precedences 40
11. CDFs for World Wide Message Lengths, AllPrecedences 41
12. FASW (Nr. First Run) (Nr. Subs) vs. Nr. Screens 50
13. FASW (Nr. First Run) (Nr. Subs) vs. Nr. Reruns 51
14. FALD 25 AUG. -6 SEP. (Nr. First Run) (Nr. Subs)vs. Nr. Screens 53
15. FALD 7-17 SEP. (Nr. First Run) (Nr. Subs) vs.Nr. Screens 54
16. FNSC (Nr. First Run) (Nr. Subs) vs. Nr. Reruns 56
17. FRTT (Nr. First Run) (Nr. Subs) vs. Nr. Reruns 58
18. XRTT (Nr. First Run) (Nr. Subs) vs. Nr. Reruns 60
19. XRTT (Nr. First Run) (Nr. Subs) vs. Nr. Reruns 61
20. CDFs for Screen Request InteroriginationTimes (September) 67
21. CDFs for Transmission Delays (September) 68
22. Log of the Tail Distribution for Service DeskSystem Delays (September) 69
23. CDFs for Service Desk System Delays (September) --- 70
24. First Run Traffic Flow in the Model 76
25. First Run Traffic Flow in the Model(Continued) 77
26. Flash Message Routine, with Preemption 79
27. Screen Request and Feedback Loop 81
28. Diurnal Function for 13-16 Sep. FASW MessageArrivals 87
29. Model Simulation and Actual Total Backlogs onFASW, 13-16 Sep 91
30. Total Backlogs for Simulation Runs 2 and 3
(CHAN2 Open and CHAN2 Open/Closed) of FASWTraffic, 13-16 SEP 95
31. Total Backlogs for Simulation of High TrafficLoads (CHAN2 Closed) 97
32. Total Backlogs for Simulation Runs 6 and 7
of High Traffic Loads (CHAN 2 Open andCHAN2 Open/Closed) 98
TABLE OF ABBREVIATIONS
AUTODIN
COMNAVCOMM
CDF
CLTMR
DTG
MAPU
MSG
NAVCALS
NAVCAMS
NAVCOMMAREA
NAVCOMMSTA
NAVCOMMSYS
NAVCOMMU
NAVRADSTA
OPTMR
PR
PREC
SCRN
SCRN REQ
SUBS
SVC
TD
TTY
Defense Communications System AutomaticDigital Communications Network
Commander, Naval Communications Command
Cumulative Distribution Function
Closing Timer (used in the model)
Date-Time-Group, a message ide ntification
,
e.g. , R 021944Z SEP 71, a Routine messageoriginated on 02 SEP 1971 at time 1944Z(Greenwich Mean Time)
Multiple Address Processing Unit
Message
Naval Communications Area Local Station
Naval Communications Area Master Station
Naval Communications Area
Naval Communications Station
Naval Communications System
Naval Communications Unit
Naval Radio Station
Opening Timer (used in the model)
Priority or Precedence (used in the model)
Precedence
Screen
Screen Request
Subscriber
Service
Transmitter Distributor
Teletype
WORD A teletype word consists of 5 teletypecharacters
WPM Words-Per-Minute
ZULU TIME Greenwich Mean Time
10
I. THE PROBLEM
This study concerns the message traffic loads on the
Naval Communications Fleet Multi-Channel Broadcast System
and the problem of determining the most efficient use of
the 8 traffic channels in delivering teletype message
traffic to the ships at sea.
The Commander, Naval Communications Command message,
R 021944Z SEP 71, officially commissioned this study. A
copy of this message is shown in Appendix A for reference
and to provide an example of a Naval Communications message,
Appendix B provides background information on the
organization of the Naval Communication System and a des-
cription of the Fleet Multi-Channel Broadcast System.
A. THE QUESTION AS POSED FOR SOLUTION
The original question as it was posed for this study
was: "When a significant backlog of any precedence message
exists at a channel pair broadcast position, such that the
primary channel delivering first run traffic is overloaded,
when should the assigned secondary channel be activated for
first run traffic and when that backlog ceases to be signi-
ficant, when should the secondary channel be deactivated
from first run traffic?".
In order to discuss the problem further we must first
consider how the primary and secondary channel pairs are
aligned and used in different traffic load situations.
11
B. TYPES OF CHANNEL PAIR OPERATION
Table XVII in Appendix B describes the f : iet multi-
channel broadcast alignment and the designated use for each
of the 8 channels. This study considers only 6 of the 8
channels. We note from Table XVII that these 6 channels
form 3 pairs of channels which serve different types of
ships copying the broadcast. They are: channels 1 and 2
for the Destroyer force, channels 3 and 4 for the Service,
Amphibious and Mine forces and channels 5 and 7 for the
major warships. Channels 2, 4 and 7 are each designated
for use either as a 1 hour delayed broadcast or as an over-
load channel for the primary channels 1, 3 and 5 respectively,
This allows these secondary channels to be employed in one
of two different ways depending on the traffic load
situation.
1. Situation 1
When the traffic load for a channel pair is such
that the primary channel is not significantly backlogged the
secondary channel is used for the 1 hour delayed rebroadcast
of the primary channel's traffic. This alignment thereby
provides the subscribers of the channel pair two chances to
copy a message correctly and completely. Thus if a sub-
scriber misses a message or a portion of a message on the
primary channel the subscriber may then wait for one hour
and attempt to copy the message on the rebroadcast channel.
If the subscriber should miss the message both times he then
must use the procedure described, in Appendix B, for obtain-
ing the missed message. This configuration assumes that by
12
providing this redundancy in traffic delivery that the
number of service requests for reruns will b reduced com-
pared to having only one opportunity to copy the message.
Further, it is noted that, for a subscriber to originate a
screen request and to receive a reply and/or the desired
rerun, the experienced normal time required for such action
is in excess of one hour. Hence the 1 hour delayed rebroad-
cast appears to provide better service provided all sub-
scribers use the system as this alignment intends.
On the other hand there may be situations in which
the urgency of the message is such that the subscriber may
not want to wait and gamble on the 1 hour delay, only to
possibly miss the message again, or perhaps equipment prob-
lems may prevent a subscriber from being able to copy the
rebroadcast.
2 . Situation 2
This situation provides for the case when the
channel pair traffic loads are heavy, and significant back-
logs do build up such that a decision has to be made by the
NAVCOMMSTA to activate the secondary channel to transmit
first run traffic in the same manner as the primary channel.
In this case both channels of the pair are used to clear
the backlog of traffic that has accumulated and to handle
any anticipated increase in traffic arrivals which may
cause any increased backlog. At the same time, however,
this configuration precludes any facility for rebroadcasting
the first run traffic as was described in situation 1 above.
It is also assumed that this configuration will also prompt
13
more screen requests to be initiated by the subscribers
since it intuitively seems reasonable that mere messages
may be missed since twice as much first run traffic is
being delivered to the subscribers of the channel pair.
In cases where a broadcast channel has no delayed
rebroadcast facility use is made of what is called "heading
recaps." Heading recaps are a periodic rebroadcast of the
headings of messages previously transmitted on that partic-
ular channel. Although the broadcast of the heading recaps
will consume some of the valuable times needed for trans-
mitting messages which are backlogged it is reasoned that
this feature will have an effect of cutting down on the
number of screen requests which were prompted because the
subscriber was trying to determine only if a missed message
was of concern.
Figure 1 diagramatically displays the above des-
cribed situations, where channels 1 and 2 were the chosen
channel pair for illustration.
C. DISCUSSION OF THE PROBLEM
Under conditions when no "significant" backlog of any
message precedence exists the channel pair operation will
operate as described in situation 1 above. However when a
"significant" backlog starts to build up it may then be
necessary to use situation 2 in order to make a more timely
and efficient delivery of the traffic.
The problem of this study is to determine what is meant
by a "significant" backlog and thus determine the point at
14
Situation 1
Arrivals
850 wpmBurpee
850 wpmBurpee
Rerunand
OtherMessages(By Hand)
Grid
$
->
Flash (Z)
Immediate (O)
Priority (P) .
Routine (R)
TransmissionChannels
#1 Primary100 wpm
First RunTraffic
V#2 Secondary
100 wpm1 hr. DelayRebro adcast
Situation 2
Arrivals
850 wpmBurpee
850 wpmBurpee
Rerunand
OtherMessages(By Hand)
Grid
^Flash (Z)
^ Immediate (O)
Priority (P)
"; Routine (R)
TransmissionChannels
#1 Primary10 wpm
First RunTraffic
/ N, \\ I
i/ "O. #2 SecondaryP" —
• — .^.y 10 wpmFirst RunTraffic
Figure 1. Types of Channel Pair Operation.
15
which the channel pair is switched from situation 1 to 2 , or
vice versa. At present this decision is mad by (i) observ-
ing how the system has behaved in the past, (ii) by observing
the system in its present state, and (iii) by using experience
to predict the future state.
The experienced communicator knows that the traffic
arrival rate at the broadcast position foliows a diurnal
fluctuation. He has also observed when the channel pair
operation was changed to the situation 2 alignment that the
service desk after a time delay experienced a surge of screen
requests since the rebroadcast channel facility was discon-
tinued. This surge of screen requests which produce message
reruns will most likely contribute further to the backlog
and thus the backlog will get worse rather than better.
Therefore when the backlog becomes significant the decision
maker may decide to hold the system in situation 1 and hope
that things get better, or he may make the decision to go to
situation 2 and hope that the surge of screen requests, does
not contribute to the backlog in a significant way.
This method of decision making leaves something to be
desired and this study was conducted in order to investigate
the two alternate situations and to determine values of the
decision variable for when switching should take place.
When the NAVCOMMSTA activates the secondary channel for
first run traffic, rather than as a rebroadcast channel,
there is a 30 minute delay requirement between notification
to the subscribers and the time the channel is activated.
16
This delay time used by NAVCOMMSTA San Francesco, and assumed
common among other NAVCOMMSTA * s , is needed for subscribers
to prepare necessary equipment to copy the secondary channel
all the time. Notification of the intent to activate the
secondary channel is sent to the subscribers on the primary
channel.
17
II. THE APPROACH TO THE PROBLEM AND ITS SOLUTION
A. THE DECISION VARIABLE
In order to answer the original question it is first
necessary to determine when a significant backlog of messages
exists. Let us say that a backlog is considered significant
if the expected or average time a message of a certain
precedence spends in the broadcast queue and transmission
system exceeds the limits of the speed of service criteria
shown in Table XVI in Appendix B.
Actually the time standard referred to here is smaller
than the speed of service criteria in the table / because the
message has already spent some time in transmission before
reaching the broadcast position.
During the analysis of screen request messages in this
study it was observed that these messages took an average
of 2 hours in transmission from the originator to the ser-
vice desk in the NAVCOMMSTA. If we observe that these
screen requests are almost always of Immediate or Priority
precedence and if their numbers were evenly divided then
the average speed of service criteria would be approximately
150 minutes. Thus 80 percent of the average transmission
time was used in transmitting the screen request messages
from the ship originators to the NAVCOMMSTA. If for example,
these messages were not screen requests messages destined
for the service desk, but rather for further relay on the
18
broadcast, we can see that on the average these messages
could spend 30 minutes waiting at the broadc st position
for transmission before exceeding the average speed of
service criteria. We allow however that not all messages
arriving at the broadcast position are from ships at sea
but that many are from shore establishments and hence the
messages were received at the NAVCOMMSTA via the AUTODIN
network which has a much faster transmission rate than the
100 wpm ship-shore teletype circuits. Nevertheless it does
not appear unreasonable to assume that an arbitrary but
conservative revised speed of service criteria standard to
be used at the broadcast could be 50 percent of the criteria
shown in Table XVI in Appendix B.
Reducing the times in Table XVI by 1/2 would result in
times shown in Table I below.
TABLE I
BROADCAST SPEED OF SERVICE CRITERIA
Precedence AverageSpeed of Service Limits
Flash (Z)
Immediate (O)
Priority (P)
Routine (R)
As fast ashumanly possible
15 minutes
lh hours
3 hours
Same
15-30 minutes
30 minutes- 3 hours
1V-12 hours
19
The decision variable of the problem can then be defined
as the expected time a message of a certain precedence
spends in the broadcast queue and transmission system, i.e.,
average time in queue plus the average time in transmission.
In addition, a measure of effectiveness can be defined to
be the time difference between the expected time in system
and the broadcast speed of service criteria.
It would then be logical to conclude that if messages
of a certain precedence spent more time on the average than
is allowed by the broadcast speed of service criteria, the
broadcast system is not making timely and efficient delivery
of the traffic. Thus if this condition exists for any
appreciable period it should be necessary to use both the
primary and secondary channels to deliver the traffic.
B. MODELING THE PROBLEM
The type of model which best fits this system is a
queueing model. The customers are the messages and the
servers are the transmission channels. The system has four
priorities or precedences of messages of which the highest
precedence is Flash. The Flash message is allowed to pre-
empt any lower precedence. When a flash message preempts
another message the preempted message is later rerun from
its beginning after the flash message transmission has been
completed. A flash message is run three times to ensure
receipt by the addressee. The preemptive method described
is known as the Preempt Rerun method as opposed to the
Preempt Resume method where the preempted messages will
20
continue transmission from the point at whicl- it was inter-
rupted.
The modeling of the feedback loop of this system is
probably the most challenging because of its various time
delays. The feedback loop referred to is that part of the
system in which screen requests are made by the subscribers
and from which the message reruns are generated. This feed-
back loop has three time delays associated wi th it plus a
message grouping effect and a change in precedence effect.
The first time delay is the period of time between the
actual time the message was missed and the time at which a
screen request was sent out by the subscriber. This time
delay was not analyzed due to the complexities of measure-
ment. The second and third time delays are the time in
transmission of the screen request to the NAVCOMMSTA and
the time required to process the screen request at the
NAVCOMMSTA broadcast service desk.
The grouping effect is caused by the fact that screen
requests normally require a number of messages to be
screened and this in turn results in the rerun messages
being delivered to the broadcast position in groups of
messages
.
The change in precedence effect is something that has
not been previously mentioned. It is observed that the
normal precedence assigned to a screen request is either
Immediate or Priority even though some of the messages
asked for may be of Routine precedence. This is done because
21
the originator of the screen' request senses a greater
urgency in obtaining the missed messages because of the
above described time delays. This upgrading of precedence
then may require the NAVCOMMSTA to answer the screen request
at a higher precedence than the precedence of any message
referenced in the request.
C. REQUIRED DATA
The data required to analyze this problem falls into
three areas. First, data to determine the type of message
arrivals at the broadcast position. Second, the message
length distribution must be known. Since the transmission
rate of the servers is constant at 100 wpm, the message
length distributions translate into the service time dis-
tributions. Third, data concerning the screen requests is
required. It is essential to investigate the time delay
involved from the request for a rerun until it is received
by the subscriber, as well as various other parameters which
will be more fully described later.
D. SUMMARY OF RESULTS
In order to realistically model the problem, data for
interarrival times of first run messages, message lengths,
and requests for sceens and reruns was analyzed. The
following conclusions were made.
i. The first run message interarrival times werefitted to the exponential distribution and thusthe arrivals follow a Poisson Process. (SeeTable II.)
22
ii. The message lengths were fitted to a hyperexpo-nential distribution with two prr portionparameters. (See Table III.)
iii. The interorigination times for screen requestsfit the exponential distribution and thus werealso concluded to arrive in a Poisson Process.(See Table X.)
iv. The transmission delay distribution for screenrequests was fitted to a right shifted expo-nential distribution. (See Table X.)
v. The delay of a screen request at the servicedesk was concluded to follow rig.it shiftedhyperexponential distribution for high loadperiods and a right shifted exponential distri-bution for low volume traffic. (See Table X.)
vi. The number of rerun messages resulting from ascreen request was found to be exponentiallydistributed. (See Table X.)
The relationship of the number of first run messages and
the number of subscribers with the number of screens and
reruns was analyzed by linear regression. The results indi-
cate that these variables are independent of each other.
(See Figures 12-19.)
The GPSS simulation model of a broadcast channel pair
was used to simulate the FASW channel pair in various con-
figurations and traffic loads. The configurations simulated
and compared by the average level of backlog were: i) channel
2 closed to first run traffic and used as a rebroadcast of
channel 1 traffic, ii) channels 1 and 2 both transmitting
first run traffic while the rebroadcast facility was not
used and iii) channel 2 alternately opened and closed to
transmitting first run traffic whenever specified backlogs
were exceeded. The result of these simulations was that back-
logs were reduced considerably by running the two channels
in parallel transmitting first run traffic and reruns.
23
III. DATA COLLECTION AND ANALY. IS
The primary source of data used in this thesis was
NAVCOMMSTA San Francisco located at Stockton, California.
The relative close location of Stockton to Monterey, Cali-
fornia allowed frequent visits to the NAVCOMMSTA both to
talk to personnel at the station and to collect data.
Although the fleet atmosphere of the Eastern Pacific
differs from other parts of the world, it is felt that the
type of data collected and that in general the analysis
results are typical of any NAVCOMMSTA.
All data which was analyzed to determine a goodness of
fit to a theoretical probability distribution was analyzed
by using the Fortran IV computer program described and shown
in Appendix C.
A. FIRST RUN MESSAGE INTERARRIVAL TIMES ANALYSIS
1. Source of Data
The data used for the analysis represented 4 days of
traffic received at the channel 1 broadcast position at
NAVCOMMSTA San Francisco. The days represented were 5-8
March 1971. The traffic load for these days was a low to
medium volume of 142 to 401 messages per day.
2
.
Analysis Results
In order to show that the messages arrive in a
Poisson Process it is necessary to show that the interarrival
times are distributed according to the exponential prob-
ability distribution.
24
The data was analyzed for the daily aggregated
arrivals and by individual precedences. Tab- e II gives the
results of the statistical goodness of fit tests. We see
that the Kolmogorov-Smirnov tests indicated rejection of
the hypothesis that the interarrival times are distributed
exponentially while the Chi-square tests indicated acceptance
for all samples except one. This apparent contradiction is
explained by noting that the interarrival times were measured
to the nearest integer minute. Hence this caused the data
to contain groups of data points of equal value, especially
for times less than or equal to 3 minutes. As is noted in
Appendix C this grouping effect causes the Kolmogorov-
Smirnov (K-S) statistic to inflate and hence causes rejection
Figures 2 and 3 represent the graphic results for
All precedences of 5 March, the data for which both statis-
tical tests indicated rejection of the hypothesis. Figures
4 and 5 represent the graphic results for All Precedences of
6 March and are shown for comparison to the 5 March graphs
since the chi-square test indicated acceptance of the
hypothesis for the 6 March All Precedence data.
From the statistical test results and from graphs of
the data it was concluded that the interarrival times could
be reasonably assumed to be distributed according to the
exponential distribution. Since this data represented only
channel 1 arrivals, it is assumed that message arrivals at
other channel pairs also arrive in a Poisson Process.
25
00LU
<>i—
<
or
<c£
a:O
oo
3ooLUa:
LL
ooo00LJJ
2fQOOO
LU-JCO<
00 Z>LUO0l-LU
I OHOC<a00I
*—>
Io
< i
oo
u.Q
>t-_)
ZLUt/>o:i-uj-< oc
ooI LU>00_JO I CO
O h-oo_J00<O I h-N^^OO
<a
• CDoo:
>LU
001—
D
a:oo •
LULUQH- t-LU 0O
< -z.
c£»-<<O0UJcllus:
LU_JLUQ.MSl<-<<00oO
OtuaraLU
<
H m in • inominin CMnoo ooom (*•<.&&uj^o^o o^cmo^o^ o^o^mo^ o • on c*
LUa:
r-tvOcoco «-<ro>d-r*- r^-^-uNjn c\j-HmoOvtcOvO in—iom oocnjcni (\jmcor--
vor->tm o^rvj—<— mmcoo sooh-voCO <\IC\J (NJ (M(\l *H (\J CNJCsJ
p-^v0vO^o mminvo or\jo<f- mo^n
O'-nooLUCM-UlU
LU LULUo£. aLaL
ocosomcoc>r\j.—
i
OHiHi-I
OlAOULUCM-ULU
LU LULUOC c£o£
CNJOCOO<j-st>n^-coO<fc\j
oomin~5 • • •
LUCC
O^OOOvf-comc\jroCMnoj
ooooLUCM-ULU-5 •->-?LU LULUOH alec
c\lomco
-trOvor*",_|<\J.-H.—
I
v*-inr*-f*-
r-rocor-
N>tONr^<ff*-coincome^(%!•—«—•>—
l
<Mor~or-CT>s0C\J
Of- in CM
OCM^OrH(\J—lr-<C\|
(\jroc\iinoo ro—<mcnjo-h—<
rnosivOcocrOvDro(NJrOCO'-H
NOOh
cMvomoOOcor-o<\imr\j^ooo
mooinminborn4-^r-vO^ooo
h-OfOco mcMincr* 0<tO—< OOOojcOsoo^o^ Ovj-oor*- sooo^cxj ror\imco
•4-rno. in vO >to r-ivOh-o ooooor-ro>-<>—i —i-i"-—14- -4-—ic\j
vtrnoor^- sOr^-Lnovj oo^i-Or-i r^-cocor-iina^ooro rOOu\co Orinoco cosO'-iro
roo^coh- >j-ro^-tco ococoin vOr*->fm<\j c0i-t >4
-<—TO «o«-<i-i
h>oon vOrO'-'O c\jcoinr»- mcr>CMno^-vOC^ ogvtCNjxO -4-nJh-ro O-hO^co•4" r-f-H CO r-lf-H -H c\j
joq-d^ _joa.Di joq-o: joaa:< < < <
<
in
c£<
a:<21
CO
26
6 12 18 24Interamval Times (minutes)
THEO
X
30
Figure 2. Log of the Tail Distribution for InterarrivalTimes, 5 MAR., All Precedences.
27
THEO
6 (2Interarrival Ti
18 24me s (minutes)
x
30
'
Pl9Ure 3"
5DS„
f0r ^-arrival Times5 MAR.. All Precedences
'
28
5.0 i—
4.0 —
PnI
3
Interarrival Times (minutes) ,
Figure 4. Log of the Tail Distribution for InterarrivalTimes, 6 MAR., All Precedences.
29
Interarrival Times (minutes)
Figure 5. CDFs for Interarrival Times,6 MAR., All Precedences.
30
B. MESSAGE LENGTH ANALYSIS
1. Source of Data
The data for message length analysis is from two
sources. The first source contains two samples of messages
and was taken at NAVCOMMSTA San Francisco. These samples
represented the traffic sent on 5 October 19 71 on channel 1
(FASW) and channel 5 (FNSC) . The other source of data was
the Naval Electronics Laboratory Center. Th is data was
obtained from the World Wide Traffic Demand tudy data bank
and it represents all messages sent on a fleet broadcast
in various parts of the world on 8 October 19 70. This
sample therefore represented the Fleet Broadcast System as
a whole and could be assumed not to be biased by any area
effects
.
The FASW and FNSC samples were taken by measuring
the messages in teletype tape form. This method of sampling
provides for a high degree of accuracy in determining the
length of a message. Teletype tape contains 100 characters
per foot which equals 20 words. It should be noted that
the tape includes all teletype characters which are processed
by the transmitter distributor when sending a message such
as spaces, blanks, line feeds, shifts to upper and lower
case print, etc. , characters which are not easily identified
on a printed copy.
The message lengths of the World Wide sample on the
other hand were determined by measuring page copies of the
messages and using a regression equation to determine the
number of words per inch of page copy.
31
2. Analysis of Message Lengths
The general plan for this analysis w- s to attempt
to fit a probability distribution to the message length data
by precedence and then to compare that fit to the world wide
sample.
The first fit attempted was the exponential distri-
bution. The results of this showed that the message lengths
were not distributed exponentially.
At this point two observations of tho above analysis
were made. One was that a message has a minimum positive
length, since each message has to have a heading which has
a date-time-group , an originator and an addressee plus a
text. It was estimated that such a minimum would be approx-
imately 20 words long. This led us to fit the data with a
right shifted exponential. However, the second observation
that was made was that the graphs of the log of the recipro-
cal of the tail distribution, or simply called the log of
the tail, showed that the data in every case had a decreasing
failure rate at least for message lengths up to approximately
500 words. One particular distribution with a decreasing
failure rate is a mixture of exponential distributions known
as the hyperexponential distribution.
These two observations led us to fit the data with
a right shifted hyperexponential distribution with two
parameters
.
The remaining question was whether the FASW and FNSC
data which was taken from one day only was representative of
32
messages sent on other days and on broadcasts throughout
the world. This is the primary reason that the world wide
sample was obtained.
It was found that the world wide data behaved in
the same manner as the FASW and FNSC data and that the right
shifted hyperexponential made a very good fit. It was noted
however that one of the major differences between the two
sets of data was that the world wide data had very few data
points which exceeded 1000 words while such data points were
very much in presence in the other two samples. Since the
analyst personally took the FASW and FNSC samples it was
decided that these large data points were not freak outliers
,
but were very much a part of the distribution. On the other
hand it is noted that in reality, message lengths on the
broadcast and in general do have an upper bound to their
length which is estimated to be approximately 2000 words.
This is an apparent contradiction between the empirical and
theoretical distributions. It is resolved however by observ-
ing that the probability of getting such a long message is
indeed very small.
3. Analysis Results
Table III shows the results of the goodness of fit
tests for message lengths. It should be pointed out that
for all goodness of fit tests that not only were the statis-
tical tests used in making a judgment on the fit but also
interpretation of the log of the tail and the Cumulative
Distribution Function (CDF) graphs. As is noted in Appendix
C/ the Chi-square statistic for large sample sizes tends
33
to inflate and careful attention must be made to the selec-
tion of the number of intervals and their widths. In this
analysis these drawbacks of the chi-square test were care-
fully controlled. When the results of the K-S test and the
chi-square test conflict we choose the K-S test results
unless a graphical interpretation could explain the reason
for the rejection result.
We see in Table III that the K-S test results indi-
cate that the hypothesis should be rejected when all
precedences are aggregated while only in the case of the
FNSC data for all precedences does the chi-square test
indicate rejection. Additionally the K-S test indicates
rejection for Flash and Immediate precedences for the FNSC
data. It is noted that the Flash message samples are
included only to give representation of the parameters
associated with this precedence since the respective samples
were very small and give little meaning to any goodness of
fit tests.
Figures 6 through 11 show the log of the tail dis-
tribution and CDF graphs for the aggregated precedence for
each of the three samples.
In the cases where the Table statistical results
indicate rejection for All Precedences of each of the three
samples we see that the empirical curve in the log of the
tail graph deviated from the theoretical curve in the message
length range of greater than 600 words. However the CDF
graph shows a reasonably good fit to the theoretical
34
K • in in • mm 1-
l-_J <O0NG"> 0> <Oh-r- O c^c o o
oor> • CT^O^CJ^ O •ooo^ LU sam CJN
UJUJOO z • • • • 2 • • • "5 • • • •
OCH-UJ UJ< a: OCT
=>(3 OO^NvO CO vOOO^OO orn^o CNJ
OO (- or*-org o CO.-tCjN CT> cor^-o CO
1 < • t • • • » • • • • • • t •
>— H- oc^mm CJNO^-t v0 in^tm 4"
X 00 r-4CNjCNj 1—
«
r-li-H m i-H —
«
UooI LL oi^-o-h o OrOvOh- s0 ^-iNor^- sO
H« O r-IHOuj
K K h-h- f- h-UJ l-_l LfMAOO^ o oua^o o mu~ n oo 00 Z) crocjNO UJ LULU0NO LU O^C tT> LU
< UJOO • » • • -> -$"0 • • -J • • • ~3
oo 001— UJ UJ LULU LU LU
on t OL c£ a: a: CC ex:
UJ ^s: (- Ocorntn v0 ^CO^tvO CO (\JC\JO m
00< h- com cm o incMnoN -0 r-^sr CNJ
OCT 1 H i >J->j-^ro r-l inr-cno m OCM c-t
O N^OO LT\»-t i-t»-< 1—
1
m^-trHO f—
i
(\|f~H-H rHLL
•
00
• • • t • • • • • • • • • •
ooh- •< ininoin LO mmmm m om^ o_l a: c\j(\imr\J CNJ c\jc\jc\Jxi- c\j mro^ i—4
3 UJoo z-» or-mm o incoo -o m o CM CNJ ,o CNJ
UJ Oa .-4CNJCNJCNJ o r-.tO—l m 1—
1
r*-c\jo vO
a: « I2 vOCOOnO O O tnCT>00 ro 2 mooo -t
K-r-4 OO OvOl^f- CO 00 oococo l> cosom mi- a£—' <£ • • • • t "Z. • • • • • O • • • •
i—i O u_ LL _J
U_ O- i oror-r"- o mtMOvt m cc coco.4- CO
o < (M^M^- o Orinoco <l- o c\jr-o mLL CCCl. rO'-«OrO o •fOOCh n0 3: <tt>H mO Q. Ococnjcnj CNJ omnh cnj -Hro-4- vt
• • t • • t • • t • • • • •
0000 <UJ Q romoost <—
1
^vO>trO o coom Oz |_CQ l^-vt-vt^O in inf^-mo vf" h-vOsO vO
o oooos: HQOO o r-4000 o ooo Oo o:uj< oooo o oooo o ooo oo UJ -J • • « t • • • • • • • • • •
otu •
s: >• < UJ f-KNI^rn xO ohiao CJN o<i-m o
(—1 a:t-o >OiaOh vO C\|—«i-H0"l CO a^m<o m1—
1
<oo • • • • • • • • • • • • • • •t—t CLUJQ fOOOCNI in r» cnjcnjcnj vO i-^OO o
1— CNJCOOst" r- (Njcoi^-ro CO oor- COUJ-J
oo cnjcnjcnj cg »HrO(\l CM r-trg-H i-4
CO< •z. orom-o ^mr-ir- m ooo ON
H l-< • • • • • • • • • • • • • •
00 UJ mtnr-cNj o ^-ixor-ro CO a>f-t>t Xtujs:
Ico-4-mao CM CMAhO cnj r-oi^- CO
(NJ(Mi-t (M r-4r0CNJ CNJ rHCNJ'-l r-l
uj-JLUQ_rvl tAvOOOO CO vJ-CNjrOxQ m >*T^CO m5!<-<
i inr^cNj O HO^ffl o CNJOfO vO
<00OO
a. or
|Hr-( m Hl-|r-( r-t^t CNJ
1rvlOCLOC <_j_j rvlOQ.cz: Oclcx: <_J_I
35
0.0
8.0 -
6.0 —
I
4.0 —
2.0 —
X
300 600 900 1200Message Lengths (words)
1500
Figure 6. Log of the Tail Distribution for FASWMessage Lengths, All Precedences.
36
300 600 900 1200Message Lengths (words)
1500
Figure 7. CDFs for FASW Message Lengths,All Precedences.
37
10.0 r—
300 600 900 1200Message Lengths (words)
1500
Figure 8. Log of the Tail Distribution for FNSCMessage Lengths, All Precedences.
38
300 600 900 1200 1500
Message Lengths (words)
Figure 9. CDFs for FNSC Message Lengths,All Precedences.
39
5.0r—
4.0 —
I
200 400 600 800Message Lengths (words)
x
1000
Figure 10. Log of the Tail Distribution for World WideMessage Lengths, All Precedences.
40
THEO
600 600Message Lengths (words)
Figure 11. CDFs for World Wide Message Lengths,All Precedences.
41
distribution. Since the hyperexponential distribution is a
mixture of two exponential populations one i terpretation is
that the message length come from two exponential distribu-
tions with the probability or proportion parameters p and 1-p
as shown in Table III. It seems reasonable that all message
lengths can be considered to be distributed according to the
right shifted hyperexponential distribution.
C. SCREEN REQUEST AND FEEDBACK LOOP ANALYST 3
1. Reason for Analysis
The analysis of the entire screen request and feed-
back loop of this queueing system is a key part to the solu-
tion of the problem. For if the system had no feedback then
the solution of using both channels of a pair for first run
traffic is obvious, since there would be no reason for
rebroadcasting the first run traffic.
The investigation of this area poses several new
questions. First it is known that a certain percentage of
messages are missed during the first run and for some sub-
scribers these messages are successfully copied later on the
rebroadcast channel. In order to make some judgment of the
effectiveness of the rebroadcast channel we can ask, "How
many of the subscribers really do copy the secondary
channel?" Next it is known that when messages are missed,
that the screen requests usually contain a request for
screening more than one message. This implies that the
subscribers do wait for a period of time before they ask
for screens or they may miss several messages in succession
or a mixture of both. This time delay was not analyzed
42
since it would be very difficult to collect data from the
subscribers
.
When a screen request is originated there is a
transmission delay between the origination time and the
receipt by the NAVCOMMSTA. Also, when the screen requests
are received by the NAVCOMMSTA there is a time delay for
processing the request which is related to the number of
messages that have to be screened and to the number of other
screen requests waiting at the service desk.
This entire process results in the feedback of
messages to the broadcast. The distribution of rerun
messages, times between them, and their relationships to the
number of subscribers and first run messages must be
analyzed.
2
.
Source of Data
The data for all of the screen requests and feedback
loop analysis was obtained from NAVCOMMSTA San Francisco.
3. Number of Subscribers that Copy Rebroadcast Channel
A sample of 14 days of data was available for this
analysis. During the period, 26 May-8 June 1971, subscribers
were required to report to NAVCOMMSTA San Francisco periodi-
cally as to whether they used the rebroadcast channel. Addi-
tionally when a subscriber submitted a screen request he was
to indicate whether he was using the rebroadcast channel.
Table IV indicates the results in average numbers for each
channel.
43
TABLE IV
NUMBER OF SUBSCRIBERS USINGTHE REBROADCAST CHANNEL
NR. SUBSREQ SCRN
NR. COPY & COPYNR. NR. NR. NR. NR.SUBS SECONDARY SECONDARY
CHANNEL 1STRUN SUBS SCRNED RERUN REQSCRN CHANNEL CHANNEL
FASW 293.1 14.6 26.2 6.5 3.9 3.4 0.8(23.4%) (5.8%)
FALD 243.4 19.5 24.8 5.4 2.4 2.6 0.4(13.5%) (1.8%)
FNSC 165.9 11.8 39.2 5.1 4.8 3.2 2.0(27.2%) (16.9%)
Although this is a small sample and the area loca-
tion for the sample does not represent the system as a
whole it does however show that the secondary channel may
not be used to its fullest benefit. If there is to be any
conclusion drawn from these results it must be that a
surprisingly small percent of the subscribers indicated that
they used the rebroadcast channel. An explanation for this
may be that the majority of the subscribers either do not
desire to wait for an hour to attempt to copy the missed
message and instead originate a screen request or they
obtain the missed message from another ship.
4. Analysis of the Causes of Reruns
For this analysis two sets of data were available.
One set covered the period of 26 May-8 June 1971 and the
other the period of 25 August-17 September 1971. The
44
information in the sample contained daily strtistics on the
number of first run messages, the number of . jbscribers
copying the channel, the number of screen requests processed,
the number of messages required to be screened and the
number of messages which had to be rerun. This data repre-
sented four different channels, FASW, FALD, FNSC and FRTT,
the single channel fleet broadcast which is not part of the
multi-channel system.
The August-September data was broken into two parts.
During the period 7-17 September a First Fleet Exercise
named ROPEVAL 3-71 was conducted and during this period the
Operations Evaluation Group (OEG) conducted an experiment
of broadcast channel realignment on the FMUL broadcast [1,2].
During this period channel 4 was removed from use as a
secondary channel to channel 3 and was converted into a
dedicated exercise channel designated XRTT. The XRTT
channel carried only exercise traffic to the exercise
participants and thereby lightened the load on the other
channels during the exercise. This experiment had no direct
relationship to this study except that the data collected
during the pre-ROPEVAL period and the ROPEVAL period did
provide for some comparisons. One such comparison was in
the channel 3-4 configuration. Here the subscribers had a
backup channel for rebroadcast for one period while during
the exercise they did not and hence this would hopefully
provide some insight into the effectiveness of the rebroad-
cast channel.
45
The exercise time period also provided for moderately
high traffic loads and a larger number of subscribers.
Additionally the exercise channel XRTT provided an oppor-
tunity to look at a high volume of traffic being transmitted
under simulated wartime conditions while this channel also
had no backup channel for rebroadcast but used only heading
recaps as did channel 3 during this period.
Various statistics on screened and rerun messages,
called service statistics, are shown for the various
channels during the August-September period in Tables V-IX
and for the May-June period in Tables XVIII-XXI in Appendix
D. These service statistics show no obvious relationships.
In the service statistics Tables the Service Request
Rate is abbreviated SVC REQ RATE, and is determined by the
following equation:
SVC REQ RATE = ,Nr. Messages Screened(Nr. First Run) (Nr. of Subscribers)
This rate is used by some analysts of communications as a
measure of feedback in the system which includes the rela-
tionship of first run messages and subscribers [1] . Due to
the great variation of this rate over the periods analyzed
it was not clear whether there is in fact any relationship
among these three measures. Therefore a simple linear
regression analysis was used to determine if any such rela-
tionship existed [3]. An attempt was made to determine if
there was a linear relationship between the following:
46
Number of First Run Messages vs. Number of Screens
Number of First Run Messages vs. Number of Reruns
Number of Subscribers vs. Number of Screens
Number of Subscribers vs. Number of Reruns
(Nr. of First Run) (Nr. of Subscribers) vs. Nr. of Screens
(Nr. of First Run) (Nr. of Subscribers) vs. Nr. of Reruns
These relationships were chosen, as in the case of
the SVC REQ RATE, because intuitively one would suspect that
an increase in the number of first run messages broadcast in
a day and/or the number of subscribers copying the channel
would lead to an increase in missed messages and reruns.
a. Results of the Statistical and Regression Analysis
An important item in Tables V-IX, and those in
Appendix D, is the percentage of first run traffic that
result in reruns. This measure indicates the additional
work that is placed on the system due to the feedback. We
note that generally this percentage is between 2-4% even
though the number of first run messages and the number of
subscribers vary from channel to channel. Two exceptions
are 8.2% for FNSC (Aug-Sep) and 18.2% for XRTT during
ROPEVAL 3-71. Recall that ROPEVAL was an exercise simulating
wartime conditions and hence this increase of reruns during
this period is not surprising. Probably the explanation for
this is that the subscribers sensed a greater urgency in
obtaining missed messages plus they did not have a rebroad-
cast channel associated with XRTT. This would tend to
indicate that the rebroadcast channel may be an effective
47
feature of the system. On the other hand recall that during
the ROPEVAL period channel 3 was operating w thout a rebroad-
cast channel as a backup. Looking at the pre-ROPEVAL and
ROPEVAL period for channel 3, in Table VI we see that the
percent of reruns rose 1.3% while the number of first run
messages and the number of subscribers were also greater
during the ROPEVAL period. This simple comparison appears
to indicate that the presence of the rebroadoast channel had
little effect on the number of reruns. An important appli-
cation of the simulation model (described later) is to
resolve these apparently conflicting observations.
Figures 12 through 19 show representative graphs
of the regression analysis. All graphs represent the 25
August-17 September period. It is noted that the regression
lines were not restricted to go through the origin even
though it is obvious that if there were no messages trans-
mitted there would be no feedback. Therefore the reader
must be cautioned not to extrapolate the regression line
beyond the range of the data shown. In interpreting these
graphs one must consider the grouping or spread of the data
points and the coefficient of the control variable. For the
FASW graphs in Figures 12 and 13 we see that the regression
line is nearly horizontal, i.e., it has a slope near 0.
This indicates that the number of screens and reruns are
independent of the number of first run messages times the
number of subscribers.
48
LU co^ r-»m co r- cm r*- Is- ir» in r»- m 1
oin co cm h- <f vO —1m c* CM f- 1
C_LU rOvDOOvtO(\isOC>NOcocoo —1 1O -H CM >—1—! CM r-4—1m C\| \Q CO 1
in1
K- OOHOOOOOOvOHHO 1—1 1 OOOOOOOOOr-tO O 1 O|
o< 0000000000000 1 00000000000 O o^>_ • •••••••••••. •
1
• ••«•«•«••• • •|
00 0000000000000 00000000000 O \
00_3<3 romcNJOLnOyooi^-NQ^r-o in oocooocMOmcoom vO i
_H' _LU
_LU • ••••••••••• • • «••*•••••• • • ; Q_
LUO- —s—!CMoOooN0mmmm<—
1
CM CMrOCMO'-''-<>-<OOvO'-H 1—
(
CMI
00 Q_ LU
O V (_•—
i
"^ 1—«
1
t- 00 oocnjolo vo mo vOroo «t OOmOOOcommcMco CM O h-O0 -_o- • •••••••••••• • • •••••••••• • • _— _uu in>OfMr-iPsjc\jroco^TvjrorOr-4 CM 1 rciCMjNCOiA^rcifCKJ^c CO O LU
K- uo: 1—» iHr-HOHH <-4 m —i i
< 00 LU
h- .1 X00 ^2 o<-i'^'orw ocMr\Ln-ocovO>o >* ^vOvor*-orMvoosOLf\a -H O 1-
OO.D • •••••••••••• • • ••••••••1 • •1
LU __ CMmmoooommcocoinO CO f-Ii—irMOi—iCM—iOiHl>-r.i CM CM o_
o =>l- 1 Ol-H _oo UL> LU.-I
oC or _JLU _ r~ fMoo00 1^ ro vo cor— lt»o m f—rOsOCOOr\|i-ifOfMvOi-^ <f- O LU
00 8*_ • •••••••••••• • • •••••••••« • • _o ONSOOOvOmiAOONO O ^oro^vtoo^NONJ-cMr— r*- O O 2_
0. 00 CvJCNJr-i (M p-tmrg—imcMO CM vOrOrM'—<cMrMfM>-<i—i.—• .—
<
.—
1
1—
t
<LU __— —
«
X00 o O
1 2 cocornrO^"OvtvOOOc\jrovO f- r-tCTT— mrM<t-0^CMrOLncM h- CMo &*'_ • •••••••••••• • #••••••_••• • • h-
Z> o c*mc*om*-<momocMoo sO cM>tONj-Lnr— msj-mcMr*- O m 00
< 00 i-ir-H —!—icocmcm f—
1
-H r-tvt'-* r-t 1—1 <Oan _____
—
!
__ <
LU
O-(_)C?O0LU
O LTi --1
_COCT>c>vOi--icM--<LncMmir\inmi--< ! CMvJ" cMror— r-LOsO^ocomvOco c—i^O m^n
_ <_ in i-H r~ CM LU_<
% r-l _Xo
__•_C__
—4 m CM 00<
cMCMmO>-<omcM<-tcof~.-ti-< -10 •^o^o^Lnr-vONtOvOcM mo <r-o__LU r—li—*-—1 -Hi—[CMCM*-! !
rOr-t -H H(f|-(
1
HH1*rH O
_ C_ r-* ,-41CM LU •
oo<u.
c•_
h- a> CM OOO-Z>LU
00LO -4" fO -H LO CM CO vO COO COO --»1 00 or^-mr-invj-cncocMino (NJCV cc-t
(__ vt-u^r*- <-*m <f- sO <j-1 -4-«t CMsOCMcMCMCMCMCOOr"- coin CMLT\ OO
2:0 CMl
CM in CM <r-• 00 —
!
2h>
• 00<_C0
1 r«- O >t y »
CMO3LU
t >o •—>Is- r*- vO 1
—
t cm (\j «—1 I rH>fr >tc\jooco^H—<cooomin 1 om 1 Hfl-J ZD CMCM-—• -_J(M«—li-trHi-Hi—
1
1 <JS <—1 CMrnroromrnro^^mcM r-m OCM _l<CD 00
1
•—
•
1 m in LU< 1
2_iAt- KO
00 00CM
1m | __CM
<1 XLL
I h- r-t co on vO m vO r- cm 1 vOCO cMsor^TOcMmr^-rfir—cMr— OCvJ1 LTlN
1moM^-<~<>i-om>fr—icmoo^vO
1
1s- a* os inoococMcovO--Hcoo
I ^CT* O^co OO•_ 1 -tmmmrHCMrorororom-H'H
1COCM cMinsOvO>i-mcosONO^-<f 1 ^<f 1 cMm
__>1CO in
I O-.or » t
.
1 H- 1- LU
1 0000000aQ._Q.11_ a _a__cx_CL_o.c_.c__ 1 h-LU
IDDD3DDDUJ ujujujujuj 1- LU LU LU LU LU LU UJ UJ Hi LU LU h- _j 1 O
h- 1<<<<<<<0000O00000G0 0O0000000000000O000000 < 1 _
< COUJ CDLU l-LUO 1 in vo r- co i-h r-i cmm <fm vO _> r— coc^O'-icMro^-^sor- _> o>
1 fM<\|(\|(\|CMmmoOOOOO vo< OOOHHHHHHrHW 0O< l~<
49
+
wxoo ^
1 oouco
?i w uCO u s
0)
^ •
. O u>
O w ^o-§OJ w p
CO
M «
o E
o w
o £ cCD r
H 3— Eh «to -p(U w
u•H
O w Cm
O a) ,
oj a ^S
c3tt &
O -pCO
— o gCm
O HCO fe •
• Hn2 0)
o P
1oo •H
Cn
+4f
suaajog -jN
50
+
+ Xooo
•
o+
•
II
+
x oooOJ
+
4-+
+
+
+
+
+ +++
f++
++4
oo
05
uCDO &
Oo
OJ00 OJ
suniay un
CD O
•HUuco
OOJ
OOoCD
CO
CD
eHO EH
O
CD
tnf0
co
co
CD
o S
u•Hfa
o
CO
c
uCD
is
to
>
CO
en
!3
CO
n•Hfa
<fa
00
CD
tn
fa
51
oLUa: lu
h-o<>cxoo
v.oo
zZDOqTLULUC£
oo cco —•1—
<
v.H 0000 2TO—
t
ocujt- oo:< oO1- —
—
00 v.2ooO
LU 2! a:o Z5H-1—
(
ct"oo
> LU-^a: CCUJ z00 b?QC
oQ. 00UJ00 o1 zo &*?cx
z> o< 00
_, __co z
ex-j ooUJ 00 LUZ exz =*<X zo «ow a: a:
2TLUQ a:-J< aLL *z
cXiXzo• O0
i—
i
> • O0OCCO
LU ZD-J 00CO< l-O- 00 00
H2•zocoZaL
LU
I-<o
mooo^>tco (MvooonOsqoco—'co^hcmco ["-.-i^OvtOOOr-icOOO oooooooooooooooooo• ••••••••••••ooooooooooooo
oo•
o
co co f-i co —< cm o> vO cmm cCMCMcOOfMr*-Of"-sOCM<-<
|OOCMOO—IOOOOO|OOOOOOOOOOO
1
• ••••••••••1OOOOOOOOOOO
1
inio
o•
o
inOo•
o
inoor-cor*-cooinor--oo• •••••••••••••-ifOHHfO-^OONOOr-lO
r-•
t—
i
mrMOOt^-mootnoo1
• •••••••••«f—li—ICO t—li—t CM >~4 CO i—t—4 CO 1
0> I
•
1-4
CO•
>-*
ocoococor-oocoor--oo• ••••••••••••
r\iiri>4-aNC\i(MmoaN >i"'-^-^f^
CO•
O COoO COoOO CO CO c• •••••••••fl
»4- COO CM >t vO CO CO CO CO CC •
CM i-4 —4
o•
oT-t
I CO•
0>
o>c\i-4-r^>o<froOr-ior^Loo• ••••••••t*«o>to-4incMOocooooo
•
r—'-icM—<OOfOCMr-4Chu~• ••••••••••
r-ic\ivOH(NJNOinroHr-<•
CM
CM•
CM
0^0-0omr-oooooo• •••••••••tittnr*-inco»tcMvCior--ooooh-LOCM r-HsO CM sl"0
i-4
- co•
r-l
CM
co>tcoOco^ocOr-i(Mf^-m• ••••••••••coooOvOincofOcovor-rOcOr-tincOrHCOCM.-<cMco
CO•
CO
in•
0>f—
1
cM^ininNOOCMOincocoinm• ••••••••••••
^ir-r-ic^f-roL^Of-fcM^HOLn.-ico •-*
in•
•-«co.-<cM(Oh-inr>-cocoo• ••••••••••
u^vOOCMinvJ-CMCMr^r-coO -4" CM.-H
<*•
•
inr-4
CO•
—4i—
1
LO CM >0
CMvl-r-^cOcOcOcoO<l-c\lcO.-4«-« OCMco
rovOr-^->torMr*-cococM r-inin
r-coCO
cm r- mcocM.-iinoin<-«ooocM-40 o>t
in
v0
^r^^H^r— mcMr-icMcovOCM i-» CM'-' o
i—i
CO
r-vOIini-4
m•4-«-<vtcor-coinor~-coin.-ir~
CM LOnO r-H COm s
cO-n(M
CMcOCOCOO^'OvOr-tNOOOrHCMO -»0 OsOCOr-l
CM
OCM
min coocoCO
CO o CM
vomN*->tc\jo*0ir\vOvt-or><\jCMCM^Hr-Hr-4,—Jr^r-HrHrHr-l rH
Oin
.—
1
cM>t^or--msOO>ococ>ocmcmc\Jcm<\jcmcmcOcmcmcm
0*0CO CMCM
moCOCM
CO in o^cocor-coNOvOsO'-<-4- incor--(\jcor^o^r*-oaococ\jincoao<\jcocMCMC\i<-icMCMCMCOrOcM>-<'-«
1 OvO1 sl-CM
CO
^OCOCMh-mr-lrHrHr-4^cOvj-ror^m^vj-ocorH^CMc0COcOcOCMCM-tcO4->l"
OcOr-rOCO
t-
1>4"s0
oo>r-HCM
i r-
OOOOOOOQ.fl.CLQ.aQ.33Z3Z3333UJUJUJUJUJUJ<<<<<<<000000000000
insor*-cooo--ir-tCMro>i'in>oCM CM CM CM CM CO enOOOOOO
a
COLUz>>00<
CLCXQ.O-Q.CLCXCLQ.CLCLLULUIULUUJUJUJUJUJUJUJoooooooooooooooooooooo
r-cooor-^cMco^-invor*-OOOHHHHHHi-»i—
I
COLU
00<
-LU
o:
exUJoo
\-OK1 c£OXz><o
LUini—CM<Zoo
o>-k-ioo
QCLULUOCLLU
CL •
LU CO100K<_J3LU
a: 2o-4-z:LL <_JX
_JLUOLUZzzzz<to<xlooO LU
••OO
h-Q.3OOLU<O0LUO Clor^-uj<.-t:sa i
a:i*~ooco exLUD<clOO
t-iLUOOQiCX<LUCXO
O 2LULU"-"1/1IO3H-<
LUooox<2!3mOaLZ
Nt-ZXo
_J _lLU LUz *zz>-z<_)<IZIooo
• 1
LU
h-a
52
X
XiHoo
•
oI
o
+
+ +
+
4+
+
+ +
L
o co 3
O utf
O <i> +J— & CO
•H MH •H •
u Cm co
CO C
O 3 ^ a;
o wo . to00 n •
I"?fr .'
W MCO CO S0)
g <x> •OH 1 CO
O^O 03
• >o
^Sro ID 3CO CN C/}
CO
(1) Q •OS2* Cm —O 3««
•
•P ^rCO rHu•H (U
O fe
o .
u
CT>
O * •H
r\\ 2 Cm
O O OCO
SUB3JOS 'XI
53
X
+
+
+
+
+
+
+ +
+
+
O00
oCD
O OC\J
OooCM
oooo
oooCD
OOOCD
OO
OOO
CO ^~.
u cQ) p£< PdHU +J
U to
w uJ3 »H3 foW
M
to
g
w0)
to
to
0)
S
3o «
^1
2
to
c<u
0)
uC/3
u -
2 H— 2
cu to
to >CO
r- to
t$r- to
P •
< 2fa —
IDH
tnH
SU99JOS *JN
54
oLUc*:lu
o<-i
oo
00
z>oaruj
00 LUOCo tc—
I
—
—
h- >v00 00•-
1
zoh- oCuj< OQit- 00oo —
—
•^.zLU 00=3o Zee*~
1
13 H-> a:ooa: LUr-
•
LU Cd00 z
Wa:a oLU 00oo .
^ oo Z=5 &*(*< o
OO»-»
in 1
z-J CCLU oaz O0UJz a:< %Xo z^-» •o
q:qc:
o zujO0 C£zUL O
•zaca:
• zo—
i
00t-H
> • 00a: cd
LU ZD_J 00CO< H-Oh- 00 CO
hs:
•zoCOZee
LU1-
<ta
COOO v0 rH^ O vtO in 00 —t \0
r--cMcor— r^oocosror^-cominco*tcM-*fMCMCMvrcocOOcoO^-fOOOOOOOOOOO• ••••••••••ooooooooooooo
OOcMcomcMr-tCMco-HvOinO
r-irOvOr-»c\jOrorOLn(Nlt^-c\jr«-
o»-i<}->j-oaN Ocooco»-imin
r-» Is-o com co >o v0 r>-o co co in
.—I f\J i—l i—
I
^-ti—I•—I »—» t—
4
O—irOf^-LONtLOOO^OvJ-O• ••••••••••••O'OLnrOOOrHr-ILOsOCO^vOOt—(i—»—» i—• i—t cm c\j
<f>-HO^-OinvrcOvO>t^o>d-rM
r^->-icMroOsOCMcoo>or<-r-«ir\,-i^Hro^-iLn in—< cm cm in h- -3"
COCMOO—iinOcOC>OvOOCO• ••••••••••a
r*-mcor— r-cMcM—icoo^—ko^oin >t ^ cm —« cm cmcorncob <4"
r-to^LnLnvtcor^-sOO-Hf-vtvO
—^r^OocMCMOcocOcoOCMcmcmco —< CMrHLor\iLnr-i>f
^vtr-r-0'HCM-«Cr>COCM<}-cOcMNd-cr^cNjrOvj-or-—to—<c>c—ICM <H —<«—I
OrHOOO-^HHNMHHrO
r-)COrMr0I^-C0r-trOfMLOr-(I^rH—tsQOJ-'-icOocMOcocMmoCM—< CM C\l ,-) r-H ,-1 CT\ CO i\l CM r-l CM
uoooooonao-aao.OOOOOOOUJ LULU LULU LU<<<<<j:<<o0o00O0OcOOO
mor-coo^o—<—ic\;coNi-mvOCMCMCMfMCMCOrOOOOOOO
COoCOo
LT\
CO
rO
m
LO
-0
rM
in
COsi-
CM
cor-
CO
CMvJ-
CM CMCO
vfCO
CM
LO
f*-CMCM
o
CQUU
O0<
vOor^<}-mcM<t-rv-r*-mcincocOcoOcOco.-»f^eooO—ICM—<CMs)-OCMOO—
•
ooooooooooo• ••••••••••ooooooooooo
coco-4-r-l^-Ovl-cocoinin
—<NfCOr-lCMcOi-ICO'-lOCM
aoor»-cor-cM-ooco>d-c
co—ico^o—4mcocococMr-i-li-l >-HCM f-l CM
LncooOvOr«-ONOcococ.r
vtOCMTivOsOCMr^COCMr-'
co—icMf-oocoo—i>tc^
r*-vOin*tc\ir-4ȣ)Lr\cr>CT>'~i
nJ-COCMCMCM.-^'-icMcO—i—h
LOOLO^-ICOi-HLncOLAOrO• ••••••••••Oh-inOaOsOCMOCO—ILO
CM CO CM CM LT\ i-l CO —l—l
or-ocMc^vOLooor^coc\i
•-HO'-HOvtcor-vOONom—ifOCOCMCM—i CM
cococo—iin—<cOv}"co—icmCMaocMcoomsj-ocMcOvt
Is- in in in >t co Ln vj- -h -J-
«*
CMC— vOrMinOcOCOO-Hst-sfOvj-o-oOvt^r-vor--CMcOCONtcOCMv-OCOCMCMCM
Q-Q-a.CLQ.CXQ-O.CLCXa.LULULUUJLUUJUJlULUUJLU00 00 00 CO 00 OO 00 OO 00 00 OO
t'-cOCnO—iCMrONj-invOr-OOO—ii—1—<—-i<—
i•—I.—i—
I
CM
CM
o0>
LPl
f-0
CM
X)
COCM
-o
00
O
C0r-4
in
OCOOP-co
CO
in--^
C\li-<
CM—
<
vtCOCO
o
CQLUo>oo<
oCM
O
a-
CM
CM
CO
CM
inCM
-0
C\J
CO
r-r-
CM
OCMin
co
CO-4-CM CO
OCM
in
.—I CMO-HCO
CO
r-l CO
CM CM
l-UJo>l-<
oocfLU
a.
LUOCT
LU
LUX
a:OLL.
<XO
OO<oo<oacCOLUa:
oo<oLU •
COO.3LU
OO00
<r-
I
r-o
_j<LUzmZCM<XLLOO
LU
I-o
55
X
+ +
+
+
+ ++
f
+ —
+
+
X
+
++
o .
o CO
o PCD
(U
CO
•
O u 2:
O CD
O •H CO
ID UU
>
to ^-^
JQ CO
3 X!tn 3O C/2
O •
,o 53 Usfr
10
IS
CD ^^e c•H pEh «o
o CO
CD
4->
CO
o tn M
ro W10
-H
0) •
£
OO Oh Uo wC\J
4->
CO
•H
p4
En •
o •
uH
o 2 CD
o ^3On•HCm
CDro C\J
CO 0>
56
o i
LU |
OCLU |
1- 1
o< 1
>cr^ I
00 00 |
o i |
•—
1
v. |
r- oo |
OO ZL 1
t—
i
z>o |
K C£lXI I< LUgC i
t- OL 1
00 —— |
v* |
IXI 00 |
o Z.OS 1
•—
1
CtTLU 1
> OOC |
a: 00 |
LU ———1
(-0 ^2 1
00 ID |
O- zo: i
LU 31- 1
00 ccoo i
I LUf-l |
O or: r
Z) 2 1< 8*ai 1
O 1
—
»
00 |
-J i. i
|
LU Q 1
z Z 1
z &?ct: I
< o 1
I O0 1
o-J 2T I
3 DC 1
s: UO 1
u. 00LU I
I cc 1z 4* 1
oz Z 1
• rj I
LU cCcd 1
-I zrixi i
o CC 1z»-« D 1
00 •Z 1w oTa: IZO |
1- 00 |
KCL •00 1
U. OCTCO 1ZD 1
00 1
•—
<
hO 1
>—
<
oOoO|
—> -•S 1>•2 1
LU ocx> i
-J Zoi 1
CO 1
1
<H LU |
1- I
< 1
Q 1
OrorOCNiaor~>UfOco30cOr-inrO'OvOr-iCNlr-co^OCNjcNjroOMOOOOOOOHOvfHooooooooooooo• ••••••••»•••ooooooooooooo
in
O 1
o•
o>
rHmror^mrHroc\jLnr«-»rOr^^Ovtr\Jr-trj>>-HOroc\jo f*o »-• —• r-oo i-4o cnj
ooooooooooo• •••••!•(••ooooooooooo
rH•4"
rH
o•
o
COrHrH
O•
o
owNiriOoomoNmco• •••••••••••Irom-Hco—icvjcNjm <j- c\j rH ro rH
0> :
•
covtotsjomooNOo• •••••••••HONvJ"00OinOvtH(ri
rHro
CNJ
•
CO
mcoromoorooocor"»r\jo r- OvOvomor-ooooo CJN • Ovto>ooomr-cor^a>co-<o-t
.—I ^—C .-1
CO sJ-O^-cocomcocOvomcui—1 rHrHfOrH
orH
0>
o co -j- rom o>o i-tm -h lp, r- -4"
• ••••••••••inOrHCNjOOCNICNJCNJCOr-ICO CNJ
r-l
4"
•
co
r— coo ^o lo in room >d- o.
• •••••••••a<MO^-mco\Oc\iOv£>o<f"
—i
• •
CO
r->i-f-if\jroNooovj-Ntomo
vOCr«sD^-tmoo>^-Os±'-<aaN Lri
vO(NJ<-t^-roc\jc\im<fo~>coojc\i
CNI
•
roco
cocommmocoocooin
>*• inrOvOfMfNj r*-c\Jro
CNJ
t
4"
CO
•
roro
•••••••••••ar-mcomrHrocoNtmOrHoo^
CO iH CNi
<NJ
•
or-i s r\jo r«-o ro ro st rg rg• ••••••••••vOOcorv-rOsOco-^cO(\jrH
(NJ rHHlfl rH
ro•
(OrH
in•
rHrH
>* O CNJ
oOOcocni—irHcocNicNj^cosom 4-ro >J-inm<J-rOrO>-<rHrO'-ifo rororo
1 r^co
CO CNI <f
commr^-rHCNjvOr— corHvj-comI—ICO •—1 r-4 CNJrH
i—
i
r— cnj ro r- >$• —* ino >4- <-*orHrHCNJfO rH
r rOrHCNJ r-4
rH
ooinrHCNJ
1 o^
r-OrHr^-ror-rnvtcoLninrHoCNIrHrOrH c\)i—i-nro Ocnj
CNIO1 C0<Mro
>Oroco>tc>r-cococoino-r-im<NjtnroOr-i <-* c\j
rH
OCNIs0(OCO
1 CNJO( ^-ror-
co in 1 CNI
Lom>to^(y"-i"-<roc\ior^r^r^rHrHrH .—1 1—( r-( i—1 rH
1 oo1 SfrHrH
OrgrocNjrHCOOOcOvOmrH_lrHrHrH rH o
rH
1 «to1Vj-rH
1 CNI
LO in1
CO
COOCM^*-<0<NIOCOmOCNJ-OCOmvj-vtocoroo^r\irHinr*-oororocOcOrH<\icNlrocoror\j(NjcNj
1 OC0LOCOr-<\j
I
CO
t-
<NJroOvOvtcOvOcoin>t-tOinOOOCOCOrHinrHrNjrHCNICNJCNJrOCNJrHCNICNJCNICNJCNJ
Oino^-
CNJ
I—
1OCO
1nj-cni
1o
oOoO <J5oo cl a. ex a. o_ o_Z)Z)Z)333Z>ujujluujixiuj<<<<<<<1>OC/)OOOOC/)00
insOr^cooOrHrHCNirOvj-invO(NCNICNJCNICNJCOrOOOOOOO
o
C0LU
O0<
cxrxrxcxcLCxrxcxcxcxrxlululululululululululu00 00 00 OO 00 00 00 (/) 00 OO 1/1
r^-coo^OrHCNirOvfinvOr-OOOrHrHrHrHrHrHrHrH
O
COliJ
3>00<
r-LUo>r-<
OO—
I
C£LUCL
LUCCt—
I
t-
IXI
LU
Xr-
o
or=>oQLU00DLUCrT
LU
OOQ.
<OLUC£
O
o<IXI
X
LU
O
57
X
X(Noo
+
+
+
+
+—
4- 4
+
+
oooCD
O Wo u
o £
U
o «>
o .O n
w0)
6•Heh
2 «»
1 ' en
CO
0)
OooCVI
ooo
c
«
•H
Mz
>
in
ACO
MZ
C
-Pw
H&4
Eh
Cm
U
CT>
H
C\J
CO Cv) CD
surutey *jn
00
o
OO
H z>c?< aruj1- UJQi00 a:
UJ >vo 00•—
1
zo> oCuja: KJCHLU 00oo ^za 00 Z)UJ Za:00 r>(-1 OCoOCD UJf-4
3 a:< z
fr^a:—
»
o-J 00UJ -
Z az z< &>CCX oo 00
UJ ___00 Z>—
*
a:
o oocc oo ujUJ arX %UJ
Zo •oUJ oca:t- ZUJ< a:o*-• QQ •ZUJ a: ex:
Q z:o** 00
1- • 00h- crrcQoC z:i5X O0
l-O• oo ooX •-is:»—
<
•zUJ crriD_i -Z.OLCO<H UJ
1-
<o
r-Lnvor^r-^ocMvtco^^-(\Js0lT\^-t^-00O'-<C0r-l>l-OOHHOOHtNJO^Oooooooooooo• ••••••••••ooooooooooo
ma^vOvt'-io^h-r^roooco• ••••••••••orovO^->tr^-sOco-4TOO
o-4-v0r-iirir-<ir\r0vj-mc\j
ror*-r^-(MO-H-4"OOoorg1—4.—
I
f\ll—(r-H,—
<
cooNtofNiocMr\r*-sOo
--<Nj"rO>OOr-ioocorooorHC\lrHi-t"-HrHrOr-((\l
r^inLrvr-»Lnc\it\jOinc\ist
NGc\ir--v0<Nir>-somr-<in'<o
o^r-vfa^rocr-covo^-tvoo•••••••»•OvO(MvOvO<-<OLni'OinO^
c\icoo-«j--Hr>-ooro<-iLn
'Hi-ixOr-<LnLnr*-.j-vOr\ivi-mosOstiriNOr-Lnvt-
vOc^oo^c\jooir\r-tAm-
.-••-1000000000
LOi-i(\iOro-tLnc\jco^-noinojcOvO>t^Lnmooiri
<M <\J ro <f -^m vT <f (\j
Cl.Q-Q.CL£XaQ.QLCLa-Q.UJUJUJUJUJUJUJUJUJUJUJoooooooooooooooooooooo
r-coo^OrwtMoT^^Nor^OOOr-lr<f<HrH-IHH
vOo
o•
0-UJ
vt oo•
in f-l-l
1
o• u_
(NJ O—
1
oo
f\J i—
<
• CCCO UJf-4 a.
UJcL
o •—
i
• i-CO z>t UJ
UJvt" X• H-
0\J
^ o
to
oin
OtNJ^4"-—
t
r-
4
r\JO
tNJ
(MOoo
a>
oc
oUJoo
UJa:UJ
00a.<
o
o<UJX
UJ
59
+x OOO+ 00
CD
Q)
Sh
Uin
+XCM<-\
O o w• o u •
o+ •
o u53
+\s+\£> •H
UU
•
• m >** X!rH
1OO
3CO
X!il o
CM
• 3If)
+
++
\
oooG>
OOOCD
OOOto
0)
Eh
mQ)
id
m0)
S
-p
•Hfa
•
2
•
u5c"
w
•Hfa
«
>H
EhEh
X
•
CO•H
0)
cn•Hfa
1I 1 1 4
o o o o cDCD Cv] co *
SU98IOS *JN
60
ooCD
CO CO
c-~0) pXi u•H 0)
u &uO ra *
oo 2in •
• (0
u >2CO CO
oo B
•H
•9
c/}o EH
CVJCO
•
dJ £0^«0 S-.
to CCO Po 0) tf
oo -P
CO
o 3 Mp^; •r4
-pCO t
^ Uo •H So t, ^o • HCD
U HPiX
o•
o .-H
o CD
ro U
suniay *jn
61
The channel comparison mentioned above is shown
in Figures 14 and 15. We note that although it appears that
these regression lines have significant slope the scale of
the graph causes this and one should note again that the
coefficients of the control variable are nearly zero and
hence there appears to be no significant difference in the
way channel 3 was operated.
Figures 16 through 19 provide results for the
FNSC, FRTT and XRTT channels. We see that the XRTT regres-
sion line has the largest slope of all the samples shown,
however we must note that the sample size is nearly one half
of the other samples.
If any conclusions are to be drawn from this
analysis it would be that the number of reruns are indepen-
dent of the number of first run messages and the number of
subscribers. However further analysis in this area appears
necessary in order to fully accept this conclusion.
Regardless of what conclusions can be made,
these regression equations were used in the simulation model
(described later) to mathematically simulate the effect of
the rebroadcast channel on the system.
5. Analysis of Time Delays in the Feedback Loop
Since the model is in the form of a computer simula-
tion it was required that each time delay of the feedback
loop be analyzed and described for use in the model.
The source for this data was the broadcast service
logs from NAVCOMMSTA San Francisco. These logs contained
62
the following information: the Date-Time-Group of the screen
request message, the time the screen request arrived at the
service desk, the time the screen request processing was
completed, the time an answer to the screen request was sent
out on the broadcast, the number of screens each request
contained and the number of reruns which resulted from each
request. Logs from two different months were used. One
represented a high volume traffic month which was September
1971 and the other a low volume traffic month which was
December 1971.
Four time distributions were analyzed. These were,
the interorigination times of the screen requests, the inter-
arrival times of the screen requests at the service desk in
the NAVCOMMSTA, the delay in transmission times for the
screen request messages from the originator to the NAVCOMMSTA
and the delay in processing the screen request at the service
desk. Additionally the distribution of the number of reruns
per screen request was analyzed for use in the model.
a. Interorigination and Interarrival DistributionAnalysis Results
For each of these distributions the times between
successive origination and arrival times were determined and
then tested for goodness of fit to the exponential distribu-
tion by using the computer analysis program. In the case of
the origination time, the date-time-group of the screen
request was considered as the origination time of the request
In both cases the hypothesis that these times were dis-
tributed exponentially was accepted. The results are shown
63
in Table X and Figure 20. This result implies that screen
requests arrive at the service desk accordir to the Poisson
Process in the same manner as first run traffic at the
broadcast position. Only the interorigination distribution
is used in the model.
b. Transmission Delay Distribution Analysis Results
The delay in transmission times were considered
to be the time difference between the origination time and
the time of arrival at the broadcast service desk. This
data was tested against a right shifted exponential for
goodness of fit. The right shift was used because of the
observation that a message being transmitted from a ship to
the NAVCOMMSTA has at least some minimum time delay. Table X
shows the results for both the regular and right shifted
exponential fits. The hypothesis that the data fit the
right shifted exponential was accepted. Figure 21 shows the
CDF graph for the September data sample. It is interesting
to note that the mean transmission delay for the two sets of
data were nearly the same. The sample mean for the December
data was 119.6 minutes and for September it was 120.8
minutes
.
c. Service Desk Delay Distribution Analysis Results
The service desk delay times were considered to
be the time difference between the time of receipt or
arrival of the screen request message at the service desk
and the time the reply to the screen request was completed.
It should be noted that the times measured here included
64
both the time the screen request spent in qupue at the desk
and the time for processing at the desk. Thus was purposely
done in order that this distribution could be used in the
model to implicitly simulate the delay resulting from other
screen requests for other broadcasts and/or channels being
handled at this same desk.
This data was tested against a right shifted
distribution. The right shift was again used by the obser-
vation that each request however small must Lake some time
to be processed. Table X and Figures 22 and 23 show the
results of these tests. In the case of the December data
the right shifted exponential was accepted as the underlying
distribution while for the September data, a right shifted
hyperexponential was used for the best fit.
d. Reruns per Screen Request Distribution AnalysisResults
The data for this analysis represented the
number of reruns per screen request for all channels pre-
viously listed for the August-September period. The data
was fitted with a regular exponential distribution and the
hypothesis was accepted that the reruns per screen request
data is distributed exponentially. The results of the test
are shown in Table X.
65
00zo»-3CO*-*
cC
00—
<
QCl
Oo
<COoLUUJ
a:oU-
oo
300UJcc
0000
oooO
XUJ-JCO<
003UJUJ00cct-w< cc
3a>00 J-t <Xo
oo
003UJ00
O0K UJI ex
00<1 t-^00
00•<
cc
oa.»-
l
DCL
oa: a.a.
<a
I- COO000 5IQ£lU<
UJ •
s: >< UJ
<oo •
O.LUQI-oo
l-<00 UJUJS
UJ
CLr^J.
<00oo
a
3COt—
I
ex"
H00
00
<
O>—
I
CCocCUJ
inON 0^• •
CNJ r-H o* •
s0 CO
in
onocjn
o >fr
0>
c\l
(NJ
oo
cooo
coin
inCO
oUJo
oUJ-JUJex*
m
s: z z:
o
cmooOo
0^
r- -4-
co in(>*- rH
m
<\j
coCOcO
oo
z.a
3CO
oo
00UJ
<>a:CX
-
<ccUJ
co 00»o co• •
-4- CMCNJ rH
ON
o^
cnj
CNJ
oO
co(M•
CNJ
O00
ro
00
O ONUJ ON~5 •
O
<
CNJ
00oo
0^
o CNJ
in CNJ
<f rH
in COco CO
ro
o o_UJ UJQ 00
3COHH
cCh-00
00
0000
00
<CC
<
ooCNJ CO• •
ooujon-5 •
UJcc
CO CNJ
-400•hoom
• • •
MvQ ohCNJrH
•4-0 cor—
ON ONON ON
CNJ CNJ
CNJ COIs- inoot •
<fcoCOCOoooo• •
mmuj • •
O CNJCNJ
CNJ CNJ
ON ONQNO
f-ONvtOO00 v0
oo
OCNJ OCO
l-l << <<
<< <<
comoooooooo
OsOsOvO
vfvt-
vOvO 0000
O0>HHiHi-t
ooCNJCNJ
nOvO00 00
ON ONcocoCO CO
LULUDQ
CLQ.LULU00 00
3CO»—
i
CCy-oo
00UJ
>-
<-JUJoN^
OOUJoLUo>CCUJ00
mm oom0nc7> UJUJ0N# • ->—> •
LUUJCCCC
CNJh NtOONr-f- o-tm• » • • •
|N-vQ ONOrHvtmH
coco omvo
era-*
CNJvj-
miNj
rHH• •
<t<
<<
<t-f-
oo
CNJCNJ
CNJCNJ
• •
COCO
h- ro-
coco
>OvOCOCO
ooonLULL) ON-5-0 •
LULUCCCC
vt-CNJCO^r-coCNJ CNJOHHO
O OC\J OCNJCNJ
<<o
t »CO<<t0Nt »coZZCNj
CO vtxt
000000
CNJ CNJ CNJ
co 00 co• • •
ON ON ON
000CNJ CNJ CNJ
OO aoooco
CO 00 00mmm
ONONcr*rococoCO CO ro
or-
mt
ON
0^
3 CJN
co co-I CNJ
CC HI- •
00I—
I
o o
00LU3aLUCC
LULUCCo00
ccLUa.
00z3cCLUC£
<
COCNJ
rO
CNJ
CNJ
o
00LULUQQ
Q.Q-CLUJUJLU00 00 00
66
200 400 600 800 1000Interorigination Times (minutes)
Figure 20. CDFs for Screen Request InteroriginationTimes (September)
.
67
THEO
200 400 600 800 1000Transmission Delay Times (minutes)
Figure 21. CDFs for Transmission Delays (September)
.
68
300 600 900 1200X
Service Desk System Delays (minutes)
Figure 22. Log of the Tail Distribution for ServiceDesk System Delays (September)
.
69
1500
Service Desk System Delays (minutes)
Figure 23. CDFs for SErvice Desk System Delays (September)
.
70
IV. THE MODEL
A. GENERAL DESCRIPTION
The model is in the form of a General Purpose Simulation
System/360 (GPSS) computer program. GPSS is a simulation
system designed for simulation of queueing systems and hence
adapts very well to simulating the fleet broadcast system.
References 4 and 5 fully describe GPSS.
B. MODEL CAPABILITIES
The model generates transactions which are the messages
in the system and moves these messages through the model for
queueing and processing in a very similar manner as the real
world broadcast system. Since each of the channel pairs of
the broadcast operate independently of the others, the model
was designed to simulate only one channel pair of the fleet
multi-channel broadcast system.
The model has essentially 3 basic components or routines
which interact with each other. They are (i) the first run
traffic flow for Immediate, Priority and Routine precedences,
(ii) the Flash message routine with preemption, and (iii)
the screen request and feedback loop routine. For the
description of the model we will use "channel 1" to refer to
the primary channel and "channel 2" to refer to the secon-
dary channel.
The model is essentially very simple in its flow charac-
teristics and has much flexibility in its use. This
71
flexibility is described by listing the following features
which can be considered as measures of controlling the model
The user may change or specify the following control vari-
ables, distributions or methods listed.
i. The daily number of first run messages to begenerated for the simulation period.
ii. The percent of each precedence of the first runmessages generated.
iii. The individual message length distributions foreach precedence.
iv. The mean message length for each precedence.
v. The diurnal message arrival function.
vi. The number of subscribers.
vii. The backlog levels by precedence to be allowedbefore opening and closing channel 2 for trans-mitting first run traffic.
viii. Allow Flash messages to preempt other messagesusing either the Preempt Rerun method or thePreempt Resume method.
ix. The mean transmission delay for screen requestsor the distribution of this delay.
x. The percent of screen request to be processedby the Broadcast Control Station and the percentto be processed at other NAVCOMMSTAs
.
xi. The service desk processing delay distribution.
xii. The mean service desk delay for the BCS and/orthe other NAVCOMMSTAs.
xiii. The mean number of reruns per screen request orthe distribution.
xiv. The mean transmission delay for reruns to reachthe" BCS after being processed by the otherNAVCOMMSTAs
.
xv. The control of whether rerun messages processedby the BCS are allowed to go to the head of theline of first run messages waiting in queue.
72
C. DESCRIPTION OF THE MESSAGE FLOW IN THE MODEL
The flow charts shown in Figures 2 4 through 2 7 provide a
simplified picture of the message flow through the model.
First consider the traffic flow for Immediate, Priority and
Routine precedences. These messages plus Flash are generated
according to an exponential distribution with a mean inter-
arrival rate specified and a specified diurnal function.
After a message is generated its precedence is determined by
a percentage function specified. After the precedence is
assigned the model routes the messages by precedence to be
assigned their appropriate message lengths from functions
specified and then puts the messages in queue by precedence.
At this point in the model the Flash messages are handled in
a slightly different manner than the other messages. This
is described below. The precedences or priority numbers
assigned by the model, depending on the precedence assignment
function specified, are as follows (listed from lowest to
highest with designations in parentheses)
1-Routine First Run (R)
2-Routine Rerun (RRR)3-Priority First Run (P)
4-Priority Rerun (PRR)5-Immediate First Run (0)6-Immediate Rerun (ORR)7-Flash (First Run and Rerun) (z)
.
The model chooses the highest precedence and in order of
arrival within precedences when advancing transactions through
the model. Thus messages waiting in queue are chosen by
highest precedence and on a first in first out basis for
routing to the transmission channels. We note that when
priority numbers 2, 4 and 6 are assigned to reruns processed
73
by the BCS, these messages will be transmitted before their
first run counterparts. Hence this simulates allowing the
reruns to be put at the head of the line.
When a message is routed for transmission the model
checks to determine the number of backlog by precedence and
compares it to a specified value of allowed backlog for a
given precedence. If the backlog for any precedence exceeds
the allowed backlog the model will start a 30 minute timer
(or a time specified) which represents the notification to
the subscribers of the intent to activate channel 2 for
first run traffic. At the end of the 30 minute period
channel 2 is opened for first run traffic. Whether or not
the timer is activated the message proceeds to channel 1
for transmission. Although the flow chart best illustrates
this test as occurring sequentially between the time the
message departs the queue and before transmission, this is
not the way it occurs in the model. Actually all the above
described assignments and tests are made at the instant in
simulation time when the message is generated. That is,
when the message is generated even though it is part of the
queue, the message proceeds through the model until it is
refused entry to some GPSS block (program statement) . Thus
the messages proceed through the GPSS model to the BUFFER
block and the main GATE 1 before being stopped. For statis-
tical purposes the messages do not depart from their respec-
tive queues until they pass through the DEPART block and
this occurs only when a channel is available and the message
is allowed to SEIZE a channel in order to be transmitted.
74
The message is held in the transmission channel (ADVANCE
block) for a period of time equal to its assigned message
length. When the transmission is complete the message
releases the channel and is terminated and removed from the
system. The main GATE 1 closes when a message SEIZES a
channel and opens when the message RELEASES a channel.
If channel 2 has been activated for first run traffic,
then the model processes the messages through channel 2 in
the same manner as in the primary channel. Messages waiting
for transmission are selected in the precedence order
described above and each time a channel is finished with a
transmission, or is available, the model will move the
available message to the appropriate channel. When a mes-
sage is processed by channel 2 , the backlog of the Priority
and Routine precedences are checked against a specified value
to determine if channel 2 should be closed. If channel 2
can be closed this will activate a timer which runs for the
duration of the message length of the message in channel 2
and then closes channel 2 to any further first run traffic.
It is noted with emphasis that the secondary channel in
the model does not process messages when it is considered as
being used for rebroadcast of the primary channel traffic.
In the model this feature is handled through a mathematical
relationship which will be more fully described below.
The next part of the model to be described is the Flash
message routine. This is described separately to point out
that although the Flash messages are generated as a part of
75
First Run Messages
AssignPrecedence
AssignRoutineMessageLength
I
Flash
AssignPriorityMessageLength
AssignImmediateMessageLengths
RoutineQueue
PriorityQueue
IImmediateQueue
TEST1
OPTMR
BUFFER
Hold InTimer
30 min.
IOpen CHAN
2
(GATE 2)
CHAN16 CHAN2
Figure 24. First Run Traffic Flow in the Model
76
CHAN1
MessageSEIZESCHAN1
Close GATE1
MessageDEPARTSQueue
TransmitMessage
MessageRELEASES
CHAN1Open GATE 1
Hold inTimer forTime-MsgIn CHAN
2
IClose CHAN2(GATE 2)
MessageSEIZESCHAN 2
Close GATE1
MessageDEPARTSQueue
-0TransmitMessage
MessageRELEASES
CHAN 2
If CHAN2Still OpenOpen GATE1
Figure 25. First Run Traffic Flow in the Model (Continued)
77
the overall first run traffic described above, these messages
follow a different route through the model because they are
allowed to preempt other lower precedence messages. When a
Flash message arrives in the system it immediately preempts
any message in channel 1 and begins transmission. Just
before transmission and in the simulation time instant of
generation the Flash message is assigned its message length
along with a 25 word header and then the entire length is
multiplied by three. This part of the simulation represents
two things. First before a Flash message starts transmission
on the broadcast channel a heading is sent which reads,
"ZUJ FOR FLASH • ZUJ FOR FLASH" etc. , and means Stand
By for a Flash Message. This header also causes attention
bells to ring on the subscriber's teletype thereby drawing
attention to the fact that a Flash message is about to be
transmitted. The second item is that a Flash message is
always transmitted three times in succession to ensure re-
ceipt by the subscribers.
The Flash routine also provides for the situation when
more than one Flash message may arrive. In this situation
if channel 2 is being used for first run traffic and chan-
nel 1 is already processing a Flash message then the second
Flash will preempt any message in channel 2.
When a message is preempted by a Flash message, the
preempted message is handled by the model in such a manner
that when the Flash finishes transmission, the preempted
message will be run again from its beginning, if the model
78
PREEMPTCHAN1
DEPARTQueue
TransmitFlash
RETURNCHAN1
To NormalUse
AssignMsg Lgth
Add 25> WordsMult. by 3
1
FlashQueue
PREEMPTCHAN 2
DEPARTQueue
TransmitFlash
RETURNCHAN 2
To NormalUse
Figure 26. Flash Message Routine, with Preemption
79
is being operated in the Preempt Rerun mode. If channel 2
is open for first run traffic and a message is preempted in
channel 1 and if channel 2 becomes available before the
Flash has finished transmission in channel 1 the preempted
message will be routed and transmitted on channel 2.
The third part of the model is the Screen Request and
Feedback Loop of the broadcast system. Screen requests are
generated according to an exponential interorigination dis-
tribution with specified mean value. When the screen
requests are generated they are assigned a transmission time
from a right shifted exponential distribution with a given
mean time. This holds the request in an ADVANCE block for
this period of time before allowing it to proceed through
the model. It is noted that more than one request can be
in this ADVANCE block at one time thus simulating any number
of screen requests in transmission to the NAVCOMMSTA. The
model then randomly determines according to a percent speci-
fied whether the screen request will be handled by the BCS
or by another NAVCOMMSTA. Next the request is assigned a
service desk system processing time and is held in an ADVANCE
block to simulate the time a screen request spends in the
service desk queue and on the service desk being processed.
This time delay distribution with its specified mean repre-
sents the competition a screen request for the channel pair
being simulated has with other screen requests for other
broadcast channel pairs or other broadcasts. When the
request has finished processing and is ready to proceed,
80
INSTA(BCS)
Scrn. Requests
IDelay in
Transmission
Yes
j£ServiceDeskSystemDelayI
AssignNr.
Reruns
AssignPrecedences
Route toAssign MsgLgth and toAppropriate
R P Z
orRRR PRR ORR
Queue
OUTSTA
No
ServiceDeskSystemDelay
AssignNr.
Reruns
AssignPrecedences
TransmitTo BCS
IRoute to
Assign MsgLgth and ToAppropriateR P Z
Queue
Figure 27. Screen Request and Feedback Loop.
81
it is then assigned the number of reruns that have resulted
from this screen request from an exponential distribution.
If the number of reruns is equal to zero the screen request
transaction is terminated and removed from the system. If
the number of reruns is greater than or equal to one, then
each rerun becomes a message itself and is assigned a prece-
dence and an appropriate message length and sent to its
appropriate queue to await transmission. The option of
allowing reruns to go to the head of the line was described
above. If a screen request was processed by a NAVCOMMSTA
other than the BCS, those reruns are assigned a transmission
time from the transmission delay distribution with a speci-
fied mean and held for that period in an ADVANCE block before
joining their respective queues. This time simulates the
time it takes for the reruns to be transmitted via AUTODIN
to the BCS. It is noted that in this case the reruns cannot
be allowed to go to the head of the line since these rerun
messages arrive at the broadcast position in the same manner
as first run messages and therefore are handled in the same
manner.
D. THE MODEL AND THE REBROADCAST CHANNEL SIMULATION
As was mentioned above, this model does not rebroadcast
first run messages as though they were being sent on a 1
hour delay rebroadcast channel. The secondary channel in
the model is used solely for processing first run messages
and when it is not doing so it is not used. The effect of
the use or non-availability of the rebroadcast channel to
82
the subscribers is simulated through the control of the mean
interorigination times of the screens requests. This is
done by using a representative regression equation of (Nr.
First Run) (Nr. Subscribers) vs. Nr. Screens for the channel
pair being simulated. Thus by specifying the number of
first run messages and the number of subscribers for the
simulation period/ the model determines the number of
screens that will be handled. Then by further specifying
the average number of screens per request the model deter-
mines the number of screen requests to be generated and with
this information the model calculates the mean interorigina-
tion time by dividing the number of requests into the
simulation time period. In the real world system it is
assumed that when the rebroadcast channel is being used,
that the number of screens requests is less than when the
secondary channel is not being used for rebroadcast of
first run traffic. Then if this assumption is in fact true
the analyst need only decrease the mean interorigination
time for the screen requests when the secondary channel is
open for first run traffic. This therefore simulates a
higher number of screen requests being generated and handled
at the service desk and thus more reruns are generated.
This is done in the model by one of two ways. The regres-
sion equation used can be changed when channel 2 is open or
simply the number of screens per request can be changed in
order to effect the increase of screen requests. Note that
this change in the mean interorigination time is made at
83
the time that the secondary channel is opened or closed for
first run traffic. Thus we can observe how the increase in
the number of reruns affect the system and since the time
delays are built in the feedback loop we can also observe
any surge in reruns which may occur after the secondary
channel was opened for first run traffic.
E. VERIFICATION OF THE MODEL
As the model was built, each routine added was run
separately to verify that the logic design was correct and
the transaction flow was being performed correctly. The
means and variances of interarrival times and message
lengths, etc., generated by the model using random number
generators and the specified functions, were checked for
accuracy. Appropriate modifiers (explained in model docu-
mentation) were chosen to ensure that the model generated
the function values with a reasonable accuracy for the mean
values desired.
One important verification was made by running the model
for the M/M/l and M/M/2 queueing systems. That is, the
model was run without the feedback loop and the Flash pre-
emption routine and with exponential (M) interarrival and
service times for one server (only channel 1 open) and two
servers (both channels open) [6,7]. The results of these
model runs were compared to analytical calculations for the
average server utilization and the average queue length and
waiting times. These comparisons showed that the model was
very accurate.
84
The model was also verified in its final form by using
data obtained from OEG which was gathered during ROPEVAL
3-71 [1] . This data represented the actual hourly number
of arrivals and backlogs observed during the period of
13-16 September on channel 1 (FASW) . For the comparison
runs with the model, parameters of the model were set at
values that were observed during this time period. The
parameters which were not varied for the comparison runs
and for later described runs are shown in Table XI below.
The observed traffic loads, number of subscribers number
of screen requests and number of reruns are shown in Table XII
TABLE XI
MODEL PARAMETERS HELD CONSTANT
Flash Immediate Priority Routine
Msg LgthMean
% of FirstRun
% of Reruns
AllowedBacklog for
OpeningCHAN 2
ClosingCHAN 2
89.2
1.5
1.5
245.3
22.5
22.5
10
257.3
35.7
35.7
50
1
182.6
40.3
40.3
110
2
85
TABLE XII
FASW 13-16 SEP OBSERVED TRAFFIC LOADS
Nr. Nr.Nr. Nr. Screen Msgs
Day First Run Subscribers Requests Rerun
13 SEP 422 38 6 6
14 SEP 668 40 8 4
15 SEP 598 40 13 10
16 SEP 480 33 6 36
Totals 2168 33 56
To simulate the daily and hourly fluctuations of traffic
arrivals during the period 13-16 September the model used
the number of first run messages shown in Table XII above
and the "diurnal" function shown in Figure 2 8 below. The
specified dirunal function allows the model to determine
the proportion of a day's first run traffic that will arrive
or be generated each hour of the simulation run. Another
function in the model specifies the number of subscribers
copying the channel pair each day, the numbers used are
shown in Table XII above. The percentage of first run
messages and reruns that were assigned each precedence are
shown in Table XI above. These percentages were the observed
aggregate percentages for the 13-16 September period being
simulated.
86
CM
oCM
£LUJCO
CD
<rCM ^-*
OCM
UJ
1-CO"™ 3
CL _l
CMUJCO3N
CO>-<
u.oUJ
00o
CDO o
C\J
O
to
>•HUu<CD
to
CO
en
S
CO
<fa
OhfaWVD
ro
MOiw
Co
-PUc
fa
•H
cn
•HQ
COCM
CD
UPtPHfa
SlVAIeJUV Nfld lScdldSAVQ dO NOIldOdOdd AlUnOH
87
In the simulation the Broadcast Control Station (BCS)
handled all screen requests. The parameters used for the
feedback loop were:
i. Mean Number of Screens per Request = 8
ii. Mean Number of Reruns per Request = 1
iii. Mean Screen Request TransmissionDelay = 120 mins.
iv. Mean Service Desk System Delay = 75 min.
To determine the number of screens (messages to be screened)
that would be handled each day the regression equation,
Y = 44.36 + .00065(X), was used, where X is the number of
messages transmitted the previous day times the number of
subscribers. This equation is taken from the above described
regression analysis for FASW (channel 1) during the
25 August-17 September period. Recall that during this
period channel 2 was used for rebroadcast of channel 1
traffic. The model determines the mean interorigination
time for screen requests by first calculating the number of
screens and then dividing that number by the specified mean
number of screens per request. This gives the number of
screen requests. By dividing the number of screen requests
into 1440 minutes the result is the daily mean interorigina-
tion time for screen requests.
To compare the model results to those actually observed
during the period 13-16 September the model was run in two
different forms. First the model was run with empirical
message length functions and with empirical functions for
the service desk system delays and the number of reruns per
88
screen. Secondly, the model was run with theoretical func-
tions for all distributions except Flash message lengths.
The Flash message length distribution was left as an
empirical distribution since the size of sample tested did
not allow us to conclude the exact nature of its distribution.
The results of these comparison runs are shown in Table
XIII and Figure 29 below. By comparing the average queue
lengths and the average wait in queue we see that the model
is conservative. We also note that the model with theoreti-
cal functions is more conservative than the run with empirical
functions. In comparing the backlog curves in Figure 29 we
note that the model tracks well. That is, the model shows
peak backlogs build ups and declines at nearly the same times
as were observed from the actual data.
It should be pointed out that we cannot say that this
comparison validates the model since each simulation run and
the actual observations for this period are observations of
a random process. Even if the actual data could be observed
again in the very same circumstances as the period of 13-16
September the results would not be the same, nor would
simulation model runs with different seeds for the random
number generators be the same.
F. MODEL SIMULATION RUNS AND RESULTS
1. Description of the Simulation Runs
The model with theoretical functions was used for
this experiment since it was determined above that it was
89
Q>KLU000
LUXXI3I-<LUO2TD-JO
UJXOJDI->OJO<3_l
C?
UJUJoo U-OS1- >LU»-<_l <Dh3 o00UJor: o
LUz aCo OL>—
1
»-< -io LUI—
1
Z CMu_ z*H <uu0£ XoOLU OZD>
LU —
l
-J >UJ <QO os: LU
_J OC<<*
• HZZi—
i
o a:•—
«
t- o>—
*
00XUJ _J z-J <ar=>CO hza:< O LU
H k a:
z_J 3<o^o;
oo
LU
<
f-« iCO | &
i-i iCO i-l
•i
t •
LO 1 CO 1i-«
CM 1 en i LO
vOLoegm Q\ \Q 0*1 >1" 0^ <"0 CO c*-rococo inCO--I cr CM CM CO 1 mi-4co—< r-
•-) *-* i-t .-H
>tC0^tn CMO <—l CO •—•—* i—
i
sOOOfOCO—<oo^r^cvjcj* coc\jr\jO>frOO HOOOHfOO'O
CNJrH ^-lsO CO •-I 00 CO CM
(NJ CM co •4" in -o
0>coLr\>j- 00 4"O --» s0 vO iTv OvOinoocMLnr-
OrOCM^O i—i nO vt r- <i" coo t*~ -4" co oo* co Is-
LO^-I s0 inmcM O O^fNj!-* -oft CM t-i COrH ,-1
_i cc cc a:_j a: 0L OC-J_l \ ct: a: a£-j i ex; or ot-j
a:a.O< a:a:Q.0-OO< oia:cLQ.oo<
o QUJ UJ
z 00 002 o oo -j _Jz o o*:z r- CO3
•
oCO•
o•
CO <-4 mro ro CM
>o •4- .-1
LO . r~ 00
CO LO i cov£ in
lm
.-H .-ii
«-•
c\j CM
i Q
1CM
1o
_)1 LU O0
1LU OO
< 1 t- X H- 1 H IOh3 1 <ZI— CLO | <ZI— LUO1-
1 JD"-S2 » JD-IZU 1 z>a£:2U-0 I Do:sh3<
i s: u.
1*H
100
1S LL
1
*~*
1^
90
+CM
OCM
CO- a.UJ
CM » •
CD wto
COVOH
1
*
CO<f rt!
CM
,-.
fa
OCM
UJ5E to
CO»-
Ha. 3 MUJ _i U
CM CO 3 id
CQ"*• NlO rH
<ti
CO 4->
>- O< En
<& OrH
*u.
o -Mo
CM UJ2
rtj
oCM h-
T3C
CCD O~
Q.UJ
•H-P(0
CM CO rH™
™
P<fr e— •H
CO CO
.H
<i-T3
*•CM •
CO
CN
CU
u
CO XJ\— PO •H^~fa
CM
( S39VSS3W JO cdN ) oon>iDva
91
more conservative than the model with empirical functions.
The channel pair system was simulated under three different
situations, i) channel 2 closed to first run traffic but
considered as being used for rebroadcast of channel 1
traffic, ii) channels 1 and 2 both transmitting first run
traffic and the rebroadcast facility is not used, and iii)
channel 2 is opened and closed during the run by the timers
when specified backlogs were exceeded. Additionally the
above situations were run where reruns were allowed to go to
the head of the queue as opposed to going to the back of
the line.
Eight simulation runs were made with these config-
urations. Four simulation runs were made representing the
period of 13-16 September and the other four runs represented
a hypothetical four days in which the first run traffic loads
were increased by 200 messages per day over those observed
in Table XII above. The runs made are listed as follows:
Run 1. 13-16 SEP. Channel 2 Closed for First RunRun 2. 13-16 SEP. Channel 2 Open Whole PeriodRun 3. 13-16 SEP. Channel 2 Opened and Closed by TimersRun 4. Same as Run 2 with Reruns going to the back of
the lineRun 5. High Loads, Channel 2 Closed for First RunRun 6. High Loads, Channel 2 Open Whole PeriodRun 7. High Loads, Channel 2 Opened and Closed by TimersRun 8. Same as Run 7 with Reruns going to the Head of
the Line.
In runs 1-3, reruns were allowed to go to the head
of the queue and for runs 5-7 reruns were put at the end of
the queue. All of the runs used the dirunal function shown
in Figure 2 8 to determine the hourly first run arrivals. In
runs 2-3 and 6-7, when channel 2 was open, the number of
92
screens were calculated by using a different regression
equation and mean number of screens per request such that
the model would simulate a higher number reruns. For runs
1-4 the mean service desk system delay set at 75 minutes
while for runs 5-8 it was set at 158 minutes (see Table X)
.
The allowed backlog levels shown in Table XI for
opening channel 2 in simulation runs 4 and 7 were chosen
based on the Broadcast Speed of Service Criteria shown in
Table I. By using a familiar queueing theory equation,
L = AW, where L is the average queue length, W is the average
wait in queue and X is message arrival rate, one can deter-
mine the approximate backlog levels allowed before the Speed
of Service Criteria are exceeded [6,7]. We note that this
equation relates averages over a period of time. Therefore
the maximum allowed routine queue length, which is usually
the largest queue, was determined by using this equation and
the arrival rate of routine messages observed during the
13-16 September period. The other allowed backlogs by
precedence were chosen somewhat arbitrarily but such that
the allowed backlog would not exceed on the average, the
Broadcast Speed of Service Criteria.
2 . The Results of the Simulation Runs
The results of these eight simulation runs are shown
in Tables XIV and XV and Figures 30-32. In comparing the
average queue lengths, average wait in queue and the maximum
backlog observed plus the backlog curves the result of the
simulation is obvious. The system configuration where both
93
Q>J-UJooo
00 UJXo XDK< <ujoo 21=5-1_J Oot—t UJXu_ ujdj—LL >ujo< <Z>-Ja£ aH-
3 LULU00 11021< >UJi-iu. <=>(-
CLUJoo
UJ>o 0C"
<-t ft.
1
COf-l —1
UJOf! Z CMo zU- <LU
Xoo00 UD1--J UJ 1—
1
X> >00 <UJa:
UJz _l C£o <<*•—
I
hZZ1- O of< »- u_) 00Z)21i—
i
-1 z00 <a:3hZC_J O UJUJ 1- OLQO2! Z
-J =><arra:
• HZK> a 00
CD<
in
oo
sOOO^roco-^O^r-tOOOHnO^O
co cov0
o>omcocMinr>-
r~«$roco>trnr-o^-cm^ so
a: o£ c£_ja: oi a:_j
orctro-o-ocx
oUJ00
O
o
inCM
00
comr-t
cm
r 0-UJ_1 0—
»
UJi
O0UJ UJi-t
zs 1 Z 00Z>< 1 >ozcmozorz <-<< -J=5
I 1 x uo:I coo —
CMSI
0>CO•
inco
ocor-CMnrncM
O v0m^ f- —t r-A
>to-*ooor-
r-o <-* co r*- >i-ocm^-^-o co—<
oc cc Qi-J<x a: a: -J
or c£a_a_ocj<
co
cmin
CMCM
inm—<
a.LU_I00 UJzoz
—1<I xcoo
LUQ^Z-JOCNIUJO 1-1
cM0_Xa:z
a. a:
h- co co ro »-i soo
o -4" co >—•o ro
1*
^O^corg^OfM
OCO
CM inro
roroco^-incovo
COO-HCM^^-d"oct>cmcmCM
a: a: o£_j01 OH Qi_J
^DCQ-aOC<
r-coo
roco
>oCO
co
CO"4-
CM
O- Q>-UJ_) ZCQOO—
.
oouj < a:roZ QUJ
vOZMZUJSiZi—»<t ujoOi—O
I x aoi-a:coo O-J «—-* o
in•
f—
1
in
O^COxOr-ro r»
-4CMt*-0vO^cOCM
Oro COin >o
inr^-o-f
^CM>tOcj>cm >oco **
ct:a.o<
oUJ00a
o0>
COCM
inCO
cmin
CM
UJ
oo»<:
LU
•Oi<t— .
001CMZ
Z>za:
a: or
ozZ5
OoiZ—UJ
94
UJ
3N
>-<Q
OLU
T3C
c
o
2
*- wW
ro
13 HC I
HCN
tn uc -H
« 14-)
f0
o o o oo lO o LOOJ
™ '
uEho
•H
rtJ W3e•HC/)
o4-1
O
CO oCHrHo urH \AJ CU <D
rd q,PQ OrH CN
O KEh U
omQ)
U3Cr>
•Hfa
( S39VSS3IAI dO UN ) 901>iOVa
95
>t 11*"
1 r*- 1 Is-
1
o>1
CM CMI
i-H 00I
HLU 11 1 •
| • 1 • 1
too|
CM 1
-h >o r- l
m CM 1 in in |
ro 1
LUX 1X3h|
vor^mog cof-o^r*- r-r->J-0 cMoomh-cMno^|
<LUO 1
r>-o>-ico 0».-4 CO O^cO-mO OOCMCO co1
z:z3_i 1 0^-4 o> -4 CM 1-1 1-4j
1
to rvjr-rOsj- ^r'-coh- OrOsOoo co ro<t- co rococo 1
Q LUX 1 cMcor->j- cocmcmo 1 coo^vj-—
1
1 >$-rOCMr-4>$-0^ 1
< U-Ol- |
O >LUO 1 oco CO 1-4^ CO r-tfO O vOr-4^ CO |
-J <3_l 1
0*1
mcM CO r-l 1—1 in in in vo j
wUL LULU | cocor*-^ OO^OCM HHOfO o>>tmococMn 1
U_ luz>s:1
< >LUi-t1
momo^ COsO.—iin O^OCOCO OCOCM>tCOCOi-< 1
ac Ok 1 in CM co «fr CM •-OCM O COCOCMr-4 CM1
\-1
-4 1-4
(\J
o> CM i-4 CM -4 I
Xo -j _r _i CC cC cC-i 1— LU
1_i -j _J CC CC CC-i \
X CC 1 CtTQ.O< oco-o< cca.o< a:^aaOO< I
0.CC
oUL _J Q
LU ILU 1- 1
lO Z cm 1to in co in 1
H z 1 a >o CO CO I
_J <LU > —i • • • j
13 xoo 1
to U3LU 00 in r- l
a: LU -4 LO in CO CM |
> 0^ r- o> 1
z < • • • tI
o•—
1
Ot- LU< _J <*-J <ta: 1 fH CO r-l -0 1
D KZZ CM 0> CO CO 1
5: a:t—
4
1-to to
-jLU -J za <o:zd CM in &a HZa: CO in in CO 1
2: O LUI- CC
i-l •t .-4 H \
•
> zX _J => ^ CO O 1 >t<a:a: O CO I CO
1 CT> I
LU hZh 0^1 & I o> 1
0> |
_J O to CM CM CM1 CM
CO 1- —1
<J-
to1to tO LU X 1
OCM 1QCM
tCCMtOtO 1 l-O I
1 < O 1 < <-» < 0<^-* 1 •—(— LL — 1
LU O-JLU-^IOJZvO I 0_i_iujr- 1 t03 OLUCO |zs _|LU00LC\
1—ILULU I JUJOS 1 < to z 1
X>< zo 1 ZQ.Z I Z^'—Z 1 P-ZQ^Z |
CCZ. 1 IZJZ 1 IZOD I IZZK3 1 UJ ZD<_llO |
10<OZ> 1 o< DC I 0<OJ CC 1 SZCXLU CC 1
1 «-x CC 1 i-»X »—I -hXO->-w 1 <Z>LUI w 1
1 10 —1 xo I XOOCO 1 toaroc j
96
LJ
I-
3N
>-<
LU
Q)
CO
Or-[
U
K
w
to
oh3
M-l
mrd
uEh
^HK^O
ao•H+J
fd
3e•HW
OIW
en
cpo
U
PQ
Htd
+J
oEh
Q)
•H
(S39VSS3IN 30 UN ) 901>iOV8
97
LJ
N
>-<QU_OLJ
h-
to
<d
O
u•H
uEn
J3
•H
o
r-
CtO
>X)
w ^-«
P 0)
& en
o
o u-H \-p
•HCD
o4-1
W
oCMIS<KU
tr> as
o
,V CD
u a.fl3 O
rfl <4-> ffi
O UEh —
CMro
CD
Pcr>
-HEm
o o o oo lO o lOCJ • *"" ~—
(S39VSS3IAI dO UN ) SOOIHOVG
98
channels transmit first run traffic and the rebroadcast
facility is not used is superior to any other configuration.
Recall that the decision variable for this problem is the
average wait in queue of any precedence message such that
this time does not exceed the Broadcast Speed of Service
Criteria indicated in Table I. We also note that the primary
goal of the fleet broadcast is to make timely and efficient
delivery of traffic to all subscribers. The model shows
that there is no question as to the timeliness of traffic
delivery when both channels are running first run traffic.
So now we must question whether this configuration is also
the most efficient method. This can be answered by looking
at the feedback loop and the message reruns. Looking at the
results for the high load runs 5 and 6 where channel 2 was
closed for first run messages in one run and open for first
run in the other run. For these two runs the mean time delay
in transmission of a screen request was 120 minutes and the
mean service desk system delay was 15 8 minutes thus on the
average it took 278 minutes (4.6 hours) for a screen request
to reach the broadcast position for transmission since the
time it was originated. Now if we chose the routine messages
for comparison, we note that when channel 2 was closed to
first run traffic the average time it took for a routine to
be rerun is 2433 minutes (40.6 hours) as compared to 326
minutes (5.4 hours) when channel 2 was transmitting first run
traffic. We also note that 15.5% of the total first run
traffic was rerun in run 6 as compared to only 4.4% in run 5.
99
To fully explore this area we further look at the
comparison of the runs where reruns were allowed to go to
the head of the line. We see that although the reruns did
not have to wait as long in queue as they did when they went
to the back of the line, we also see that the first run
traffic had a longer wait in queue on the average than when
reruns were put at the back of the line. This leads us to
ask the question, "Which type of message is most important?"
It would appear that the first run message is most important
because it has not been transmitted to any of the subscribers
copying the broadcast and hence it is really undisclosed
information while a rerun message has most likely been
received by the majority of addressees, if more than one,
and hence it is old information to those subscribers except
for the subscriber who missed the message.
100
V. CONCLUSIONS
The conclusions which can be made are that the broadcast
channel pair configuration where both channels transmit first
run traffic is the superior configuration for timely delivery
of traffic. The comparison of time delays for a subscriber
to receive a rerun show that this configuration is not only
timely, it is efficient as well. Therefore, the answer to
the problem question is that the system should always be run
with the parallel channels transmitting first run traffic
and that the rebroadcast of first run traffic on the secondary
channel should be discontinued.
101
APPENDIX A
ORIGIN OF THE STUDY
. The problem on which this study is based was proposed as
a thesis topic to this student in April 1971 by Captain F. M,
Snyder, USN, then the Assistant Commander for Operations and
Readiness to the Commander, Naval Communications Command
(COMNAVCOMM) . The study was officially commissioned as a
thesis study by COMNAVCOMM message R 021944Z SEP 71. A copy
of this message is shown below for reference and as an
example of a Naval Communications teletype message.
CZCGAA050RTTUZYUW RHELSAA006 5 2452004-UUU—RUWJAGAZNR UUUUUR 021944Z SEP 71FM COMNAVCOMMTO RUWJAGA/NAVAL POSTGRADUATE SCHOOLINFO RUWNSAA/NAVCOMMSTA SFRANBTUNCLAS //N00JW//FOR LCDR. HARLAN D. OELMANNTHESIS STUDY1. YOUR THESIS STUDY OUTLINE HAS BEEN REVIEWED AND ITSPURSUIT IS STRONGLY ENCOURAGED. COMNAVCOMM REQUESTSCOPIES OF THE COMPLETED STUDY AND ANY INTERIM REPORTSTHAT ARE DEVELOPED.2. DR. HARDY (OEG) WILL VISIT NAVCOMMSTA SANFRAN DURINGEARLY SEPT., AND IT IS SUGGESTED THAT YOU MEET OR SPEAKWITH HIM AT THAT TIME IN ORDER TO BECOME APPRISED OFOEG EFFORTS IN THIS FIELD.3. SHOULD COMNAVCOMM ASSISTANCE APPEAR NECESSARY ORDESIRABLE IN THE DEVELOPMENT OF THE STUDY, REQUEST YOUMAKE YOUR NEEDS KNOWN VIA NAVCOMMSTA SANFRAN.BT
102
APPENDIX B
PROBLEM BACKGROUND
I. A BRIEF EXPLANATION OF THE NAVAL COMMUNICATIONS SYSTEM
A. ORGANIZATION OF THE NAVAL COMMUNICATIONS SYSTEM
The Naval Communications System is composed of 2 7 Naval
Communications Stations (NAVCOMMSTAs ) , 4 Naval Communications
Units (NAVCOMMUs) and several Naval Radio Stations
(NAVRADSTAs) [8]. These stations are located throughout the
world and are organized into several Naval Communications
Areas (NAVCOMMAREAs) . The primary purpose of these stations
is to relay messages to and from ships of the fleet and
shore establishments within their area of responsibility.
The stations within a NAVCOMMAREA are organized under one
NAVCOMMSTA which is designated as the Naval Communications
Area Master Station (NAVCAMS) while the other stations are
designated as Naval Communications Area Local Stations
(NAVCALS) . Although the communication means which each of
these stations use take several forms, such as teletype,
voice and CW, etc. , this study is concerned only with tele-
type communications and the fleet broadcast system. There-
fore discussion will consider only those areas.
B. TELETYPE COMMUNICATIONS
It is assumed that to most readers, teletype communica-
tions is a familiar means of communication which does not
103
require detailed explanation, except to note that when
messages are handled physically within a station they are
handled in teletype tape or chad tape form. Hence in
further discussion when we speak of messages being handled
in a station it is implicitly meant that such messages are
in tape form unless otherwise stated.
1. World Wide Teletype Communications
The Defense Department World Wide telecommunications
system controlled by the Defense Communication Agency pro-
vides for long-haul and point-to-point telecommunications
between communications stations of the Armed Forces which
include the NAVCOMMSTAs and other stations within the
NAVCOMMAREAs . This system is known as the AUTODIN network
which is a digital high speed message transmission system.
2. Local Teletype Communications
The primary means of communications between a
NAVCOMMSTA and the ships at sea is a teletype system which
operates at the rate of 10 words-per-minute (wpm) , where
one teletype word is equivalent to 5 teletype characters.
There are essentially three methods of teletype
communication between the ships at sea and the shore based
NAVCOMMSTA.
The first is a ship-shore telecommunication link
which are time shared circuits used by several ships at sea,
these circuits provide the capability to send messages to a
NAVCOMMSTA for further relay and delivery.
104
The second method is also a ship-shore link which is
a dedicated circuit, sometimes called a full period termina-
tion circuit/ between one ship and the NAVCOMMSTA. This
type of circuit is normally used by the larger ships such
as aircraft carriers and cruisers, which normally have
staffs embarked. The full period termination circuit pro-
vides the capability for these ships to send messages to the
NAVCOMMSTA for further relay and also to receive from the
NAVCOMMSTA messages which are addressed to that particular
ship or embarked staff.
The third method is the fleet broadcast system.
This system is the primary means of delivering traffic to
the fleet as a whole because it provides for simultaneous
delivery of messages to the operating forces dispersed over
a large geographical area. This method also employs a
100 wpm teletype system which could be described as a one
way system because the broadcast system enables the NAVCOMMSTA
only to send messages while the ships can only receive
messages
.
The fleet broadcast system is composed of several
different types of broadcasts. These are the fleet multi-
channel broadcast, on which this study is based, a single
channel broadcast for ships that are not equipped to copy
the multi-channel broadcast, the submarine broadcast and a
merchant ship broadcast. In some NAvCOMMAREAs these broad-
casts are all operated by one NAVCOMMSTA or Broadcast Control
Station (BCS) while in other NAVCOMMAREAs these separate
105
broadcasts are operated by two or more NAVCOMMSTAs . Also
if the capability of flexibility exists, a separate addi-
tional broadcast may be created within a NAVCOMMAREA to
handle special traffic load situation. Sometimes a NAVCAMS
may shift a braodcast to a NAVCALS in an emergency or to
maintain proficiency among the capable NAVCALS in operating
the broadcast.
C. MESSAGE PRECEDENCES AND SPEED OF HANDLING
Naval communicaions messages are assigned one of four
precedences. Each message precedence has a Speed of Service
Criteria assigned by reference 9, which is a time standard
for a message to take in transmission from the origination
of the message to the receipt of the message by the addressee
These criteria are shown in Table XVI below. The letter
in parenthesis is the designator of the precedence.
TABLE XVI
SPEED OF SERVICE CRITERIA
Precedence Average Speedof Seriice Limits
Flash (Z)
Immediate (0)
Priority (P)
Routine (R)
As fast ashumanly possible
30 minutes
3 hours
6 hours
Same
30 minutes-1 hour
1-6 hours
3 hours-to thestart of the nextbusiness day
106
II. THE FLEET MULTI-CHANNEL BROADCAST SYSTEM
There are normally five fleet multi-channel broadcasts
operated in the Naval Communications System. Each broadcast
which serves a particular ocean area is operated by a desig-
nated NAVCOMMSTA or Broadcast Control Station. These broad-
casts have designations of NMUL, EMUL, KMUL, FMUL and GMUL
,
where FMUL serves the Eastern and Mid-Pacific Ocean area and
is normally operated by NAVCOMMSTA San Francisco [10]
.
A. CHANNEL ALIGNMENT AND USE
The fleet multi-channel broadcast is a multiplex system
which has 8 separate 100 wpm teletype traffic channels
which are transmitted on a single carrier frequency. The
alignment of the traffic channels is such that the overall
broadcast traffic load to the fleet is segregated on the
basis of ship type where each subscriber is served by two
traffic channels, a primary channel and a secondary channel.
An example of the overall broadcast channel alignment,
channel designations and uses of each channel is shown in
Table XVII below.
Only channel pairs 1 and 2, 3 and 4, and 5 and 7 will be
considered for this study.
B. THE RECEPTION SIDE OF THE BROADCAST
The fleet multi-channel broadcast system for each channel
is a guard system. This means that each subscriber copying a
particular channel screens each sequentially serial-numbered
107
TABLE XVII
FMUL-BROADCAST CHANNEL ALIGNMENT
Channel Designation Use
1
2
3
4
FASW
FSPC
FALD
FUSN
FNSC
FOP I
FHIC
FMET
Destroyer force primary traffic channel
1 hour delayed rebroadcast 'of channel 1
or overload as necessary
Service, Amphibious and Mine forceprimary traffic channel
1 hour delayed rebroadcast of channel 3
or overload as necessary
Major warships (carriers, cruisers,large destroyers, including flagships)primary traffic channel
Special traffic channel (Not of studyinterest)
1 hour delayed rebroadcast of channel 5
or overload as necessary
Weather traffic channel (Not of studyinterest)
message sent on that channel to determine whether that
particular message is addressed to him or not. If the mes-
sage is for the ship or for the embarked staff the message is
processed. If it is not for that particular ship or embarked
staff the message is ignored and filed. Hence a subscriber
must perform two necessary actions. ' He must determine from
the message heading (which contains the addressees) whether
the ship or embarked staff is an addressee or not. If the
108
message is addressed to the ship then it must be copied with-
out errors from beginning to end. That is the addressee
must have a clear enough copy that he is able to obtain all
the information transmitted without any doubt as to what
the message says.
If a subscriber has missed part or all of the heading
such that he cannot determine whether the message was
addressed to him or not, or if he has missed part or all of
the text then we will refer to such a message as a "missed
message.
"
A message may be missed for various reasons, some of
which are: environmental or atmospheric conditions, which
cause deterioration of the radio signal, equipment failure
on the ship or in some cases error in judgment of the
operator monitoring the teletype printer.
C. PROCEDURE FOR OBTAINING MISSED MESSAGES
If a subscriber copying a particular channel has missed
one or more messages he must determine whether the message (s)
was addressed to him and if necessary he must obtain a
complete copy of the message. He is first encouraged to
obtain a copy from another ship copying the same broadcast
channel, providing the subscriber has a separate means of
communication with the other ship. When the subscriber
exhausts all local means of obtaining this information his
next action is to originate a message which is called a
"service or screen request message." Such a message is
usually sent to a NAVCOMMSTA requesting them to verify or
109
screen their copy of the broadcast to determine whether the
message (s) in question is for the subscriber. The NAVCOMMSTA
will in turn reply by indicating which messages are of no
concern to the subscriber and by rerunning on the primary
channel those messages which were addressed to the sub-
scriber. A subscriber which misses only a portion of a
message may service only for that portion of the message to
which the NAVCOMMSTA must in turn originate a service
message in reply giving the subscriber that portion of the
message missed.
It is noted that in some NAVCOMMAREAs , the NAVCOMMSTA
to which a screen request is sent may not be the Broadcast
Control Station. In these cases designated NAVCOMMSTAs in
the NAVCOMMAREA also copy the broadcast and serve as
stations which handle screen requests for a particular
channel of the broadcast. When these NAVCOMMSTAs process a
screen request their replys are relayed via AUTODIN to the
Broadcast Control Station which in turn sends the reply on
the appropriate broadcast channel. We note that these replys
are handled in the same manner as first run messages.
D. HANDLING OF SERVICE MESSAGES AT A NAVCOMMSTA
Some NAVCOMMSTAs will handle screen requests for more
than one broadcast channel or in some cases for more than
one type of broadcast system. At each NAVCOMMSTA all such
broadcast screen requests are usually handled at one broad-
cast service desk. The broadcast service desk handles these
110
requests on the highest precedence first and on a first in
first out basis within precedences.
These service messages are usually referred to as screen
requests, since the service desk clerk is required to "screen"
the heading of the missed messages in the printed copy form
of the broadcast channel log to determine if the message is
for the requesting subscriber. Additionally, to clarify
terminology, each message looked up is referred to as a
"screen." Thus a "screen request" may contain one or more
"screens
.
After the service desk clerk determines the result of a
screen request he then must make teletype tape copies of the
messages to be rerun, if necessary, which are forwarded to
the appropriate broadcast channel position for transmission.
At some NAVCOMMSTAs , when the service desk clerk has finished
the screen and before he prepares the rerun tapes he prepares
a short message to the requester indicating which messages
are of no concern to the subscriber and additionally states
that those messages which are of concern will be rerun later.
Other NAVCOMMSTAs use the procedure where they include this
information with the first message rerun and only after the
entire screen request has been processed.
It is apparent that this process is a very time consuming
task and explains the reason why subscribers are encouraged
to seek other sources for verification before asking the
NAVCOMMSTA.
Ill
E. TRANSMISSION SIDE OF THE BROADCAST
Considering now the transmitting side of the broadcast
we look at the NAVCOMMSTAs internal handling of messages
which are destined for transmission on one or more of the
broadcast channels. Messages arrive at the broadcast area
in teletype tape form and are, depending on individual
NAVCOMMSTA configurations , primarily delivered to each broad-
cast channel position by two 850 wpm reperforators called
"burpees." The traffic delivered by the burpees is traffic
which has been received by the NAVCOMMSTA from the AUTODIN
network or from 100 wpm teletype circuits which terminate at
the NAVCOMMSTA from any number of sources. The burpees are
fed from these various sources through a small computer
system called the Multiple Address Processing Unit (MAPU)
.
This system reads the header of a message which contains
address codes as to where a message is destined within the
NAVCOMMSTA and routes that message to the appropriate relay
positions by delivering a teletype tape through the burpees.
In addition to the burpee deliveries some NAVCOMMSTAs hand
deliver screen request answers, reruns and other messages to
the broadcast position. The screen request answers and
reruns are then usually put at the head of the line or queue
for transmission.
Messages delivered to the broadcast position are put in
a grid (queue) by precedence and in order of arrival within
each precedence. The messages are then taken from the grid
and put in the channel transmitter distributor (TD) , a
112
device which reads the teletype tape for transmission. The
order in which the messages are taken from the grid for
transmission is on the highest precedence waiting and first
in first out (FIFO) within a precedence basis. This process
at some NAVCOMMSTAs is done by one man physically performing
the queueing process while another man pulls the tapes from
the grid and places them into the TDs for transmission. At
other NAVCOMMSTAs, properly equipped, this entire process is
handled by a small computer system, known as the "tight
tape" system. In either case the queueing and transmission
flow is the same for the purpose of this study.
113
APPENDIX C
GOODNESS OF FIT DATA ANALYSIS COMPUTER PROGRAM
I. DESCRIPTION OF CAPABILITY
The Goodness of Fit Data Analysis Program accepts any
number of data samples of varying sizes and performs
prescribed calculations and produces various graphs and
tables which are used to analyze the fitting of an empirical
distribution with a selected theoretical distribution. The
program is written to fit the empirical data to two different
distributions. These two distributions are the Exponential
and the Hyperexponential probability distributions in either
their regular form or the right shifted form.
The main program uses five different subroutines which
are named SORT, STAT, HISTO, PLOTP and UTPLOT, the last two
subroutines being used in conjunction with each other. The
main program with the subroutines first sorts the data in
ascending order and prints out the data in this form. Then
the program calculates statistical parameters and prints out
the parameter values which are later used in subsequent
calculations. The next feature provides for sorting the
data into frequency classes and prints a histogram of the
data according to the number and widths of intervals as
prescribed by the programmer. The program then calculates
and plots the log of the tail distribution for both the
114
empirical and theoretical distributions being tested. A
description of these calculations along with other mathe-
matical descriptions are more fully explained below. The
respective Cumulative Distribution Function (CDF) values are
calculated and the absolute difference of the distribution
points is determined and printed. The absolute difference
provides the user this information for use in performing
the Kolmogorov-Smirnov (K-S) Goodness of Fit Test on the
data. The cumulative distribution functions are plotted to
facilitate a graphical interpretation of the fit of the
distributions. Finally the data is analyzed by performing
the calculation of the Chi-Square Statistic and printing out
a table of results for use in performing the Chi-Square
Goodness of Fit Test.
Features of the program provide a flexibility of
selecting only certain calculations to be performed and/or
certain outputs to be printed. These features of selection
are fully documented in the computer program shown in this
Appendix.
This Appendix is not meant to be a user's guide for the
program but rather to explain and reference the mathematical
calculations used in the analysis program.
II. THE THEORETICAL DISTRIBUTIONS
A. THE EXPONENTIAL DISTRIBUTION
The exponential density function/ cumulative distribution
function and the associated parameters are given below.
115
f (x) = Xe-X (x-a)
=
, x>_a, where a is the rightshift parameter.
,x<a,
F(x) = i- e~X(x" a)
,x>a,
,x<a.
E(X) = ± + a,
y-a'
= VAR(X) =2
"
B. THE HYPEREXPONENTIAL DISTRIBUTION
The hyperexponential distribution shown below is a
mixture of two exponential distributions. The observations
originate in two populations only, with probabilities p and
1-p and parameters 2Xp and 2X (1-p) , respectively [11].
The hyperexponential density function, cumulative dis-
tribution function and the associated parameters are given
below.
£ , . -.2, -2pX (x-a) , ~ /n ., -2 (1-p) X (x-a)f(x) = 2p Xe ^ + 2(l-p)Xe trt
, x>a,
= , x<a,
F(x) = p
=
'
1_ e-2pX(x-a)l
+ (1_p)'] 1_ e-2(l-p)X(x-a)
, x>a,
, x<a,
where a is the right shift parameter.
y = E(X) = ± + a,
X =V-a'
116
a =
P =
\?n d ^y^ — ]l
1 1
X2 _2p(l
2
-P)
h
2 21
a2
y+ 1-
III. STATISTICAL AND GRAPH CALCULATIONS
A. SAMPLE STATISTICAL PARAMETERS
The analysis program has a feature in which preselected
values for the mean, the right shift parameter a and the
hyperexponential parameter p can be read in instead of having
the program calculate these estimates from the data. When
this feature is not used some of these parameters are cal-
culated by the subroutine STAT using the familiar formulas
shown below.
N N
XBAR = X = Iv VAREST
i=lN
= N^T 1 (Xi" *> '
i=l
We note that
XBAR = V = i + a = ^^ + A,
hence
,
LAMEST =(XBAR - A)
The capitalized names are those used in the program for
these various parameters.
117
The estimate of the hyperexponential parameter p is
calculated using the same formula shown above except that
XBAR = y and VAREST = a .
The right shift parameter a can also be specified to be
the minimum order statistic of the data sample.
B. A GRAPHICAL PROCEDURE OF TESTING FOR EXPONENTIALITY
When comparing empirical data to the exponential distri-
bution, for goodness of fit, this graphical technique
provides an appealing method of either supporting or denying
the more purely statistical comparisons to be described
below.
If the empirical data is really distributed exponentially
with a cumulative distribution function as shown above then
the following graphical comparison can be made [12], For
the exponential distribution the log of the reciprocal of
the tail distribution (called the log of the tail for
brevity) is:
, 1 (x-a) . ^ „y = log j_F (x )
= —jj-S assuming y > 0.
Thus if we plot y against x, we get a straight line with a
slope of — and the line will cut the x-axis at the point x=a.
If we have n data points in the empirical data, we can
sort the n points in ascending order forming the order
statistics, i.e., x, <_ x? <_ £ x . The empirical
cumulative distribution function is defined as
F(x.) = - .
l n
118
If we let y = log i_F / x \ • Then by plotting y. against x.
the plotted points can be compared to the fitted straight
line as a test of the exponential assumption.
It is noted that the program has the option of using
a preselected mean or using the sample mean estimate in
calculating the straight line. Thus, this graphical com-
parison can be used to make an independent estimate of the
mean by determining the slope of the empirical data. Then
the data can be rerun with a preselected mean to attempt
a better fit.
When the log of the tail distribution is used with the
hyperexponential comparison we get a decreasing failure rate
function for the hyperexponential distribution. That is we
get a concave curve. In this case the graphical comparison
can also be used to determine how close the two compare.
This method of distribution fitting can be used when
empirical data is analyzed for the first time. Through the
use of the log of the tail graph we can determine how the
distribution behaves and find out whether it has a decreas-
ing or increasing failure rate and thus plan further analysis
on the data.
C. THE KOLMOGOROV-SMIRNOV GOODNESS OF FIT TEST
The Kolmogorov-Smirnov Goodness of Fit Test is a familiar
test and therefore will not be described here [13]
.
It is noted that the program only calculates the absolute
difference between the F(x) values of the two distributions
and prints the results. Therefore the user must scan the
119
points to find the maximum difference and then enter the
appropriate Kolmogorov-Smirnov table to determine the
results of this test.
The Kolmogorov-Smirnov test is regarded by most
references as a more powerful test than the Chi-Square
Goodness of Fit Test but it has one drawback, that being
that the Kolmogorov-Smirnov statistic becomes inflated when
the data has large groups of points which are of equal value.
D. THE CHI-SQUARE GOODNESS OF FIT TEST
The Chi-Square Goodness of Fit Test is also a familiar
test and will be described only briefly [12,14,15].
It is well known that the chi-square goodness of fit
test has several drawbacks. Among them are its large sample
character and the dependence upon the careful choice of the
number and the widths of the intervals. Therefore this test
should be used with caution. For further discussion of
these characteristics see reference 14.
It is also noted that the program has the capability of
either reading in a specified mean or estimating it. This
will affect the number of degrees of freedom used when
testing the chi-square statistic against the appropriate
table values. The chi-square goodness of fit test with an
estimated mean uses (k-2) degrees of freedom or (k-1) degrees
of freedom when the mean is preselected, where k is the
number of intervals (or classes) used in the test, and where
the x-axis is divided into the intervals x, <_ x?
< —xk-l
120
The chi-square statistic was calculated in the following
manner. Let o. be the observed number of data points in the
i interval and let e. be the expected number of data points
in the i interval, where e. = np . and where n is the
number of data points in the sample being tested and p. is
calculated as indicated below for the appropriate distribu-
tion.
For the exponential distribution:
x. + l
i=/\e-<t
P^ =
-X(x.-a) -X(x. J^ 1 -a)-a) ,
.
1 l+ldt = e -e
1^ X / • • • f jC~" rib f
and
.-/ , -X(t-a),,.- x ^ xk_i-
a)
.
Xe dt = e , l = k-1.
^k-1
For the hyperexponential distribution:
xi+l"V, 2, -2pX(t-aK 0/1 x , -2 (1-p) X (t-a)2p Ae ^ + 2(l-p)Xe c
P,- =
X.1
dt
-.[.-2pX(x
i-a) -2pX(x
i+1-a)
-e
-2 (1-p) X
(
Xi-a) -2 (1-p) X (xi+1
-a)+ (1-p) e
and
i
= pe
2p2Xe"
2P X (t" a)+ 2 (1-p) Xe"
2 (1 -P» X {t'^_
k-1
-2pX
(
xk_ x
-a )
dt
-2(l-p)X(x -a)+ (1-p)
K" X, i=k-l.
121
The value e. was restricted to the condition of having
e. > 5 for each interval [14]. If this condition is not1 —
satisfied then the observations of that interval are added
to the previous interval and the appropriate integral is
recalculated. This is repeated until this condition is
satisfied.
Finally the chi-square statistic is determined by this
formula
2 £ (o,-e,)2
stat 1=1
This statistic is then compared to the appropriate
chi-square table value to determine the results of the test
122
IV. DATA ANALYSIS COMPUTER PROGRAM
CC GOODNESS OF FITC DATA ANALYSIS PROGRAMCcC PROGRAM DISCRIPTION:CC SORTS DATA IN ASCENDING ORDER AND PRINTS DATAC CALCULATES PARAMETERS: MEAN, VAR t STD.DEV., LAMESTC AND HYPEREXPONENTIAL PROPORTION PARAMETERS PI AND P2CC HISTOGRAMS SORTED DATACC CALCULATES AND PLOTS THE NATURAL LOG OF THE RECIPROCALC OF THE TAIL DISTRIBUTION FOR BOTH THE EMPIRICAL ANDC THE THEORETICAL DISTRIBUTIONSCC CALCULATES THE C.D.F.'S FOR BOTH THE EMPIRICAL ANDC THE THEORETICAL DISTRIBUTIONS AND DETERMINES THEC ABSOLUTE DIFFERENCE BETWEEN THE TWO C.D.F.'S FOR USEC IN THE KOLMOGOROV-SMIRNOV GOOONES OF FIT TESTCC PLOTS THE C.D.F.'S OF THE EMPIRICAL AND THEORETICALC DISTRIBUTIONS ON THE SAME GRAPHCC CALCULATES CHI-SQUARE STATISTICC PRINTS A TABLE OF THE CHI-SQUARE CALCULATION RESULTSC
REAL X(450),Y(450,4) ,Z(450)REAL YY(450) ,XR(450)REAL FREQ(IOO) ,RANGE( 100)REAL FREQ1 (20) , R ANGE1 ( 20 ) , T ITL E ( 20
)
REAL P(100),E(100) ,XX( 100,3)REAL INC, LAMESTINTEGER TYDIST,RSINTEGER DPS,PPS,HPS,LPS,KPS,CPS,CSPS
CC DEFINE: NUMTIM— NR OF SETS OF DATA TO BE ANALYZEDCCC DEFINE: TYPE OF THEORETICAL DISTRIBUTION TO BE USEDC TO FIT DATACC TYDIST— FOR EXPONENTIAL DIST SET TYDIST=0C FOR HYPEREXPONENTIAL DIST SET TYDIST=1CC DEFINE: RIGHT SHIFT OPTIONCC RS—REGULAR OR RIGHT SHIFTED DIST WITH DEFINEDC VALUE FOR AA, I.E., REGULAR DIST AA=0.0C SET RS=0 OR READ SPECIFIED VALUE FOR AA BELOWC RIGHT SHIFT SET RS=1 THEN AA=MIN ORDER STATC
READ(5,1001)NUMTIM,TYDIST,RS1001 F0RMAT(3I5)
CC DEFINE: INI NR OF INTERVALS USED IN (FIRST) HISTOGRAMC AND FOR INITIAL CHI-SQUARE CALCULATIONC (MAX=20)C IN IN IS THE TOTAL NR OF INTERVALS (MAX=40)C TO BE USEDC IF IN GT 20 THIS PROVIDES TWO HISTOGRAMSC IF ONLY CNE HISTOGRAM DESIRED SET IN=IN1
123
C INCD— INCREMENT DETERM INATOR . USED TO CONTROLC THE WIDTH OE EACH HISTOGRAM AND CHI-SQUAREC INTERVAL, I.E., I NC= (B-A) / I NICDC A,B LOW AND HIGH RANGES OF HISTOGRAM(S)C INCS— IF GT 40 INTERVALS ARE DESIRED FORC CHI-SQUAPE CALCULATION INDICATE NUMBERC DESIRED (MAX=100).C IF INCS NOT DEFINED SET INCS=0C INCSD-INCREMENT DETERMINATOR FOR CHI-SQUAREC INTERVAL WIDTH. NOTE: MUST BE DEFINED WHENC INCS, C, AND D ARE DEFINED.C CD LOW AND hIGH RANGES FOR CHI-SQUAREC INTERVALS GT 40C IF INCS NE THEN C AND D MUST BE DEFINEDCC READ STATEMENTS 1101 AND 1201 CAN BE MOVED INSIDE OFC 9999 DO LOOP TO ALLOW CONTROL CHANGES ON INDIVIDUAL DATAC DECKSC
READ(5,1101)IN1,IN,INCD,A,B,INCS,INCSD,C,D1101 FORM AT (3 1 5, 2F 1 0.2, 21 5, 2F 10. 2)
CC DEFINE: PRINT SUPPRESSION OPTION. IF PRINTOUT OFC INDICATED INFORMATION IS DESIRED SET=0, IF NOTC DESIRED SET=1.CC DPS
—
PRINT OF SORTED DATAC PPS
—
PRINT OF DATA PARAMETERSC HPS
—
PRINT OF HISTOGRAM(S)C LSP— PLOT OF LN OF TAIL DIST.C KPS
—
PRINT OF CDF VALUES AND KLOMCGOROV-SMI RNOVC STATISTICC CPS— PLOT OF C.D.F.'SC CSPS-PRINT OF CHI-SQUARE STATISTICC
READ(5,1201)DPS,PPS,HPS,LPS,KPS,CPS,CSPS1201 F0RMAT(7I5)
CC START DO LOOP WHICH PROCESSES EACH SET OF DATAC
DO 9999 L=1,NUMTIMCC READ IN TITLE OF DATA SETC
READ(5,2001)TITLE2001 FORMAT (20A4)
CC DEFINE: SAMPLE SIZE NCC DEFINE: OPTION ALLOWS READING IN MEAN VALUE TO BE USED INC CDF, LN TAIL DIST AND CHI-SQUARE CALCULATIONSC OPTION ALSO ALLOWS SPECIFYING VALUES FOR AAC OR FOR SPECIFYING VALUES FOR PI AND P2 IN HYPER-C EXPONENETIAL DISTRIBUTIONCC RXBAR
—
READ IN MEAN VALUEC AA—OFFSET SPECIFIED FOR EITHER REGULAR (AA=0.0)C DIST OR RIGHT SHIFTED DIST AA=READ IN VALUEC PI, P2— SPECIFY HYPEREXP PARAMETERS NOTE: P2=1-P1C IF NOT USED SET =0C
READ(5,3001)N,RXBAR,AA,P1,P23001 F0RMAT(I5,F10.2,F5.2,2F5.4)
C READ IN DATA SETC
READ(5,4001) (X(I ), 1=1, N)4001 FORMAT(16F5.0)
CC LOAD RANGE VECTORC
INC=(B-A)/INCD
124
RANGE(1)=A+INCDO 1000 1=2, INRANGE CI )=RANGE(I-1)+INC
1000 CONTINUECC LOAD A LARGE NUMBER IN RANGE(IN) SO WHEN PRINTED OUT INC F5.0 FORMAT OR SIMILAR FORMAT IT WILL PRINT AS ***** TOC INDICATE INFINITYC
RANGE( IN)=10000.0CC SORT DATA IN ASCENDING ORDERC
CALL SORT(X,N)CC CALCULATE PARAMETERSC
CALL STATU, N,XBAR,VAR,S)CC AA DEFINES THE OFFSET IS A RIGHT SHIFTED DIST IS USEDC
IF(RS.EQ.O)GO TO 1310AA=X(1
)
1310 LAMEST=1.0/(XBAR-AA)RLAM=0.0IF(RXBAR.EQ.0.0)G0 TO 1610RLAM=1.0/(RXBAR-AA)
1610 IF(TYDIST.EQ.O)GO TO 1710IF(P1.NE.0)G0 TO 1710
CC CALCULATE PI AND P2 PARAMETERS FOR HYPEREXPONENTI AL DISTC IF REQUIREDC
P1=0.5-0.5*SQRT( 1.0-2.0/(VAR/XBAR**2+1.0)
)
P2=1.0-P11710 IF(DPS.EQ.1)G0 TO 1810
CC WRITE SORTED DATA AND PARAMETERSC
WRITE(6,1002)TITLE,i X( I) ,I=1,N)1002 FORMATC 1> ,T10, 'DATA POINTS AND ESTIMATED PARAMETERS'
X* FOR: ,20A4//(10F11.2)
}
1810 IFCPPS.EQ. DGO TO 1910IF(DPS.EQ.1)WRITE(6,2002)TITLE
2002 FORMATt 1' ,T10, ESTIMATED PARAMETERS F0R:',20A4)WRITE(6,2102)XBAR, VAR, S, LAMEST ,N , RXBAR ,RLAM, PI , P2 ,AA
2102 F0RMAT(//T7, , XBAR=',F11.2, ' VAREST= • , F 15 . 2,X' STD.DEV.=' ,F11.2,X' LAMEST=«,F11.7, • SAMPLE SI ZE = ' , I 4/T7, • RXBAR= •
,
XF11.2,' RLAM= f ,F11.7, • P1=',F6.4,' P2=',F6.4,X« AA=',F6.2)
1910 IF(RXBAR.EQ.0.0)G0 TO 2010XBAR=RXBARLAMEST=RLAM
CC ZERO OUT FREQ VECTORC2010 DO 2000 1=1, IN
FREQU ) = 0.02000 CONTINUE
CC DETERMINE FREQ OF DATA IN INTERVALS FOR HISTOGRAM ANDC CHI-SQUARE CALCULATIONC
Nl = IN-2'DO 3000 J=1,NIF(X(J).LE.RANGE(1))FREQ(1)=FREQ(1)+1IF(X(J).GT.RANGE(IN-1))FREQ(IN)=FREQ(IN)+1DO 3100 1=1, NlIF(X( J) .GT.RANGEd ).AND.X( J) .LE.RANGE( 1 + 1) )
XFREQ(I+1) = FREQ( I+D+l3100 CONTINUE
125
3000 CONTINUEIF(HPS.EQ.1)G0 TO 3900
CC PRINT OUT FIRST HISTOGRAMC
CALL HISTOdNl,FREQ, RANGE, TITLE)CC DETERMINE IF MORE THAN ONE HISTOGRAM IS DESIREDC
IF( IN.EQ.INDGO TO 3900IN2=IN-IN1NSTART=IN1+1DO 3200 J=NSTART,INRANG El (J-IN1)=RANGE(J)FREQH J-IN1)=FREQ( J)
3200 CONTINUECALL H ISTO U N2, F RE QltRANGEl, TITLE)
CC CALCULATE VALUES FOR PLOT OF NATURAL LOG OF THEC RECIPROCAL OF THE TAIL DISTRIBUTIONCC CALCULATE LN OF TAIL DIST FOR EMP DIST PUT IN Y(I,1)C CALCULATE EXPONENTIAL F(X) AND PUT IN Yd, 2)C CALCULATE STRAIGHT LINE BENCHMARK FOR GRAPH PUT IN Y(I,3)C NOTE: CALCULATION OF THE STRAIGHT LINE IS NECESSARY ONLYC WHEN TESTING A THEOR. DISTRIBUTION OTHER THAN THE FXPC CALCULATE LN OF TAIL DIST FOR THEOR DIST PUT IN Yd, 4)C CALCULATION MADE FOR N-l DATA PTS TO AVOID TAKING LNIO)C3900 NS=N-1
ARG1=NIF(TYDIST.EQ.1)G0 TO 4010DO 4000 1=1, NSARG2=N-IARG=ARG1/ARG2Y( I,
1
J=ALOG(ARG)Y( I,2)=1.0-EXP(-(LAMEST*(X(I )-AA)) )
Y( I,3)=(X(I)-AA)/XBARY( I ,4) =AL0G(1.0/(1.0-Y(I,2) ) )
4000 CONTINUECC INCLUDE LAST DATA POINT IN THEOR CDF FOR CDF PLOT BELOWC
Y( N, 2 ) = 1.0-EXP(-( LAMEST* (X(N)-AA) J )
GO TO 41104010 DO 4050 1=1, NS
ARG2=N-IARG=ARG1/ARG2Yd, 1)=AL0G(ARG)Y( I,2)=P1*(1.0-EXP(-2.0*P1*LAMEST*(X(I )-AA) ) ) +
XP2*( 1.0-EXP(-2.0*P2*LAMEST*(X(I )-AA) ))Y( I,3)=(X(
I
)-AA)/XBARY(I,4)=AL0G(1.0/(1.0-Y(I,2) ))
4050 CONTINUECC INCLUDE LAST DATA POINT IN THEOR CDF FOR CDF PLOT BELOWC
Y(N,2)=Pl*d.0-EXP (-2.0*P1*LAMEST*(X(I )-AA) ) ) +XP2*(1.0-EXP(-2.0*P2*LAMEST*(X( I )-AA) ))
CC PLOT LN OF TAIL DISTC4110 IF(LPS.EQ.1)G0 TO 5110
WRITE(6,1102)TITLE1102 FORMAT {• i« ,T10, PLOT OF LN ( 1 .0/ 1 .0-F ( X ) ) FOR: ',
X20A4//)DO 4100 1=1, NSYY( I)=Y(I,3)
4100 CONTINUECALL PL0TP(X,YY,NS,1)DO 4200 1=1, NSYY( I )=Y(I ,1)
126
4200 CONTINUECALL PL0TP(X,YY,NS,2)DO 4300 1=1, NSYY( I )=Y( 1,4)
4300 CONTINUECALL PL0TP(X,YY,NS,3)
CC CALCULATION OF THE EMPIRICAL C.D.F. AND THE STATISTICSC FOR THE KOLMOGOROV-SMIRNOV TESTC WRITE C.D.F. VALUES AND THE K-S STATISTICSC
DEM = NDO 5000 1=1,
N
Y( I,1)=I/DEMZ( I)=A3S( YU ,1)-Y( 1,2)
)
5000 CONTINUE5110 IF(KPS.EQ.1)G0 TO 6110
WRITE(6, 3002)TITLE3002 FORMAT (• 1» ,T10, C.D.F. VALUES AND KOLMOGOROV-SMIRNOV '
X'STATISTIC FOR: ' //T10 , 20A4//T13
,
«X« ,T20, «EMP DIST «
X'EST DIST K-S STAT'/)DO 6000 1=1,
N
WRITEC 6,4002 )X( I ) , (Y( I ,J) ,J = 1,2) ,Z(I
)
4002 F0RMAT(T9,F7.2,T20,F8.4,2F11.4)6000 CONTINUE6110 IFtCPS.EQ.UGO TO 9110
CC GRAPH THE EMP AND THEORETICAL C.D.F.SC
WRITE(6,4202)TITLE4202 FORMAT!' 1' ,T10, ' EMPIRICALU ) AND THEORET IC AL ( + ) CDF •
X'FOR: « ,20A4//)C ADD 0.0 IN X AMD YY VECTORS SUCH THAT THE CDF PLOT WILLC AUTOSCALE FROM 0.0
N2=N+1XR(1 )=0.0YY(1)=0.0DO 7000 1=2, N2XR( I )=X( 1-1)YY(I )=Y( 1-1,1)
7000 CONTINUECALL PL0TP(XR,YY,N2, 1)DO 8000 1=2, N2YY(I )=Y( 1-1,2)
8000 CONTINUECALL PL0TP(XR,YY,N2,3)
C9110 IF(CSPS.EQ.1)G0 TO 9999
CC REDEFINE AND RELOAD RANGE AND FREQ VECTORS FOR CHI-SQUAREC CALCULATION. IF INCS=0 THEN BYPASS ROUTINEC
IF( INCS.EQ.O)GO TO 0099CC STORE VALUE OF IN FOR NEXT DECK OF DATA TO BE PROCESSEDC
TEMPIN=ININ=INCS
CC LOAD RANGE VECTORC
INC=(D-C)/INCSDRANGE( 1)=C+INCDO 9000 1=2, INRANGE( I )=RANGE( I-D + INC
9000 CONTINUECC LOAD A LARGE NUMBER IN RANGE(IN) SO WHEN PRINTED OUT INC F5.0 FORMAT OR SIMILAR FORMAT IT WILL PRINT AS ***** TOC INDICATE INFINITYC
RANGEt IN) = 10000.0
127
cC ZERO OUT FREQ VECTORC
DO 9100 1=1, INFREQU )=0.0
9100 CONTINUECC DETERMINE FREQ OF DATA IN INTERVALS FOR CHI-SQUAREC CALCULATIONC
Nl-IN-2DO 9200 J=1,NIF(X(J).LE.RANGE(1 ) ) FREQ( 1 ) =FREQ ( 1 ) + l
IF(X(J) .GT.RANGE( IN-1) )FREQ{ IN )=FREQ ( I N ) +1DO 9300 1=1, NlIF(X( Ji.GT.RANGE (I ).AND.X( J) .LE. RANGE ( 1+1)
)
XFREQ(I+1)=FREQ( 1+1 )+l9300 CONTINUE9200 CONTINUE
CC CALCULATE CHI-SQUARE STATISTICCC ZERO OUT XX(I,J),P( I) ,E( I)C0099 DO 0100 1=1, IN
pm=o.oE( I) =0.0DO 0110 J=l,3XX( I ,J)=0.0
0110 CONTINUE0100 CONTINUE
CC LOAD INTERVAL BOUNDARI ES ( RANGES ) AND FREQS IN XX ARRAYC SUBJECT OT E(I).GT.5.0.C ALSO CALCULATE P(I) AND E(I).CcC CALCULATIONS FOR EXPONENTIAL DISTRIBUTIONC
IF(TYDIST.EQ.1)G0 TO 0111M=lXX(1,1 )=AADO 0200 1 = 1, INTEMP=0.0DO 0300 J=M,INTEMP=TEMP+FREQ( J)XX(I ,2)=RANGE( J
)
IF( J.EQ. IN)GO TO 0320XX(I+1»1)=XX(I 2
)
P{ I) =EXP(- (LAMEST* (XX ( 1,1 )-A4) ) )-EXP(-( LAMEST*X(XX( I,2)-AA) ))E( I)=N*P(I
)
IFIE ( I ).GE.5.0)G0 TO 03100300 CONTINUE0310 XX(I,3)=TEMP
M=J+10200 CONTINUE
CC FOR LAST INTERVAL TEST IF EUJ.LT.5.0, IF SO STORE INC PREVIOUS INTERVAL AND RECALCULATE E(I-l)C0320 P(I)=EXP(-(LAMEST*(XX( I,1)-AA) )
)
E( I)=N*P(I
)
IF(E(I).GE.5.0)G0 TO 0330XX(I-1 ,3)=XX( I-1,3)+TEMPXX( I-1,2)=RANGE( IN)XX( I ,1 )=0.0XX( I ,2)=0.0XX( I ,3)=0.0P( I-1)=EXP(-(LAMEST*(XX( 1-1,1)- A A) ) )
E( I-1)=N*P(I-1)P( I) = 0.0
128
E(I)=0.0GO TO 0400
0330 XX( I ,3)=TEMPGO TO 0400
CC CALCULATIONS FOR HYPEREXPONENT I AL DISTRIBUTIONC0111 M=l
XX(1,1)=AADO 0201 1=1, INTEMP=0.0DO 0301 J=M,INTEMP=TEMP+FREQ( J
)
XX(I ,2)=RANGE(J)IF( J.EQ.IN)GO TO 0321XX(I+l«L)«XX(If2)P( I )=P1*(EXP(-2.0*P1*LAMEST*(XX( I, D-AA) J-EXP (-2 . 0*P 1*XLAMEST*(XXU ,2)-AA) ) ) + P2* ( E XP (-2 .0*P2*LAMEST*X(XX( I, D-AA) )-EXP(-2.0*P2*LAMEST*(XX(I f 2)-AA) )
)
E( I)=N*P(I)IF(E(I ).GE.5.0)GO TO 0311
0301 CONTINUE0311 XX( I ,3)=TEMP
M = J+10201 CONTINUE
CC FOR LAST INTERVAL TEST IF EUJ.LT.5.0, IF SO STORE INC PREVIOUS INTERVAL AND RECALCULATE E(I-l)C0321 P( I )=P1*EXP(-2.0*P1*LAMEST*(XX(I , D-AA J ) +P2*EXP (-2.0*
XP2*LAMEST*(XX( I, D-AA) )
Ell) =N*P(I
)
IF(E( I ).GE.5.0)GO TO 0331XXU-1 ,3)=XX(I-1,3)+TEMPXX(I-1 ,2)=RANGE( IN)XX(I, 1)=0.0XX(I,2)=0.0XX(I ,3)=0.0P( I-U = P1*EXP(-2.0*P1*LAMEST*(XX(I-1,D-AA) ) + P2*
XEXP(-2.0*P2*LAMEST*(XX( 1-1,1 )-AA))E(I-1)=N*P(I-UP(D=0.0E( I)=0.0GO TO 0400
0331 XX(I,3)=TEMPCC CALCULATE TOTALS OF P(I), E(I) AND XX(I,3)C0400 XSUM=0.0
PSUM=0.0ESUM=0.0DO 0500 1=1, INXSUM=XSUM+XX(I ,3)PSUM=PSUM+P( I
)
ESUM=ESUM+E( I
)
0500 CONTINUECC TEST TO FIND THE NUMBER OF INTERVALS IN XX(I,J) THAT AREC IN ORDER TO DETERMINE THE NUMBER OF DEGRESS OF FREEDOMC
DO 0600 1=1, INIF(XX( I ,2) .EQ.O.O)GO TO 0610
0600 CONTINUE0610 N I NT = 1-1
NDF=NINT-2CC CALCULATE THE CHI-SQUARE STATISTICC
CHISUM=0.0DO 0700 I=1,NINTCHISUM =CHISUM+( ( XX ( I , 3 )-E ( I ) )**2)/E( I)
0700 CONTINUE
129
cC WRITE THE CHI-SQUARE TEST RESULTSC
WRITE(6,0502)TITLE0502 FORMAT (• 1« ,T10, 'CHI-SQUARE TEST RESULTS F0R:',20A4//
XT10, 'INTERVALS' ,T2 7, 'FREQ' ,T45,
•
INTERVAL' ,T65,'EST OF'X/T8, 'LOW ,T17t 'HIGH' ,T27,' COUNT' ,T47,'PR0B» ,T60 T
X'NO. IN INTERVAL' )
DO 0800 I=1,NINTWRITE(6,0602)XX( I, 1) ,XX( 1,2) ,XX( 1,3) ,P( I ) ,E( I
)
06 02 F0RMAT(F10.2,4X,F6.2,F10.0,F21 -4,F20.2)0800 CONTINUE
WRITE(6,0702)XSUM,PSUM,ESUM,NINT,NDF,CHISUM,XBAR,XLAMEST
0702 FORMAT (T6, 'TOTALS' ,T21,F10.0,F21.4,F20.2//T10,X'NO. OF INTERVALS=' , I4//T10, 'DEGREES OF FREEDOM= , I 4//XT10, 'CHI-SQUARE ST ATI STI C=« , Fl 0. 2/ /T10 , EST OF MEAN=',XF10.2//T10,'LAMEST=« ,F10.4)IF(INCS.EQ.O)GO TO 9999IN=TEMPIN
9999 CONTINUESTOPEND
SUBROUTINE SORTIA,N)DIMENSION AIN)NPASS=Nt-1DO 1000 I=1,NPASSNSTOP=N-IDO 1000 J=1,NST0PIFIAl J).LE.A(J+1))G0 TO 1000TEMP =AU)A(J)=A(J+1)A( J+1)=TEMP
1000 CONTINUERETURNEND
SUBROUTINE STAT I X, N, XBAR, V AR, S
)
REAL X(N)SUM=0.0DO 1 1=1,
N
1 SUM=SUM+X(I)XBAR=SUM/NVAR=0.0DO 2 I=1,N
2 VAR=VAR+(X(I )-XBAR)**2VAR=VAR/IN-1)S=SQRT (VAR)RETURNEND
SUBROUTINE HISTOI I N, FREQ ,R ANGE ,
T
ITLE )
DIMENSION FREQ (20) , RANGE (20) , J OUT (20)
,
TITLE (20)DATA NUTH/' •/,«/****•/WRITE (6,4) TITLE
4 FORMAT( • 1* ,///,8X,20A4//)JN=ININT =IF(JN.GT.O) GO TO 10INT=1JN=-JN
10 DO 12 1=1, JN12 JOUT(
I
)=FREQ(I )
WRITE (6,5) (JOUTI I) ,1=1, JN)5 FORMAT( 'OFREQUENCY' ,2016)
WRITE (6,7)7 FCRF,AT( • -« ,128( '-'
) )
C FIND LARGEST FREQUENCY
130
FMAX=0.DO 20 I=1,JNIF(FREQU).GT.FMAX) FMAX=FREQ(IJ
20 CONTINUESCALEJSCAL=1IF(FMAX.GT.60.) JSCAL= ( FMAX+59 . )/60.FSCAL=JSCALDO 50 1=1, JN
50 JOUT( I )=NOTHMAX=FMAX/FSCALDO 80 1=1, MAXX=MAX-( 1-1)DO 70 J=1,JN
• IF(FREQ(J)/FSCAL.GE.X) JOUT(J)=K70 CONTINUE
IX=X*FSCAL80 WRITE (6,2) IX , ( JOUT ( J ) , J= 1 , JN
)
2 FORMATt I6,4X,20(2X,A4)
)
WRITE (6,7)IF( INT.EQ.l) GO TO 16WRITE (6,3) (RANGE(J) ,J=1, JN)
3 FORMAT ( 'OINTERVAL' , 2X, 19 ( F 5. 1 , IX ) , F5 . 1//
)
GO TO 1516 DO 51 1=1, JN51 JOUT( I )=RANGE( I
)
WRITE (6,6) (JOUT( I ) ,I=1,JN)6 FORMAT
(
'OINTERVAL' , 2X , 19 ( I 5 , IX) , 15//
)
15 WRITE (6,1) K,JSCAL1 FORMATt 'OEACH , A4 ,
' EQUALS ',12,' POINTS'/)RETURNEND
131
oooooooooooooooooooooooooooooooooooooooooooooooo•-* c\j rn -4"m vO r*- cooo i-h r\i co -^ ir\ o f- co cr>o <-* cm r*> >J" lo vO I
s- co cr*o 1-1 c\i ro «4-^ >o P- °ooo —* cvjro^tLn^or^-coOOOOOOOOOi-h,-4.-^.-h,-i.-i,-^,—i.-Hr^pu<Nj<\j(\jr\jrMC\j^<Njr^OOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOO.CLfXa.CLQ.CLa.Q.Q.Q.Q.a.QLC^Q-aCLQ-CLQ.ac^Cl.Q-n.CLC^CL(^Q.£XaCLC^CLC^DDOOOOOQCCOOODCOQCOOCOOOODOOacOOOOOOOOOQOOCGOOOO_U_J_J_J_J_J_i_i_J_J_J_l_J_j_J_J_j_)_J_l_J_J_j-J_J_i_i_J_i-J_J_J_J_J>J_J_j_J_J_J_J_l_J-J_J_j_JO.CLO-QuQ.Q_CLlXQ.CLCLQLCLCLQ.CLa.CL^CLCi.CLQ.Q.CXQ.Q.a-Q.CLCLQ-O.CLCLC^a.(Xa-Q-a.Q.C^
c£ooo •
zluqs: 1 O
ULh- 3C 3 X IJD 25 •-H-J
z o O Q- 3DS I- XQ.00*—" -I -J < •—o»—
'
<3q; UJ UJ Qi IK 00 SOOQ- CO CO O 00too. UJ 1—-J K O 00 • LU-JO l-l C\J 00 Za: 000 xo<Z 1—
1
t-HLULLI cc KUJ< Q o X Ooo a: ClO -J
a. O o f- O.DO hh LU_JhO X X X 00 00 Z<oz 1- 1- ZQ- LLUJZ _J< mU-J«-H UJ UJ o< OH—' CLU. 2:0.—I s 2: CC 1— a:Z< X ooo \- O »-UJ LULU•o o o CL UJ UJ «»l— Z_l l-X
oi oo z z < >00 • oox < UJ»—UJ —
»
l-H >—
1
cc cc<~>zl O.UJ hOhU • >*• 00 00 oxoxo. h-<> Zoo 00Z-<X * 3 3 CH_)H-< 000:0: LU Qhi-ih-CL -J uj< a: a:oo s:uj h-a:<< < UJ UJ ZQiUJZO •-* DI- K0.2: a: UJ z z OOoiO LLLU CK OOQoo cc o o CD 00 >f- CC—* >-_)\-\— w o o Zo0 5ZLU<-h U-'QiOO <a: <CL33UJ a~ >x XOUJ a. a:i-Q-<X 00 OO 00 xarctH- hUO u_a a:ot- K UJ 1—4 l-H oOh-OO a: 00 <3a: «—
•
H- LU oz ZUJ< CCOOIL >J- < o o >zo o 0_l_l ZQ. > •
o * Z z z orosuj a. 00- 00QO _l —
i
K—!.#—1. >-H Z3 Kf-UJ >->—UJ H< OUJf^Zl < Q -JO _J OUJ <> Jhl h- zo<hO . UJ a: <z < >U_»-HCr: Z_lh- O-UJ <_lO-JI— a: o o>-< o U.CCOQD 03 >-iX <2<H >— 00 OO-J 00 OO UJO SIX ccy- x><uo —
»
o CC < <J>h-^l 1-H-OOCQ a: UJ UJ t-H o t-—
.
cc ooctrt— UJ<»-H 000 LU5TI/) 3 < H < UJOO ujO LLI.-HQ^UJOO s: 3: ujZ xo
aruj o 00 oo < Q. > >z CD •—h|— «cr Z£.Ct Q-H 1—2:LULLlX a h- 00 t-H mQ MtH z:>-u-z_i oo>- z »-H
x>t- o z MH o «"* H-UJ I--J o_i - U_U__J UJ>-4 00^;HO 51 UJ o o > •—•_) << Z2UJ UJ CX -J 12 Zh •
(- •» 2: 00 OO •» 00 _) oo oxzx UJ—.< Ka: <2IXZ-J< z 3 CO OO X OO UJOO UJ h-<K Q. «»-H LU O Q.oo •M O < < -— clo: z Xoo Mh Zh- 00O<
a: oo >- ar h- o (—•-ioooooo OO >-H hhLU ~Z.CCQ. oot-a: UJ •» < LL u_ LL OOZ 00 1—
1
t—II—!—
4
mq:z O o.<o\- IZO O X o o o MO l-H(- OOLU Oh O h-o Q-Ot- 2 — UL O < —la: oo oo oo uja: 02UJ_J <uo UJ Q. o a: cc CC z zz QUJMMM ZOO. 1-0 JDIa. a: < o h- o o UJ a£ o arxxxx »-H h- OLL 0.2:1—
Oa:u_ o o z 1— t- CO Zuj Zh- t-H-h-h-H- _l II • zUJ LU UJ _l o o u 2 UJOO u_0 z < _lO 00Z OOOOUJ OO o. 1—
1
UJ UJ 3 ID x< OHi\j(n OQiCLZ 000 • •
t-H l-O-J (- > > Z 3— s— O II II II II 000 *-* <o T-i
H- HI Z < o _J O. O-J—
1
X3 OO »-<ci;o 2 _j 1—4 a z o_j< h-O O alU-lOO HH < cc o t-H o<o UJcc o. ax _J o o o -J 2:000 2: XCD CC h-LU _J 00 o < h-3 3 MI < UJ o UJ00 Q. UJh- o o X >- Z 2: 00 2:
000000000000000000000000000000000000000000000000
132
oooooooooooooooooooooooooooooooooooooooooooooooo^inLOLOLOLninLOu^LOir\voo»ooo^<)^vO<)r^^t^r^i^r^^r^r^f^cocococ»ooooooooooooooooooooooooooooooooooooooooooooooooG-Q.C^a.(^CLC^Q.a.CLQ.a.O.(XaQ.aa.CL(^CLa.(^(XC^Q.Q.a.Q.aQ-I^CLQ.CL(XCLQ.CLCLQ.Q_a.Q^OO0OOCOQCacCOO0CCDQD0CO0OCC3OO0OCC0OO00C00ODOG0O-JJJJJJJJ-I-1 1 I I I l_J » I I I I ( ( —
I
) t 1 —
I
I I I —
)
I —i_J_i—l_J_J_i—1_»—I—I—I l_J_)CLQ.CLCi.<^a-<xa.a-CLCLCLQ_CLO.a.a_a.a.aa-0-c^c^a.cLCLa.cLCLQ.Q_Q-acL
ooOLU U_XZ \-C£ I O
<O0 OLU I
ILXoO ZOcOOLU -JOh-LU CvIS'-' <-J •_)
_)Z OLLLU CLvO<\S)OC UJOQ OOOm OLUUJoOXZ h-Zt-h-U.Dh->-.t-.-<ozuj Joa<ujs:(/)i-'Doiu02:ili>ar3'—<Z—'U-Z JQos: i-o ll ll.<< a_ lu
Z •— 512 1—1>-< CC — 00 •
DWXDGciZQ i^h-DIZm<zo o uj«_j a.1-1 Zm oOmLUX Z5Z<ZZ XUJmOOXI— hSOJQl-OU-KD t— *-• IOzzxz_jzc\j • <t-
>—i— <D wz LUOZ UJ>5IcD'-Z3ZooUJXZ»-"ULX "-"Z ZO— C£t-<ZHhh-ZHHlMM <
t/)«ZOZhl- OOSZLUO • LUZ —•—>-*
o
m 00 H-dizoi <xzuj 2:0zh-<cc:olui—2 cc »o_i>—
•
LU>—<XZ LU —1Z 21 Q-Xli NlhODIDQw<>-'0 olui— 1 h-.zx5: QCOh-Q H- XH-hU
• LU(—XZOJDO urnUJm rvl LU< D 0-Z LU LU XX h-Z JZ<I^Q3h-OOLU 00<0 H—ZOh- oOu_lLU>OZ 0<(—
oOX ID DZ I OLU |_ h- to |_o 1—^S—>S _lZLULUm t-H/)LUi-( DQ.—ZOO OLLLUXX •"LU^h-2: H-l- 3H-<_IImDo^z^m t—o z«-<i—
x
uj»-it-< a.z_ioo 1— <lu»- OD< wLUZZZZluoo»— a: 01— xo— "-Q<>-'LUQ'-«XLUI— OH-
MLULLLUO OOLUDQ->- »• OwZZZLUZQOh- ozzz <lui— <zq:ODa:oouja:Luoo DeoJZOIIO-I 2D ODa.<N(-a;(/)H<K-5vj-a:oo
• •
C\J
QoXKLU
^^<^U^U^U^^UU<J>U^L^LJ(J><^i^UU{J>U^UU^L^UU^U^^^^U^U^UU<^U^<J)U
LU 1 < 00 -JX H-4 •> LU_J Oh- LL X LUZ s o>-< ZO
Z O < CDw # <2 <a:CDZ > 2: = 00LU_J <>—<m CD 00 _IO 0£IQ-> 1-0H- • •1— LU _JLU r LUt— LULU OZOZ z OOZ X hH + 1- a:x o_<LUO 2: LULU h- 2Z r kjz h- t->-a:*-' X) DZ >—
<
•-<»-<LU 000—>\— _l -JLU »«u_ >-a: r or > »•
Dm <CC 000 LUO. •<OaiO LU1 00 >o LU X r XLUOLU LUXxo z Doo KLU OUOh- coi—a. o»« iam -Jl- CD • < 1-
LU co> <z «» 1/>UJ_J20 KZXI- -J LUI- >LU oo_j LUXQ-LU_J aoKZ ZOO CD< 2: K- -J >h- za zM <D [s-LU K-M QC LUZo; • X -JLU cc 02 OQCD LULU -JLUMao Ol- -J>- LUO ft OLU XC£ -Jt-
v0 1— -h< CDZ >- h-OI-< MZZIS zo 2m —
t
OLU OKh 2moo-> t-HLU O • _J • zx ZO -00 a:«<rz —J LULU 21 -11-2: <>- t-i_)00o0LU t-Q.h-LU'-' l-_J aisro m<3 t-Q.i-i|-> •
m 2: ~<LU woes 2 2! •LU t— 000:00 -JLU00O>- U-CO XLUM ujm MOO OLULUmX)- a. co
oz 1 < l-l-Z LUI—Z M4 _iar>Xi_)rQ_<X UJJ z— C£<.t-< Z2 Q.< CC lu s;- <_i
< CO ^»—*y lum-s: LUC£ O -JZ -j1- «Z LU —
«
xo LULU q£ooolu< •(-H
zo> _IC0 LUfOLU H- LULU 2X OLU >OLL 002H-lCO'— -J 00 X ZI »-»- U_>2Ct>-"0 LUQCV. >-l_l hOK ^ccy- LUO OiLUDDI— OoOCl-»0 2_j 2Z LULU cc ODZOZO ZLUzi- >—
1
1 <2T 00 1- 2: 9- LUO LULU <oX"H OS Z O m^O LUI— 00 <OOoO l-<UZJ LU 2! -CL 2-*a: ZD< Z)4- -ImO 0000<x< XO D2ILL 1 u. JZ U-O Gl ZOOlu 1 d CL>-t _ID 2LT\ <c£ UJZ" rOZ OLUxo <a: OZ • • >o aC<. Z O OZ•»<riu oTO O'-'N^ C£OvO LL <X <LLO cCQZ O ^Z"^ ^Zv. < !—••--< mOOXLU LU •-M^ <^ c\J OO >-LU LU OZX—LU LUX zz« z -* LU • qc:lu_jq: ••> —
(
t- CDh- O M O »-r^ >rH uja:Oujoooi Z2LUO—I Mill*- mSw <M h-aujxxo MO2H- -J O • KXLU h-DLU XLL • uzi-2iu <-J
t—
(
H-O UhO uzo K < < t- K_la:_i2 >—
<
LU z UJmZ 00Z< OTZLUO LU a:CLU< <a: Qi •< q:z< -l<Z <LUQ_t-< «Z LUU-IDZ O h-O ^2:0: —it—\CC lu aL XXLUQiLUOl-OO z < 00 1 OZ 1 CDZO o2a:oz LU— Li — >—* 02 z«~> —
.
<mU_ 000 C£XLU t— _i O Xmcnj >-LUNt _l a£ »QO < LU1-LUO j LUQC X— X— om OS UJZQ O
ZCOLU LU X OJ<LU LUI— LU LULU • OXoOt-"_jai zu_i-t C£. CO f-O IZO X Xh-O UL= DhO< 00 OO_Jm < >0 t- z l_ »-2 hZH z 1— LU LU-JO _J LU< z< >—<LU l-H QLUOLUQ. O LU~ 1 > Zla: ZDa: LLOTQ. K- za:jia < z2> a
a:
CD —<(.— >»• Ms:— >—<CLi—
1
O_)Q.
<<Q->—< 00 OOOLU2:
133
ooooooooooooooooooooooof«- oo (X>O «~i cm ro 4"m <£> h- oo cr«o r-i c\j ro <hmo r- co cf>
CM^O^OOOOOOOOOOH^HrlHrH^rHHHcXQ.c^cvc^a-Q.Q-Ci.a.Q-CLa-Q.Q.a.a.a.Q.D.Q.Q.a.ODOCOOOOOOOOOQOOOOaOOCO
oooooooooooooooooooooooOr-tcMrO^Ln^O^-ooO^O—«c\icri>j-ir\sOf>-coc^o-Hc\j
CVQ.CLQ.Q.Q.CLQ-CLQ.CLQ.QLCLQ.Q.CLa.Q.Q-CLQ.Q.oooooaooaoooDOOoGooooooCLQ.Q.Q.OuCL(XQ.CLCLQ.CLCLQ.Ci-a.Q.O.Q-a.Q.Q.Q. 0.0.0-0.0-0.0.0.0-0.0.0-0.0-0.0-0.0.0.0.0.0.0.
o
o>-
' 2 OL1—
1
Oz z•—
1
-Js o —i
z t-UJ < z
IDX X< < 1-Z z O
-JSC ^ Q.
o oUJ UJ
X I oo O z
O -l
cc C* CCo o oI- h- oO O_J _l H-a. Q. 00
<Q. CL -J
• 3 3H H h- c£O LU LU 3_J 00 00 OD. Q
H 1- OUJ a o 2:X zr zrK z • z • z
<r-i <^ UJU- o u Xo a: a: 3:r
•O •O •
UJ o o a. a.o II o II o 33< 00 II 00 II H-I--J LUC£ LUOi LULLI
a. 3D 33 0000-JO -JO
z <o <o l->-•—
1
>o >o O-J» Z z za:
H >- X LU3 Z z DO.Q. -JUJ _)UJ >—oK Jl JZ cCcC3 <s <3: OO.O £ s r UJ
UJOUJ<tcc-HOQiU.c£uj<coo> •
o:uj<0oo<oo o.UJoujUJX
xua ohou-ZXl-O—3C _J
UJ2T_JhIO<Zhl-OUJ h-zi-oacuj<coujh- I-<OUJU_KUJX<00 h- l-
HOhlZ-J<0t—id. •—
<
a: OctUJZQ.UJUJxo coi-i-I- < zz> _Jh-.LU
Oa:i—<uj>Q.OOCCQCO-CL
OXl-CL<
OctUJO\-OUJujxO-KXujujo
00<•—-J
CLCCUJO001-3
00UJ_Jxo\-cC
uj-Jars:O^-iCLUJ003 i-OO UJ<MTHlh-
O. 00CX.-Z._ja:<i—jOuZo ~xujujcc:00X-JO.
h-i—cc •-.<LUf— I—
oo<r o3X<ZI— »-h
UJ ••!)
XOUjoOI— OOcOoO •
<>—'LUQ_uja. ZI—O >-*-*
0<l— COK-JQ.X 3a. ujio<za.a:
O <coZOOUJQiZ)
JOH_IUJ UJUJ<->u_xxOlLIDhH
X<
m
oz<
<\J oo
o >—
<
— z 1-~< <<rcc k
a:—
—
3duj 0loo •> 51DZ« Oo<x Oz<*:<- z— UJ vO r- CO i-H
z -xz in _Ji7*—» »•—
<
< O•.-<~.z O }- f- h- h-
>- -•>- H O0*•—'*—' •* O OX>UJ~» O CC O O— o>fr OO- »-Z«— IL »-* .-» -^i —
»
1— -»<LU ^^ X z X zO^cto 1—
t
z < 1—
1
< 1—
1
_l —z • ^-t z z z zCuw < 1- s: X X >- >-Xujo: —O O O z • • • •
LU 0^- Z • o3 CMOtNJO^I- 1— I— h-zzz Za: UJOsJUJOvJ «•_!•—0-— _J-^O-*mOUJ —3 X • UJ • UJ t—1 •>—1 •—1 •>—* •—
1
l-»-"_l 00O < r-l »r-4 •
3oo< COO S 1 -^ 1r-K 1—41—1.X—t x»-<>^.>oz> <o II II II II
—II*-
II — II *- II
QiUJf-H m£ O XZXZHXXX z>-x>-zCO2:3 II
— z <•-<< 1—
<
=t<— —<— <i«^i—
1
3^-0 Zli t—
«
21.2:2: 2:ou_2-u-2:u_2:u.sooouj *:-< LL XX>>0—<X-h.<M>M>
o CO
ooooooooooooooooooooooo Ui^U
134
oooooooooooooooooooooooooooofO>tinvO's-oo<>o^^(Nrf^vtLnsor*'Coc^O'-<(NirOv}-invoiN-ooaN
oooooooooooooooooor»-r~^r^r^r»-r>-f^r^coa3coooaocococooo
CLCLO.CLa.Q.QLQ.CLQ.Q-Q.CLQ.Q-Q.Q.CLQ.Q.CLQ-Q.Q-CLCLCLQ.oooooooQcocooooaoocooooooaoo Q-C3LQ.CLO.CLCl-a.Q-Q.aQ.CL a. O.CLCLCLOOOOOOOOOODOOOOOOOQ.aaaaaa.aaaaaaQ.Q.aaaQ.aaao.a.Q.aaa Q.Q.aaQ.a.a.a.aQ.aaQ.aaaaa
co co
22 CO33 O CO2 •—
i
Occ •» » U- i—
i
3 a «• »- LL2 2 »- LU mm o
- -« •—
i
-^LU ^- • • —
1
Oo s: s: <*<* l- OO -^ CO •—
i
-J X > 3 O <-*r-\ > COa o-» _J LULU 1—
1
CMK Q o . Qf\J a »• •• o CM3 2 2 O • m m l-H H
< < 2ZO LU II II •fe CO V--J •»LU > s r 2 LU cO—1 X X i-l • a: *« l_4 I LU< < < •a: 3 z z s: o — 2 -•O s: -^ s: -^ lu:d o X *-* X O 2X vi- >- o oo •» x s: C\J _j s:o »» *» zo K- • • •• X LL LL.
t- 3 2 s 2 <o CO LULU < 1- o H- *LU •—
<
LU H ois: < _J_I s: X X h- X 2o LO 2 s: 2 s: * • -1 << X lu-»s: lu~.s:o X > 2a: • muu _ ZXm o ZZh
o CO •» cO k *:o 2 00>-COCO LU < - o l-H •>
LU 1- X X * • LU OOsO »»1 | _J os:x X 0512
_J LU < LU < >--H X ^v-vcOX>- < h-X< s:— I-Xm< o -J s: _J 2. •• • 3 ——-X- » o •s: MX -s:u o < X < > xo 22 CO s: »x )( < s: »xCO o w o «— wLU CO >—IH-l^^XX a DO- #s 30—o «~» to LU CO LU h- LU SISZOIALO S- • »x s:— •
h- o J _) 1 _l LU o • _J x>-o^-< LU mho oo • • i—if—»Q O3 • X < >- < > —la < 1 1«-« 2 XXZr-lr-IHUJiH 222-th
LU < K O o a_ Q-3 u XX •-><<3 1•«• # o + MM3 1 -K3 o LU CO LU CO 3 ho CO <<s0— h^ZSOXXX »XXrrOSSOZZ
2 1- • 1- a. 1— a u 3Q SS-h 2 30 <(xs:SSXIS *~ <a_s:s:—
t
o 2 3 3 O 1— x>lu< a: OwQ II •-iLULLSLLLL 1—
1
oo ii «— u_h- 2 2 a _i a _j 1— -is: 2 -"-t-s: 3 CC 1HZXJ II II II X II II II h-22_l II II2 — 51 —i 2: _j o _j—' 1—4 ii ii t-.ct: i—o CD>D<JXXX-XSX DmJZZO u_ U_ O < a < _J <LL Q_ cocoa:0 LU2 3-hO s:< s: s: s: ll s: s: s: oo s: < s: s:o 1—1 i—
i
o o o o a. 0>-i a. X>-_£LL. Q.LU—1
oo
cooa:xo»-iLL.X>-«LL-»-iu_oa:xut-<LL
t-l in CO C\J
<J>KH-> ooo oou ooo ouo
135
oooooooooooooooooooooooooooooooooooooooooooooo
,^,^.-irH.-i.-i.-i^.^.-t.-tr\jr\iojr\jr\jc\jrMCNCNjr\j<NC\lcN^
^aa_Q-O-O_0-0_O-Q-CLCLa-O-O-O_O_CLauCLeLa_eLCLCV(iO_a_CL0_CLCia.<XDDOOOOOOCOOGOOnnnnnnnnnnnr innnmnnnnnnnnnnnnni_J_l_J-J-J_i_J_J_i_J_J_J_l-J.Q-QlQ.0lQ.Q.Q-CLO.Q.Q.Q.Q.Q.(
zx2:2:xx•» •*
2:2:0000
zz00i/)i/>
111 11 11zxa: sr<. XX_»
«-»—
»
uu • t
00z • •
< i-i-a: 00
zx.-1 XX• CNJww
f-100 00•-« ar COCOf-H
1- • •
O • DOh- t-l ozzo>O • •
z1- —2:2:0
2!t/)</)l—
ST'" z t/) t •
*->Z 1—
«
•h-h-O#2: 2: UJ_J_JO#x _J • t
• t ^z •_—«.—•OLD t 2: >zxoHO--1 XX -, 2:2: •
* • 1-$-< i QXXI-zzzzs »-»2:x v ,^,0
ST*-! 512 21 2: O(-000 •
U-SLLU- —oox • t>ococo2:
H•
—
1
—
«
LU_J
<. 1— <> LLI—
<
Q • 00<S) 0. • z
t—
1
LU r> l-l
>—
«
II LUUL u. • cC X
X LL zO • 1- •> LL•—
1
LU •
t/0 —I < -^ 0C— Cl UL f* • <tCM X«-H • 2:
l-t- Q Q l-l • 00O O-J z z • aH—{_31- <3 < < H-i LL oOO
u-s: • in -J 1 oxoo—» » l-l • • II ZO 1 Xz o</> • co XX -- II II
tmt 1—It—
1
a- LLX os~zx21 00 LU h-Z—•LLLL f-l »l—<<t
1 -X • LU <1 • wuozs:X •-0 ««« OUJOQ- — »xx< O"—1 • > Oi^Z • tt XLU2: ooxo I—
<
h-^<o •fr<Z—
—
^* X31r-< a —LUX: • • • •s • • •— *• t—
<
>*coi- •!—OO XOOlu2 a:x ^ •k • OC0_JrHr-t3: • •
02TOOI-X 1 X H-LU<: • •* • •;:- lu2!i— i—ZXZI-OHOXXILhX OJlihXXXZXJO< I Z>0<0—'I— LL^H + LLO •<'—O LLI— # • • O^
^-<0>QiXO<LL<00LJ'-4~-'X>-HrM>O</) tHU-OLUZZX 0051+ 2IQCU- II LL-h< II QLL || mWcQXO II <h- ZXXZ42:oox x 11 11 ilxqmxoq <ll<xll disso: n 11 oi
11 x 11 11 11 \-z 11 ohx<<m .i—h-3 11 jokuo 11 \~ 2: 11 i-i_—.x 11 llllh- n q_xxxox2:dZ^ZSZ 30 II II—-w n II DU-JZO<-(XO-Xu — Xw«-o<_>2:^~-.— I— <>-'H-02:ll2:s2:oo(^s:s:llllu_ll^2:oooo<^<llooll<u_ll<ollllllllll<ooolllllllu2'2:luz:XMU.Miioof.x«i/)«wM«ooMOa:xou.u.O |-<i-iu.MMU.OMMu.MMij.xoi-iwMa:xxQiiiJ
>t -H0>CM0^ OO LO nJ-•-• r-l •-« rH rsi t-4 rH
136
ooooooooooooooooooooooooooooooooooooou^'Of^oo<^Or^(NrOvtLnNOr^oo^o^(NrOvri^vOh-ooo^o«--^f\irns*- ir\sOr^-coaN Or-icnc^c^c^ro^^vt^^vj-^<f*t>tininu^inininininu^in%C'0<)vOv0^o<>vO(M <\J <\J (NJ (\l <M cm cm cm cm cm c\i cm c\i cm cm <M r\i cm f\j t\l cm cm r\i cm cm c\i c\i cm cmcmcmcmcmcmcmcmo. 0.0.0.0.0.0. a.a.a_a. a. o_ o. o_ 0.0.0. a. o-O-Q-O-O- a. o. a. o. 0.0. q_ o_o_ a.a_o. exooooooooooocooooooooodooooodoccocoooo
I I—
»
I —I—I I —I —t —I —I I —I —I I —I —
I
I —1 —
I
t —I —I —)—I (—i —I I—I —I I —I —I I —I —
I
0.0.0.0.0.0.0,0-0-0.0.0.0.0.0,0-0.0.0.0.0.0-0.0.0.0.0.0.0.0-0.0.0.0.0.0-0.
oZ<
zLULU
UJJ—C£t-U LULUCO >X 1-42W 00 »-
-4 <z o oOh- I— LU•—
o
zk< a<u_ o <« h- t/>
I— OLU «— t/)
O ZcC (M 00 -<< LU OT O t—U_ OX • t-t z> >-<3 2! I— U_ • <t—
00 ll o j 00 2:0»-« -'00 in zoo • o (M«-n <•»
I— •—
•
>-t 0O<4" I— >-< t— LL"SL Z# I >t O —> 00 OZ LU IO LU* OHO < Q K< 0011Z *-* • \- SZCM LL Q CM X h-< OO 3-t • »-h Ot- *0* 00—1 O ZrOoo Q \ OLH O LU<Q # O 00>i- l~.O 2: — KO 00 >LLZ Zh •«--• —< -H- • -*00 1-4 •
O ho —« «—«•«• t-< • # <+ •LU t— ~. OO < • •—• »LL + .-1 • 00 • tO—l < •
CC SILL O 02:00 LO OQi O OOO Or-4 OO LL3 II • »ZD>—I •« O • f-< HHi—I f-l »U_ LU • t-H
LU ZZ O* I—ZN(i h i-hLU -H- I— -ft \(— ^* 21—Z <3 UJS—ICOSILU II —1 «—O hQZKOI-J _J •
•-* Z «3 »~«02 —"+ « iUjUO<0<0 •<-! h" • Oh oo< zzzoza "-o *k-o<-h2:<ll.<i- .hds •
o 00 o<z>ocoo.m o «ozll + ilmilooh + cldzoo 2:O LU Z\\Z-i\\ I o«— cmo<—' 11 000 11 11 II <h- II 0022a£h- II C£a: a: <z:co<kq 11 oh 11 a:Hu.i-i-«zoi-i-a. 1—mwo 1—00CO Q. —3*- II O^O II O II II —20 II 3<UOwh-O II >—HI—O II h-O3 X LL2LI_0'Xt-<0(MOQr^fMa.a<oOOLL<<lJLUJ<OOU.LLUJLU<OOLU2OO LU t—1 OQ >—
••—
• LL LL 1—• QLQ •—
' C£ 0£ h-<O U- •—< a£—i LL U_ —1 00 LL >—i •—i hh cC OO U_ i—< c£ LU
oco o mlH CM r-l
UOUU O O U O O
137
oooooooooooooooooooooooooooooooooooooooooooooooo-h r\i ro -4- ino r- co <7>o r-* <M ro sj- in vO i*- oo cr.O—i <\im -4- ino r» oo 0^o <-< cnj ro >*• ino f— co g->Or-»r\jrOvt!n-or^co
oooooooooooooooooooooooooooooooooooooooooooooooo—J —
»
I —I—I —) —I —
I
I I—
)
) I —
I
I —
I
I I ) —
I
i —
I
I I —)—
I
t I I I —
I
I )—
I
I I—
I
I I —
1
I—
»
I J —
I
I t I
a.<xcvcLcvcLC^c^aLC^c^a.CLe^c^a-c^c^a.a.Q-C^Q.c^CLC^(^a.a_^Kht-hKhhKI-hl-l-)-KI-l-l-l-l-l-l-|-hhHI-)-l~Khl-f-l-hhHl-Kt-l-KHI-KH-K(-hXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXX
Z !
uuoO X X<UJ o_ SU_h- < wh- CC UJO O oo-J_J *-<a. oo zo
•• •-• Ml/)oO-UJx
U-l—o
a.I-XUJ001-
LU1-00OOoromhu_o
UJUJXoot-X
ZOOo>-<
JOo<
q£QLU>-s:<0:0:Oa:u_<ccUJ"«Q. •
—
I
OOHQfO
CJDZO»—i
J II
<Oct:OOX
o oZ Q•-. O-I 2<o00
UU^->^^<J>LJUU^J)<J>(jUU^^J>UUUUi^^L>^^D (J>UUUU<J)UU(^LJl-) <J>UOOOOOOOOO
UJ t XCO »-
00 • XcC _j UJ ZQ.O _j o<»- >—1 tK e:O 2 X 000
CC UJ UJ Q. UJUJ > UJ »— < >O0H O K • CC QCt-nXz z z 0.-ic\i OIDIQ.•—
1
< J II II QlOI— <QC (—1 0: 0.^^ uj< ccCL 00
UJ LU—.—
.
ZCuLUZO000:0
K QDDQ > CDZZ O 00X UJ UJUJ UJUJ OO zoosuji-"O- a: J-l-r-K CD _J»—it—
<
O— >xK CL 00 l-l-l-l- < -J00 00 ZZaUcCY-3 UJ OOOO »—'•—<»—
1
001—oxO UJ
_i1—
<_J-J_I_I
UJQ.Q.Q-0-UJ
X • • UJUJUJ oz>zoO CD «~» z a: h-X >~CCCC. 0:03:11,
CC X CC t—
1
UJ UJ UJ UJ UJ Cl Q.CL x i-i-uj< X XCOCOCOCO Ul< U3 OUJ <>a a O cc 2 oo: UJUJ >U_I-4CCZ Q ocoo 1-4 (J) X_J_J u.o:oox< oo; O 00 QCT1— 1— t— 1
—
00 oco OX ujO1- 20 SL cc CX) f— UJ U-ZX 0^2oo —
1
r- UJ UJ »—
1
hXX» XX 0*-hQ 0: ooo:t—_JUJ i«i < h- < OH- 000 JJ —1 CC UJ 00
UJ <_) •* 00 00 < CL uj 5: sis: 2: 1—_— eo m>-<X 00 UJ h-' 00 t—
1
>xxxx 00 U_ z s:>-ulz_jh- 00Z O z »—
4
—
»
2:2:2:5: l-O UJ<< X-J >-<
»»-l z UJ a >- (J)^ |_4 »_4 >_| z 2K-I- zzuj luZ CrToO < 2: 00 00 •• zxzxz t-a: UJ<<t oxzxO UJ Qi X CO 00 X H-KJl—(<_« Ouj JOD UJ l-<H->h- •» < < w _J22Z22 Q-O UJ XOO
1- 00 OO z oC < o: ^co K'-' 00 00 00X _l UJ •» < u_ LL U- II II II II ^.0 Xtt •}{ t—IK-It—
«
_J a. -JO. O >- O (/)—»«-».—.—
»
>-co h-_J_l OOUJQ. < O z •» LL —irvjro.^ •i i*:<< _1 0:00 00 OOt- cc a:0 UJ X O CC Of 0£ o»—^-—»^-. XUJ UJUJ OUJl—!—'I—
1
X H-H- x *^ O UJ QC IJJ UJ UJ UJ —X >a:o: QiXXXXz H z f- H CO 00000 H a: 1— 1— 1— k^— h-UJ 00 o> UJ O O s: 2ZZZZ _J ujaro: zz H- 01- 00 _l (—1 UJ UJ X <<<< -JZ >oo OOH(\jrn»—
t
Z 00 t—
(
Q. h- > > z >j- Cxraroia: <x— UJLUU. II II II II
h- UJ t—
t
UJ -J_l 1— Q.X 00 a: a: _)-. z X) 1—4 CCO O Q. x XCD 1—
»
0: UJ Xcc a. 1- LL< _J _Jca cc < _J -J 00 zX x UJ "^^^» < < UJ <00 Q. u_ <-<C\l O 0. X >- z a: *: 2:
138
oooooooooooooooooooooooooooooooooooooooooooooooo
oooooooooooooooooooooooooooooooooooooooooooooooo_J_J_J_I_J_J_I_J_I_J_J.J_J_I_J_
I
I I —
f
(—I —
)
I I —l_J —l_J_J_l_J_J_l_J_J_J_U_l_J_J_J_J_
I
I —
I
» t
Khl-hhhWhhhHI-K-l-l-l-l-(-l-KH(-hl-l-Hhhl-l-ht-H(-kf-h(-l-l-HI-hl-H|-l-l-OOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOO1
»—
1
< 00—1» LU_I O
U_ X UJZ s O 1—
«
ZOo < CD*h # <3 <a: X X
• >- 2: r oouj_j < Ot- CD oo _lO -CC3Z0->- H-O > z •—
t
UJ >—
<
o ••K UJ _JUJ C UJI— UJUJ oz -< e£ OUJX_l z ooz X -<i~ + h- c£X CL< z 2: O <0C3Q. SL UJUJ h- 2Z = <J>Z i- Kl- *—
1
«o1- O DS M »<(i—iUJ O00 2: -j DClLKO _J _IUJ ••u_ >& Z CC > - O z »-H arujz
O <<* ooO LUd •<oaro UJ OJ < h- <COUJo o >o UJ X r xujolu UJX z 2:K Z OOO 1— UJ OOOH CDH- X X UJ
o.. in i—i _ll— CD » < h- < < >- •!—-1 00 >- <z •«• IOLUJ2D l-Z 2: 2: 1- aruj<-1 -J UJI- >UJ CO_J LUXQ.UJ_J OO <Ol-< zoo co< 2: * _J >i- za. z i^ ^ —1 oo<ooO <0 r^uj K—l CL UJ Q. 00Q.
X _IUJ cc OjS DOCOLUUJ -JUJ UJ UJ UJ KH- OK _j|- UJO 1—
1
OUJ T.CC -JI- X X O OUJZ00 1- ~< CQZ > KOt-< •-Z Z UJX'-'CC ZD 2*-h M OUJ Ol-H- 3^ Zh-cr:¥~t »-<UJ O • -J • zx ZO »-00 Qi • • • 0.u_ —l ujujs: —II— zz <c»- »-<«JO0O0UJ i-a. t-t UJZ
H_J 0:2:0 *-*<XZD 1— O-hhI—> • O 1—
<
h-4 xo<UJ i—iUJ ujais: 3 5! • UJ 1— 000C00 _JUJ cC a: a: f-X U.CO lajw Uji—
1
^00 OUJUj'-'O- O-CO O >-UJK < hhZ LUt-Z 1—
1
_ia:>xo = UJ_JOUJ_J Z-H ct<*-< Z2 CL< Qi UJ }( <_i 1- i- O Ooioo
a: CD -.2: UJ>— 2: UJQi Z> -J = _j t-iUJooo UJ —» IQ UJUJ C£OOOUJ< i—i —1 _i l- >Q.--u_ _JCD LUrouj »— UJUJ 21 OUJ >(JIL 003 CL Q. 00 OO
_J 00 X s:x h-l- u->sa:»-«o UJ < CCcCCDo «—_J •-OI- -»a:h- ujO a:ujoi— 000 Q. Q. _) Q-Q._JUJ 3-J 2Z UJUJ co OOZOZO Zuj • O O Oz —i 1 <2I 00^2: •» UJO U-iU-j <Ol- 1- h- o; OXO•—
c
02 Z O «zo IUH 00 <oooo h-<0 UJ UJ O KO.IU- UJ 2: ».q: JZ*~>CC 0< r>>t -Jt-io oooo_j 00 00 <oOUJ ID DSU. 1 u_ JZ U-O Q. SoOO. O deco Q.HH -13 3m <a: UJZ»-h mz ouj 1- 1- O ujoo:
<cC oz • • >o a:< z OZ UJ O 2: 1- UJLU ceo Ov-<>t c£QsO u_ <X <ULO ct: x z: z = ouj 00CD o "-Z^ —zv. < >-••-• •—01— z • z • Z uuxo
UJ —<<•* <-^ C\J OO >UJ UJ <J>z <•-• <r-l UJ Q.I-> ujx zs-> z ~ UJ • o£LU_ia: »•> 1-1 u_ O X X UJ_J COH O -i »-f0 >.-l UJ CC O UJ 00 oc Z30 Ql ct: s: LUUJXZ i_UJ«— *—1^ *** <-l h-OuJXOO -O •O • • 01-o o . HIUJ l-OUJ xu- . OZI-2IU <_JUJ O D.a oo<
I-O Oh'sJ OSO h- < < 1— l-_JO II O 11 00 HH_J|—Q »—
1
uj z Uj«-iZ 00Z< ctTZujO UJ cco<. 00 II 00 11 (-1- Q-OUJ <al CC < a:z< -J<2: <UJQ_«-< «Z UJU-—I ujcc UJCC UJUJ cC -JUJ O l-O —'Siar •—»•—(QC uj cC xxujo:ujo O Q. OO 00 0000 LUOD-z z < OO 1 OZ 1 CQZO U2b:oz UJ -JO _JO 001— 1—
»—
t
OS 2I-» —^ <i—U. 000 a:xz <o <o l->-a -J O X—>f\J >UJ>t _l CC tDO < UJI— «-H >o >o O-J 00z _J ujo: X*~ Xw on 0= UJZO
1 2: s Za: UJ—10< UJ X UJ<UJ UJ|— LU UJUJ • OXoOmjo: ZU-I- > X UJ xozcc l-O IZO x Xl-O O u-r Oi-o< 00 000 z z QQ. y-cCt—
oo < o 1- z 1- -z H-ZrH z 1— UJ UJ Q. _|UJ _|UJ >-<o 1 1
a: _i LU< s:< khUJ 1—
1
QUJOUJQ- O UJI— _JX ji cCcC Z-Jo > ZXaT ZIDQi U-CCCl 1— zor-ixa. < -z-=> <3 <3 OO. o<K- a
a:
CD
_J
<<CLh-< 00 0000LU
" • r uj 00i-
O a. Z J
000000000000000000000000000000000000000000000000
139
ooooooor- oo cr>o —i t\jmwoooooOOO'H-Hr-H-H
oooooooooooooooooooooooooooooooooooooooOOoOOO —* r-t —i r-t r-t —i —i —* ~-* —i (\j c\j <\j rg r\j c\j (Ni rg <\j (\jmmmm ro ro romm ro >t >t xt
o. a. o_ a. Q- CL a.
»-H-i— H-h-i-i—Z)I3Z3 3=3ZD=5
01 oOU.Z
IO<»-i-o
r-
<ODUJK-
QUJU.LUX<HI-K h-OKX_l<0CX. •-.
Do:LULUCQh-l-ZZ
_|r-<UJ
r-1&.LU2 H-UJ<
XCQf-D. OO
ct:<i—ouz
—
«
LUUJOCX-JQ.Kl-•-<
h-r-< ox<z:h *-«
oujoooOOoO •
<t—UJuja. ^o >--.<l-COI-O-X Z>LUXO<CO
ooujQiZ}HXOoOLU LULU"5U.IIUJOI-I-
CLCLC^Q.Cl.C^CLCLO-CLQ.Cl.CLCl-a-CL.Cl.a-Q-IXCVCvl-hl-l-hhKI-t-l-l-l-l-H-t-(-l-l-l-t-t-(-|-KI-KKhl-l-h-HI-l-l-K|-l-l-
LUo<
~> V Qia: X LL OZ> X O •
O "H XQ 1- <O # Z> 5:2: x O >-
•• t-( •
M •> 00 LU h-^— + 1- O0^r- x 2 O •••w r-t r-< X —
.
LULU •> o 1- 1—
(
o_j • D. MZ< X > ><0 rW LU z: • a:C£00 v. X r—
(
a: <>. -* 1- H 00< •~»*t »- • COr-—<4-— h- O z UJ<m— e£ o -J r-l
0~-LU< _J Q. 2! LUZLUOX O- X z-JZTo^ Q •
<<xo o Z r- LO O LTV LLoct: ».>j- >t h- < _J O r-l r-t O 1—
1
>-(/) »-r-0 >t • <NJ CsJ CNJ mx~o>t •4- Q 00 ^•h •»
••—ION LU h- r—
1
O O O«»**» • r» O OO z: —
.
h- H h- t- ooxh ^o h- Z5 •—
1
X 1—t
— CO 2T<J- M • O O O X»->-<CO o X Q. •^.ca O O O <
H--^ ~-J>fr o r—
t
^0OO-— COM C£ >- >- 2!_J*-"r-4 •.'N.IVj —
»
h- <x X z: X -z. -HCLOwO^i^ r-t < Q (-< < »—
1
< 1—
1
Q 2:(__. r-^^ • jr *^«-^*-.-^ -Z.77 <2!r- 51 2: 2: 2: Z! Xrjai c£<*- h- r-t(\Jf0^t <.—
>
OX+X X >- > < 1oxoj<o LU w«^^»<w O •^ *ct •X • z: .x • 2: XLU CDI— • X LULU LULU Xn' •-h- 0iLU< Uj -<LU< UJM X <zzrzrrvj -<q: r- oooo < HOUJJZ J) 2! -121 or 2!hOQ^KDD zzzz OS II t-- •XO t >< •>- t> LU O X(--im^OZU 00 <<<< Z r-.^» II — II 1—1—
.
II «- II O^ II Z5 Z II
DoOoOLUO || Q —
1
00:0:0:0: r-lLU r-.a z •—1 OLUozzo <o II II II II II ^X o—o: «-»r-« ^^1—1-w.r—
1
«-»(—< t—
t
1—II O
at: LU LU LU< (— 5! c a:xzxz 01- mxLux—OX-—>>_o>-— h- h- c^z:C05I2:h-l-< t—
»
C£< >-<< r-t LU •—«r- ^ f-w «_. H—
'
2! O al<.DmmZ<QLL c£ 1^2:2:2:2: XI- ou. LL OU. LL. OLL. a _l UJcCt/iDQMQy »-• o r-<XX>->- o< Qh hXOh Xm>-Oh>- Q. ->x
r— I
in
CNJ
Or-l
inr-l
U<J><J>WJ>i-)i-) f^^JU LJ^>U<J> O <J)ULJ>
140
oooooooooooooooooooooooooooooooooooooooooooooooo>i-^>t^^^<f^^^^^^^LOLoinNOvO<>OvOso^^<)Of^i^f^r^^r^r^f^^r^cocoooOT
—
(
( i —
•
r—j i i —
i
i i—i__i » t i i —
i
* —i—i i —
i
» i —
I
i i —
i
i i —
t
i i i i—
)
t i—
t
i i i t i t i i
CLO-CLQ-CL<XCLCLCLauCl.CLCLCLaQ-eLa_Q_Q.CLO-Q_a-CLQ_CLC^Q-<Xa 0-0.0-0^Kl-l-HKI"l-l-H(-H-l-l-hhhhKhhl-(-l-l-l-l-|-Hhl-l-)-(-l-l-|-)-Kt-l-|-KI-(-l-l-(-l-
OII
oII
CO<J> a>CM r\j
OO or-1-00 KCO
CO COooo 00K 1-
—o —0z »o •0"O2: t— »—+>-LU • LLi •
J zo 2:0X • • X • • X<LUO < LUO <STOLU sioolu 2:>-Z • >0^2! • X11 <z: • II C\J<2! • II
lu ar>-<!DLU 0C<—iQlilo>s: II ooxs 11
zw >- z: 2: 1- «-x z:z<t •-»>—i<i wt-t<c£u_u_5:a:3u_u_:2:c£>-«-"-»>->CJ5'-<i-ixX
CO0*rvj
oI
X
c\Jin enC\J • coCM.-H en+
Ouu1-0 h-
2:o< Ooo: OX
ZDOo
co
LO
+luO2!
•— »— »cr: i—oz oo>- o^ •-! O t^ Q2! li-IS II UJX II
•-!< ox —•o< —r-ICO-J •
ICO «S •-<
^0 cO 2!— <-•>—'2!>->-« •»
-«—< IIw-:'f >OXM-;t(0(/)
•—• ti —» 2: • »»<ts • ••-*
11 -3-5 XO^»OHX•—1—3 -> LU -Jt CO II »-** O II <•OX II
•-« *X II 1—
X
o-Hi—zr^co >—<<oo p—
i
00»-*i—«2Z»—iO*"*S'~"'O—
«
r^rOOt-XX^OX-OQOOc^Ou.^Otf'XXOa:OQOUhmOOhhqo
<JHJ>U
0> OC> O<M t-<m
rn
OfNi
C\J
o
00c£LUco2:ZD
LU_J
<o00
C£LUQ_oo_
LU»—
Q.2:oo
_J<o00X
a:—
z 1
•—<LU
X •
— •
I -i1—1 •
LU-
LU-J<O00>
c£—z. I
1-4 LU>- •
I ^<-» •
I -JM •
LU—LU
• •
OLU00 _J
<t-OXZ.
lulu 2: 2:ooxx>tx<2:2: II II Ml o<<->—.C\J—.00ct:ot:i-iLn 11 >-hx
<o— 001-
oxx-i il II
xz <—<>-< OLU2Z2I 00_l CM>>-vO>-<II II » II O H —'———.CM— 00 II UJ-5H-C
J.—II— II'—">-LUi—1
-)-)<->X >->-•«»-i—1«— »-»3 >-»»-» >—t^"-" ZD >—<•—<<X'«^»-»
II II LULU LU002:LULU LUOO2: 1— OLULUa^a:_j_jo_iLOi-H_j_jr-<_icQ>-<in 1 oo_i_iOO«00<<H <t<C0<<H- C0OX<<zzoo o—zroo 0—2: II 1100»-« >— 00 00o 00 u_O 00 00o 00 u_OO ~> I— >-o 00X>-XXQX—0>>0>—'ODOXXXCOmco
oCO CO
inCO
000
141
oooooooooooooooooooooooooooooooooooooooooooooooor-t cm co >$ ir\ vO I*- co o^o —• <Mm vJ"mo r~- oo <j>o i-h cmm vf la sO r*- co o>o t-n cm r<*» >*m ^o r*- coo^or-icMro^Lnof^-coC>cj^C^C>0^^<>0^OOOOOOOOOO-^rHr^r-ir-ir^r^r-irHr-icMCMCMcMCMCMCMCMcMCMc^rH ,_| rH r-l ,_|^ _( ,_| r-t r\j C\| CM (NJ (\J CM C\J (M CM CM CM (\| CM CM CM CM CM (M CM CM CM CMCMCMCMCMCMCMCMCMCMCMCMCMCMCMCMCMCMJJJJJJJJJJJJJJJJJJJJJJJJJJJJJJJJJJJJJJJJJJJJJJJJCXO_CXC)-0_CXCXCLO_a-CXaa-CLCXO_0-0_CXa-ei.Ci.r^C^hhl-Khl-l-l-l-hhhhHI-l-l-l-hkhHHKI-l-l-Ht-l-l-KI-l-l-ht-hl-kt-hl-l-^Khl-33DD333333DD3DDDDDDDDDDD3333D3DDDDDDDDDDDD3D 33=53
* — en* • ~+ •«• O CM
# r-l •
•* + LU rH^» ««» •• r-H
» * —» >-. X IX.
* r-l — pH X* # w uj w cr* # UJ _J >*# # _j < w# # <— o c^ vj-
* * om oo • *.
# # l/> • > O CM# # >-0 rH •
00 + # rH —« UJ rHZ * ^LU -H CX -HO — + t-4 •» 00 -H LL•—i 00 » COX » •• •»
h- O •* ^ >fr •*f\J r^-^ CM X Xt-i O - 00 OrH . || CM O CM 00oo <4-**><4-||+X* vt —
»
O * - XX >-*'-• ^ ^a. o z o » •« o •-<•-< »"-» o •
r- t£ r- •» # l—r-r. ~»LL I— # #Q 3 X —X X - -* #-< oo i— o ir> . oXr-« •-«- o + +or: >-r- uj o r-i x Oi-. .. -. — o -
inmoo «,* h «— ~^<. r-i + oo *»• *» —
«
a: • •oh- -<• in co v» ojir\Mr-i •— »• in • » a:lu hh —. cm o> • -» oo^—-co a- r-i cr* -ft # a:CX ++-»OI— • • O CM »Q t. i-l * II • # -* LUO IXlLU—lOUJ Q* • rH • O ••—"X OtTr-l X * X * •-«
a: OOco-»oo ixi ixi ixi rH kixic£—< o< >-i—» ixj ft #O. ZZ «0-3 X • O • rH (J50 •» — rH ».. O It -K- -^
<<h- •«— ex a: • x ix o •— + »-co "« • •!( »« oa: m oiaroixioi < 3 c£. O » Oct: »»x —. •• x cc «• »• cmr-l OCO >-X #_J< Cd O X r-l X >-,r-l MB «-•• x -Jr * •1X1 II CO WJ- «X O O < >* C> ^-<r-l r-taH *•><•& |J.vOX r- HM---«|->-0 O • •*" O •-hX — + -^.i-* • + +^-\- ixio ii ^— zrcxr-x x s: o •> ai*- »q^cm ixj --<< c - lu- lu
001— I—^wmm Q. (_ . ZLUrO _)>t IXIZLU r. _J ^^H ZLU«— Jwhz -o ixi »•*- s; •«-« ii — on <_j • < •• z<—im <- Qco <_jco <oo--*— O oOO-Xoi • 3 O »<0 OCM • •< • O »• r-i •• •< •. o »-C^
-^»o -si— I i occ:-» i-s^coorH oo • —.oooo oocm ct:- coo- ^o- ^00 CM <X-» »0>- Z r-iLULU + LOLU XH —IO + 00r-l >. • O +00-!{- X-!'r
h- »*• "0<wr< »|— O »OOLUX0- -H N0rHLU>LU rH >— 1<- LUX* * —
*
Z —O >t5^S— sOOCL r-i OZZ • —I ^.LL •• • • CX -«rH m • - —.« OHI _J »l—I • »»>-X • •—
I ^ \— LU<<IrH»-. ». ^- ». rHrHrH—»—I COLL — »• r-H— •«Is- »• •
O •»— +H-^— »— H- IXI •> + O •Cdoi »r>-X —IX II I »C0 •» r-4 » O^X »CMX rHXH-a. a:oi-'jll*vOjxoa: lu ocrxx—r-icM—irnco ^^hrixmnx —ir-im i— cMincncMmo
Z5 «LU «--H • t • •(— OCliLUOO 3*-"— -J •'-HO * r_lH-l_J t-rOO »*CM O rrHLU_J r-r-lO ~r-i •
o oorrooi— ooxxo_h-txi3 ooouo •vo— vfsO^- ~* t^o—to-^HvO-D »-»o^-4-vO«-icv:Z OOC-JLUOnOCOH- h-^ wZH QC0c0cr:^K- —•!— HQtfwi- — |— + w-)_z:ciiw|~ ^-r-oc:r-i OLU II 00O II 11 CXQ->-0 II r-i3 0<<XLU<OLU< OO >- LU< O LU< mOUJ<m Xlli<Olu< ixiO 2!-5K-->h-X>-r-.r-.Ot— c^h- Q- Sill II <K 5!h-l—S-iHKl- SI— I— Sr-iJ— H- SIH- <l—SHh SZ <-•
< n-w-lu— 1— h-^-^-»-i o^zi— *-QCa:'-»>-«of: >-<cii 11 w^wq^ mo: n r-t^z^-"—<cc >~>cc-'_J IXLLOOLLOCLCUXLLCfO LUO3 IX X >ix mlCO CtTOmO LL IX OiOO OiO—O QTOOlX CiTO Oc£O IXq_ mh-^mQwmmm'JOi-iUO M<<M2u.03XMQMM2U-02li-M02XU l-i2X03:X"
4" OO f*- OI^-rH 00 ^OOLO CM0>rH CM CMh-C<"><h r^o <-i oho i-h o-ho o-'O cm oho•4" h- "4"rH4- 4"rH»t rH ^" CM 4"
*J>Ui^ oo
142
oooooooooooooooooo0>0'-t<^rrt-4-ir*Nor^co^Of-tcNra<|-mo
<\l (M f\J C\] C\| c\l CNJ (\| (\| <\1 (M (\J C\J C\| (M CNJ <\J CM
i i —i i i—
i
i_J
—
i_j —i —i i —t—t —i —
i
i
Q. Cl 0.0-0.0.0. 0-0-0.0-0. Q-ClQ- CO. O-
t-KKK-k-t-l-l-l— I— I— I— I— I— H-t— h— t—
>- X —>
a:z z o
to co »-
zX X 3< <s 2: »-
o^ S<i -Io o a.LU uu
X X OLJ U> Z• • •
O Q r-i
cc cc a:O O a
lu o Oo -J s v-z a a. to< <Of Q- O- .j
u. K (- on
o uu lu rsCO 00 o
»- oz) 1- y- a000 s
z zto z z zh- < < LUz O X1—
1
2t •
a. O a.II ~> 11 ~- Z>
u_ to- to- 1-UJ • LU • LU3-1 3-« to
a: _J _J ^*UJ <c* <c£ I--CO >o >o oa.s: ZD3 >-0 xo I—z II 11 Ouj• -~._JQ^ —.—let: —•>--< to
co_JZ> >0_I3 >torX 00<O 00<O 00O>
00 O co CO _lr-4 «•• O — O •-- 0£«-* vO—5IO 0^-5:0 0~-ujhZ «-h- ^Z-H -iZ-I~ClZ<c£ lu<z 11 q:uj<z 11 c£Lu<oa:s:=5 K5iujQiZ)H-2:ujQ!:3h-5:a:3QCH •-<Qrxa:i-i—o:ia:(— ^oc:o-i-ciOlu OrO^LLiUJC^OSLUU-'CtrO UJ2ulq: 3:ll 00:20. -jc^3:u_OQiuj
i-< i-H 1—
1
CT>00 r^->o LO^00 aoao 0000 cocoCNJO coco coco COCO
o
143
APPENDIX D
TABLES OF CHANNEL SERVICE STATISTICS FOR MAY-JUNF
or
OTLU
>aloo
oo
ZDOTC£LULUC*a:
v.00
00 zoo cc:lu1—
1
oa:h- 00oo i
t—
1
v»zK oo Z)< ZCC»- Dh-oo 0^00
UJrHUJ 0£o z»—
1
b*c£> Oa: 00UJ ^_—oo Q
ZLU &?<*z O3 00-5
1MMW
> z< OHs: UC2T
00 UJ3: c£00 =*fc
<LL z
•r>a: a:
• ZUJ1—
1
a:t—
4
»—
1
o> *zX cccc
Z^J)LU oo_JCO •00< a: coh- zz>
oo
t-o0000--hs:
*za£Z>ZcC""-~~
UJh-<a
4-or-Lnc\jr--m.-icoLncoomr>-OnOvO-—imo—<c\jLO«j-(\j'4-r0i-tHHONHOOOOOOOOOoooooooooooooooooooooooooooo
r-roorooLnLfMnr-iOin^-o^
•-i(\)r-4ir\vt^HOroOrO(\iOcNjo
rOONOOlTiOOCTOmCOO^
sOo>i-o^oo4Tor--trnLr>'-tomI—
I
t—
I
I—
I
r-H
OTh-vtvtLTiroincomcoin-HsOLn
rn -d- .-) lo 4- c\jo —io r-i r-K fh ~*o
roo^co^-ioroh-oa^^-dnrgoco
>Oc\jf^coomNOOr\jrnir\ogo>-Hc\j(\]r\jc\jmrO—iir\ r\j -<fr- <nj (\l »h
loco* IC0^LT\0^s04"00O»d"
^-OvOO^vOmmo>r-m>tco>i-i-HCM -!
cr>r*-LOc<")r\i<\i(\i<\ir^r\jc\jLO<\jm
ir>vOLOvOcoco»-tr-r-ivOLa(\jNtc\j
r-o-Hf^-NOOvO^-d-vOr-to^oi^
vj-cooo^*oh-or*-r-r,-Lr\c\iro^ot-*-* C\|r-t.-»i-lr-t,-lC\JC\J
C\Jh-h-vt^O(\JvOaDLr»0-4-vO'-<0o^mvtc^r—rno^o^vtvftNcomco
>->->->->->-zzzzzzzz«««DDDD3DDDOr~coCT>Or-ir-tr\jr04-inOrv-ao(\jNNrvjromOOOOOOOO
oo
CM
00
co
mmlo
LO
tvO
o^
C\J
sOCM
LT\<f
-HOsl
144
OSUJCC\1S
\-
o<>OCCO
CO
DOgCluujq:on
V.COzo
CO aCujo OQl1—1 CO
H —
—
CO sz—I coz>K Za:< =>H»- ' arcoCO Uj>—1
onUJ zo Wa:•—
<
u> COa: ——UJ QCO z
&>CCUJ Oz COz>-> —^—~I z> cc
< ucss: COLU
ona %_i< zLL •z>
ctra:ZUJ
• enX•—
<
aX *z
aiocUJ zu_J COCO< • COh- ct:ca
Z3CO
HOCOCOHS*z
OCT IDZOL
coOHcocococM>i'--i—imr^-mcMC>>tT*-oOOOC^rOOrO<tOOOoooomoo^oooooooooooooooooooooooooooooooooo
roinoomoncoooooooQ0(MHN(\JOf^fMOHOOOO
r-ooomoromOLooooomc^sO—io^r-<>o.-<vO<\ic\j(\irHr-i cmcm •-•'-h i-h
^OOOD^^OM^OfMOOOOcrHHMffio^inOHoooo
(\lC0r^-rncMO>0rr)O>tOOOO
ror-vornfMOOr-omooooincMr-i<^if-i cm—* i-i
omr^cor— CT'CMoomoo-to^-o
Hsoocor-oooocooi-toor-t r-4 CM (MrO
ro(\jiTir-tf\j>-ir<^>0'H>j-rNj«-t<-ic\i
ir.ininr-mor^-r^OvtooooCM i-4
^•^-irOtMvj- roc> cnjcm
00vj->tOCj> —<f\lrOvOvOOOOOr-i^H'-Hi-H —»c\jcMfMcMCMCMmc<*»
r^coocoooLncccovfr-r^-r^omvor*-cor<^^-rHo<-<Of\i'0-4"f\im
»>-»->ZZZZZZZZ<<<<<< r>DDZJZ>3Z)Z55:s:r:2:2:2:-5-5->-5-3-j-j-7
sOHcooN 0^-t--<r\iro<t-in^or^-coNNNrvjfnmOOOOOOOO
inoo
CM
CM
C\J
CM
CM
•
I—
t
CM
CM
O
^CM
mm
co
>4"tM
in
CM
Ovf
<h-UJo>
145
ouuOCLU
»-
o<oo
00
30o:lu
• LUC£a:~^»—*^
ooZG
00 aimo OQC»— 00K i
00 ^zi—
i
oo IDK ZeC< Di-K et oooo UJi-t
enUU zo &>al•—
<
O> 00CC —
—
LU Q00 Z
W&.LU OZ 00ID->
| Z>- CC< ooSL OOUJ
o£O %ooz zLU • z>
a:a:ZLU
• 0£XX o
*zLU cCcC_J Z<J>CD 00<H • 00
occo2300
HOOOOO-15:
•zcCZDZee
<
c^^«.o^o^o^oco^tl^lcoofNcor,-OCNJ—lOO<-0(\l—•<-tC\l(Mf-i^-oooooooooooooooooooooooooooo
OOMDOOOOvOMOmOOCO• ••••••••••••aOOOtMOMNO^HOrviOH
»j-i-(Oh-r*si-Ln4-coorooocNj
ror-mvi-cNjcomOLnocr'roGOi-H
r-co(M—lorn—ioor-ic\jcX)oooco
(MrorMrooo^^t-^^tMOrno-J-
ininO^ooovt^NOvOvtom
roo v0 <njom so in r-1o romo co
in<s"iCT'<-tr~-rO(\j<\l.-(i^v}-in>o>t
f-tvOrors-ooN 'H>toN fNJ<M>t(NJ^O'Hro>-i rOr^mrH(MCvj(Njr\jin
incoincoroinvt-o^co4TOr\imin
«J-04-vOOO(Dino-4-'H^OO>
h-r^mvj-corsjcNjstvOOcovo^or-im(\J—l vj- f\J CT> .4- vf cm c\i c\j
o
OjmrOr-lOCM^^rsJ.-NI^^CNJcvj
oor^ONOor^-sOiTi—iooltinOvOcx)>tincoo^;\loc^^->4-r^r\iooco
>-»->->->zzzzzzzz«««DDDDD2DD>or^-coo^Ot-i'-if\irri^mor^-ooc\ic\i<\jr\iromoooooooo
o(Ni
o
c\j
co
f—i
•
CO
C\J
—A
vO
CO
>0
—tin
in
co
inn•O-t
o^
mmC\J-£>
rOr-ic\j
<t-UJ
146
OfUJa:uj
I-
o<>ocoo
oo
DOa:ujuiar0£—*—v*00zo
oo C£UJo OQil»* oo1- 1
oO ^Z^-i 00 IDH- -z.ee< =>l-K c£oo00 UJ.-H
a£UJ zo Wo:*-* o> ooa: i
UJ Q00 2T
&*a:UJ o2 ooZ>-5 —»—
1 -z.
>• CC< oas: oo uj
a:»- 5*fc
»-cc z.u_ •o
die*ZUJ
• a:H-
1
X aX •z
a: a:UJ zo_l 00CD< tooH area23
00
h-O0000-*ZL
•zCrflD
Za:
UJ
<D
oo coo oo vOo •-« <-t cr co cr> ro>3"
coCTO^CMincM—»<—<om co.—
i
<M—lOOOOOONN>t OOoooooooooooooooooooooooooooo
cMOomooomoooocMoo«i-ONOoOfon^oooo
omomooooNOinoomocovtfNjcNJfomror-tor^oocNj^-t
cm cm in
e-v0omooo—<>tr~roor^-o
omOfHOOOcocoirnriOOo
irimoooooo^moooo(NJ'OOOQOOO'tfflOOOO
r-4 O mi-Hr-HCM r-H
sOCOCOLni-tOO^O^LfMTvrOOr^-O
COi-tO>-lCM>t'-'Ors-CMvOOO^-lcmcm m^-cM
in
•o
inCMr-4CMr-l»-lr-4(\|m>0-HONl-CM
--loooinoooMfiyOOOHO
ocxMinroinmcMmmooocM4*>t o-J-in .-t
cM^O^oooocoococOvO^OLncor*-
om^-cocM<fcovto^sOOvOoco>tf- c\| ro ro -4- cm in cm I
s-o cr —i inOt-Hi"MCMrOrHi-I^CM'-<r-4<-<'-lr-<CM
»»-»-zzzzzzzz
sor~co(^o--H—icMro^insor"-coCMCMCMCMrnrOOOOOOOOO
o
CM
I
vO
vO
CM
rofMco
CO
rocoin
co
ChtMi-(CM
CO
coco
CM
rocoin^HCM
<I— UJo>
147
zLUO i-t
CDLUo »- 23: D<h2»- _j_j<oDDIIUJ O21h-O0
_j X IwUJ K UJOOOOOOUJo 2: .-.a:
DZ X •—<i— 0^ <SILU h- irthDOZ
h- -4 h- Q. »ozs: Z!o0 3 •—1 Q£ h— v*- >—1
< o>- ZLUDOOI-H-tan •-*</) UJ 3XOf^O->-O H- </> *— LU<o <o 3 LUOLU »»t_)V-
a: -IZ ••2: x ixza. o*-« a: 00>~<Oh-UJUJUJ
s:lu •-h-2 • 51
uj oouj _iz o*-xo ce:
h- 30 luOoo f-o a: Z33 aio uj Qmzj> Q a: 3 oCL »-* i£ o>— <UJ_J—» o x2. <—• a: 2KUJOOUJUJ O Xo a.z < jsrozsri x uj
O 3 21 003 ZwMk ujo:x_jo: >-t2:aj di- a: ujo:x3I-
_j ujuj UJ X^-JUJa: 2: ID a:x3i—
o
uj zb: a: 1— oocdxo-j>-oo o di-o roa z: < <rt-o< uj ox o id y-cco <>— zroi— oujooo "-• a: 00 10 k-uj 32: Xo. z: t—o 2:<a:z:_j oc uj3 00 o t-uj xooo
os o r-i *•>- << a: uj xo 00 o 00 uj i«hoi2: uj .-1 o 11 00 ocmjj> uj o. h-x o to 2: xooh-o 00
o h- uj h- ujujc^ioujos: hh 00 2: i—o warm1-1 </)a: Q- ooszujoi— n$- uj u_ uj ouj 2: z: 0002:1— xk <cl 2: 3 •-h'-"-^ 00 2:2: >-io:2: h-x zood 02:1— Zk< 0*- w«uj h- u_h- a: "Oi-* oujm 00 t— 2:00300: 1— Z^D_j o UJ002: uj -(ooQLr->— 1— •• o^-t— o 00 oo30o:oouj z^doq:c3 <r\J aDDZ 2_JO«a: 11 H- 2: 2iu. 00 000awaji.ii 003o a. 00 uj 1—
2: Ocjoi 0.0000 h<oi- luuj(_)_j o »--o 2: ooi— oouj2:o: oo 00:00 lli 2: a:•-< a:—i»-i xujqt: huj'i<t-s:z< •-. <ouj 002: 2:0; ujujooouj^_a; 0000 CO'V< Xh-OiUJ cc I— 2!i-i3UJ i— •• wOH ZO 00 >- >- h- h- 00 2: o: llujo
00. oouj cl 2: _ioo»-(h-u_qi < 00 2:< oooz:oujuji— 1— <<2: >>i— 1— 00_jv» <2Ih- Ouj-J O UJ 00 _J o:SDWZZwwh« UjUJI— h-<r<s:LU2:_I -J Q-t— «-H|—< t-< 3 0<3 O" 21 "HO: a:OOX2:Z:MMMH2! UJ U.OZG. h-3 U_ _J 00>-<2: h- ~Z. HhOOUJU.'OOH.MoiQCOOIZIZ LULUS <2>» _< < 5; »— iODHZ3D'-"-i22<hl-aOujUJW<h-z: qtkujuj _j~z: 1- > 000 oro:wDOOQ:a:5:s:j3nHwZ£<X«-'< o<a£iu dso z: uj zuj H-.ujo;o:o:a:Q.Q.>-i>-«u.oOo:a:2:2:_iU3I u-oaa: 2: -< uj > 00:00 u_oi—<uj a: 0:0.0. -•»-* u_lo M|a hoi- o < a: > u.o:>->->>>->>«o 000 I I OOOO •"-• 00 Z< >>- —
)
I—
I
» I I —
I
I —
I
I —I—I —I—
I
H-z:^ dz+ 1 ••< h-uuq _i_i_j-Jo:o:a:a:a:o:o:<<<<<<<_j.~ioo o:—<-k- + LU.-10 uj q oouj a:o:<<oooooooi— 1— 1— 1— hi— 1—OH-< < X Oa: o:a:uj DDhhOOOOOCOCOOOOaO2:<U. Ol- _l O mOZ OOOOXXXXXXXH-l-h-l-h-h-H-
CC < 3: U.00O XXh-t- I I I I I I I I I I I I I I
h- ujq: •• •• > • _j 1 1 1 1 1 1 1 —< r\irn>J"m or*- co00 ^(Nm »tUJO.O UJ UJ UJ -J •—ICNjrO vj-Ln-Or*-'—•—IrH—4r-l—»f—I^H^HCNJ!AJC\|(NJ(MUJOU- >~ t- > O XXX xxxxxxxxxxxxxxxxxx-J O O < u.u- z: z 00
148
UJ —
.
3 < •
_J h- o< I/O — _l
> z uo o cm <5: >- id z o
z o < I- << o 3: r- x auj > -J -« o uj
2: < < z a:2: a: 00 o
UJ UJ CM •• Z Z Zh- 0£ "-i CMZ pH < < cmqt -4-
< UJ u. c\JZ< I Qi NZO •*
c£ «-»X — Z<X II I— rHZ<oO 00 OID O0|— O <XOCM in Z<X UJ i-t
o uo o xo z rH uj <iub: x xo cd z o co< x co xo 00 x<-» a: af ozi x o ou. h- v.
_J c£O<00UJ OZi-«o — O OZ 0-1 oZ< O *— 0>-" Z«Z I— ZZmOlu 3 r-»
<3 C£ <00c0LL M^LUO UJ -» CD 1—'OOLUt— <-0 •Z U-<h-r- h-c ZUJQ.Z h- >• O OOOOOI—
0< Mhi/lDOQ LUCO 1— < <a:LU—. >0_l3r-izs: u_oor-oi—a o_o z uj Qmi^z<ju zi-h »-iZ3 z a a:uj ac <oujqo »ooZOO Q«-"0>-< C^OO. o o£0__JO_ CO-'Z.H* O*-"-COr-h- OcTOLLO UJ O Oi £-£ <<<c£ 5: 0000 on o Q-_j mOnDa:\— uj c£c£Or-uj u- ujo: — lucmcmclll i—CD00 >-LULUUJ33 UJ30 oOZZZ UJOO03 <mm_IOO UJ3_JLL 00 _JZ<<OUJ3r)00
-JU.U-0 UJ 3_J< Z «IXOJD-IOUJUJOO UJ*-—iZlQi _)<>UJ 3 >IUOI i<«oa:oo or doo<0 <> 3 a: wO**«h<»<Da a:uj ooiaiZ > I--J lu oh •-.> uuoo000 ct:uj>-i zis u-uj 1— oo< cc ccujI— (— z i—acooZ UJhhU. O OO UJ H-O0UJ> <Xo0O0U0r-OOQ_UJLUUJ MlL>HC£:M>.>-k>-|j: OOUJr- LL 1— ujuizoouj z
UJ U_i-iOujoO<t<vO<t_) UJt— h- O O 33<LUh-ooO00 —O0--'00_I_JUJ_JOO l— Xoo UO CDCO cC I— ZU_h-w DOSLLwUJUJDUj XI— UJ C£. ZZUJUJr- X<0
oz hsqoooo: xi— 01— uj —'Ola: iiv-ccZOO Z XQoO UJ UJ h-OZ CD Z>- Zl— Ol— —IUJ2 Xr-OZZZaTZQ- OZUJX Z 3 O-0^302 <
Xr-OZ<Luaj o Zlu_jh- 3 qIOUJUJc^Zujooi—l-OZ ahKZM^ uj_i o z oq-q. ujjooOZUJXH-oOooUJooz —I UJZ I— I— _J ooi—ZUJ_ih- >>-ujoo3 UJ3UJ c£ oot^otooooo ujZlu_j Oh-ooooci-— a: uj3uj_j o tictzzctujD a:_J OZ00 OZuj 3UJ3 U_ —* uj uj uj »—3 ujZ3
OooujujiZi^i/jooa: ujoo-uj u_c0lululllu33OO00Z —I300O0 Z DO 3 uj i-hq^c^ 30QCXooz c?ujuju-<u_ c? ujuj 3 llo:ooq:oZ LUOLUOOOaTO >-l— 3 _J OO000OZ >h- 00
>-i— ooct: h- lui—<o < 00 lui—003 —JUJr-<Z LUUJt— CC Zm- > QL CO 0C QC _JZ HH CCO <2>-<>-i ZOOZ^liJ *-"C£OX UJDZZ<wofwM •-<
<-ict:oxuj>-"-iujzcD i— oujoo h- cooo 31— ou_> i— _i _j_i _j —i 1 __«—
1
;
(—O LU 00 UJ> >(_>3 2: 3--«2:< O0 Z LUUJh-3*H LU •-• < << < < <<<<3i-.z<^o:q:c£cc:;_d aa:z—i lu dq:>>ooo:^ci: z hh •—1«—
• •— hh —d-H^-^-i
Oo:z_joluujujujz oco.t-'U. h- zz<<<a:aza m 1— i— \~ y- \— \— h-i— 1—
Qia.'-HU.OOOOoOQ.Qi I I I I I I I I I I I I I I I<— *-**-> NH >-• —'——<—
<
I I I I I I I I I O ^rvjrOs]- on or-QOCJ>0^rMro»t lu Z ZZ Z Z ZZZZ•—ic\jro<t'Lr\ ,or~-cod><—1 >—< —*•—it—t ^-t .—Ii-h—ii—1 c\j c%iojc\j cnj Z •—• *—1 i-h —i •—• —••—« •—•
—
•
IIIIIIIIII XXXX X XXXXXXXXX -i
XXXXXXXXXX XXXX X XXXXXXXXX u_UJ
z o
oo<Oct:XO
• •
to zUJ LUO3 CC*-i
-J <h-<> OOZUJ 0:3> UJU_< 1—
1
00 U-Cd.
_oOIL
OC Oz
3:u_ • •
_l LU< HX O
0>
O X cnH-< ox •* t—
1
O 0^* >t *O rlO r-« CT.
J>tco
XX
rH
XO O XX v. Xz O XX O >v< O v.v^ r-l co
>t LOO •• «00 st" 00 m coUJ i—l r-4—
1
r-l r-l
3 »- •» •- X X_J cn ror- X X< X XX •^ ^> v. XX COLU * ^*v in CO> LTV r-o •> «»
< ro OLT\ CM h- rHO0 r-« »- •* . r-l i—l •h
CM CMvO X X CMCC •- XX X X CMO CM XX V. ^ Xu_ X ^V^V. CMCMXCM
V. 00 1—
1
r-l CMCM^CM00 CO 00 r-l
» •J-NtC-vlsJ-
UJ CO r-ir-i •» »» •* ••*••3 CM 9" •» r-l LO vOO—4f0-J •<• r-l LA t—
1
r—t rH CM CM CM
< r-l XX X X XXXX> X XX X X XXXX
149
UJo
1— 1— 1— zX 000000 O0O0UJ zK ujujuj zzi oo
cc Kl-H- CCcH arujo UJ
ooo •»
cCcCcC OOOOOOh-oOZooouj
OUJ
UJ —< ooo a: «-»_J0l UJ 00
o o_j U_U_U_ Sf-UJ oo z oO ZO. 00H-CQ O a: t—i oo_J i—<UJ rg>tv0 <o£s: uj orgfM K UJ IOo 00 aT LLtLO oOZU-ZZ O a: (-Q.z O uJojuJrO z: OUJ << O— < O•—
1
_j *• *-» ja<n a: s: Z.Zuz o •Hrom^-^r-uj UOwOU < ««O0 UJl-H
•• z> o cor^.-«> > _iar -»a: _l oz s: a: o O0O0O0 ^Ih OJfvJZOOOOOO _J <o >UJ Olr-4
o» o 1—1 UJUJUJXXXI- ZZ<GOai UJ 1—
1
oo _)h- UJCLQ-QCO C£UJ t> oookx-;;-< << UJ UJ UJ _J h- < 00 — a: ZUJ oz U-_l >t— ujujuLio->i- mo XXSQ^QicQ O < o o h-Q. os: <QZ
LUi—
i
o H(J OOOZr<lcMUJ oo < UJ -J —
1
oo < O0_J»-t
J3 (MX IZ OC3fOrUjr\jXZZ >"ZZh-! oo O o h- >-U- ooa£ OOCoo Z2 X— -JIX -5 >- >- _) a: at: o£ o o z 00 l-O z< uj XI_l < ^z 00 U.U.U. Xwo:o<i<a:uo< _l < M < OCL SIoOH-2_J la: Ouj UJ oooujw—.oxoaooooo> UJ < h- h-O |m| UJOo oo OQ. _l o^o oo i o ct o >- < OOZ V— UJ oq:z
c£u_ LL oo en 000000<00_I acciu-u-iii < _J t- UJ oz ZOluO 00 i—K < h- h-h- 00OO< o0 LU UJ DQoO o a: O0 UJ <•-• "kJOU_UJ l-O -•51 >—
i
ZZZ00OO5L<Q-Q_ UJ \- o LUI— O0|— 1— O0 UJ
X ZUJ.. mo c£ UJ UJ UJ UJOO i—
i
-^ujujI o oo< zo < Oa£Zl- ujoocj;• —a; < l-kl-SOHOQQ'G'vOSSl- X >— <o -Jinoo.LUO-I
>oz~r > cCcCUJCQ LLILU_J—iX OOlSNQSIiailHh
Oh- o:u2V(\j t— OOOoOLA<f- c£ X h- O Z<OOuj—
1
Q. OOZ z <vomi-azz^<< O" ujZ oh-H-zor.c\i:2-—«— C\J_IO< M t— h-^-j— «-» a_u_aia:—>hhi + Ow M HUZ (N ZJOI o zzzii+ +ujo:ooo *o <aT OOZOZOO<O0Z <0>-l(_) Q. UJUJUJ -"-»(_) U-JOOOOOZZ o- O0UJ OOt—MJJi—
I
IQ<Hlu. * ao;:a:>-oouQ. o<< + oox < c£<<uori 1 o CM 00 O o:a:a:joo< c£a:oujuj LO UJf- ujcl^:<0 »• LLHh 21 0000-00 UJZZH2S Of SL<. xo ujo
IO NIIXZ M UOOwOO(-fl]I V. + wO t-zooa:t-1— O0(\Jh- I— XLU 1— 1—OOO (M * oujzmujZIw ^.> < QQQjhhZI- fH & UJ_J Za^O^Q3>UJXSIOliJ o DQQDns u: Z <t + oo< UJUJ>—<LUUJOCL\ l-OCi _J <<<5i<fr>-oo LL. cvjrO OO _ju_ooa:z
_JcOO--i_l'- oa. u_ r-tCMOSZOOO^w- IO Y~\ ujooooUJ<-— | UJ2^-i^- <MC> iHfH—« ooOO.-ic\imvj- x + Ol)r- UJQ^<t— »-•
Q -a •» o cm^-vO >OO^ooooxx >vr-cx)rH l-tcvjr\i(Mf\)rsjvor^-Ln I fM UJO0 O LUOOOOOUJ p-lOl/)--! z ooOHm nJ-ujzxxo>>xxxxxxxxxxoo (——>- <llio: oos:ir\j(\i2:or-H < + + +CL^L^_JO v^\0^^> I 1 1 1 1 1 1 t 1 + iM + UJt— _J 00_J o<f-oox a:x -HrOLO-jr •^•r-ICO'—iif>oororo^HCNr04-Ln>Ol^-c»ChNi-Xi-i 2KH- OOCQOIU
UJ ._JXUJ<X 00 OOG(<l—<H»sOXXQ.O.O.CLQ.HllQ.O.XXO <(-Z LU<UJHO0KUJ t-tJi UJ HH< C^OOUJ s:i-t-CLZ<o < -J ar-J i < a: a.s:oa:< c£ll i CD LUUJ<OUJLUUJUjUJ Q-UJUJ oooisrujc^LU_I UJ> < IJJUJUJUJ_J_J>0_J_J_J_J_IUJLUUJUJUJUJUJUJUJU)UJUJ III. z:oluujujQ- a. _J _J Q-O _l •—
i
_J_J—I.JCDCQ -JICOCOCQcQCO_J_l_J-J_J-J_J_l_J>J-J_J zi-u. i—iU_UJQiQiOUJ<<OcQ< a: 0D(XJCQcQ<<o0<<<<<<cQa3ajCQcDcDCQCQcQ:'X)CQaQ O >-' < oca.
Q£'—IH ^:-< < <<<<•—<>—<00Oi»—iM>-(—!»—<<;<i<K<i<i<i<i<c-<<ii<i mZQ h-QCL •
O 1-t-o h- > i—
«
t—
1
1—1 1—i Qi C£ Q_ 1— •— Z uj U-. a£1— i—<—1^ •—
»
C£C£C£(X<I<0 <<<<<a^o;a:Qra^o;a:Q:at:a:Q;ai o Ooou_>-hZ;zz z UJ <<<<>> >>>>><<<<<<<<<<<< <•• OO-h | 1
•• i—««-H •• •—
i
Z >>>>U-U_.t LLU-U-U_U->>>>>>>>>>>> O0UJ 1 « 1 O-tUJ UJ — UJ ZH- HrnOHHy- h- u_ 1- <o Q.Q.Q.CLO.o o UJ o QfZz z o z h-
O r-i c\j r0 -J- ino h- oo o^O^ og ro'-KNJfOst-lTwO r»C0 > >-<'HrH-HrHrHt-lr-lr-(rHC\IOJ(M(N|
# * -K- -H- « -M- « «•}} * # -^ •»« # # ^ ^ # •}(• tt -K- *- »! *
150
>v Ol CL— sO LU UJ
-O —fVCO OO OO00 2:2: II •
00 UJ 00 x>< z>o—t"^ O >0
00 UJ 2: LU a: 2: in o^ r-t r-«
UJ 2: •-< 00 2: >-»<>1 ••* • —»
1 1
21 M r- 00 1 -H V--J-) 0. »>com CL ro ro«-• h- OO X h- — c\loo<< x*t • •> LU *M —1
t— 00_J X 1- ZCCh-V- LU »^CO 0000_JLU< h- 13 Z _J <hOO -\^o^ 3 3:
oo_jlu<:2:> O 2T UJ < XLLr-,- ^- • • 00 00lu<2:>>-<—4 Z UJOO—I > O—
w
—. ins —4 < <2!> >—
1— 1— oC 00 UJ00_JX t—
<
OOOOO <3 *• »>in | LL LL
*~**-*)r-cC QfLU 00_JX 1— LU ac LL-J2TZr Luroco • m «-» •—
f-ar a:-J<2; X I-LUOO a: o<o< cr:rO »r0 r-l <ar_i<r<c£«-' l-UJOtDZ<00 < >•— •^ •» < r-
_J<<C£>UJI— 002!<ujoOX a: 00^,0000 2:^00!^- S r- OO<ar>u-i^-h- 2<LUo0_J00H- UJ LUQioOLU ct:mroc> 00 00 I->LU>-«|— £X2r—
1
LUi/)_JOO LUO (~ 2:0- _(_) OLO • • < 2: Z)<— \- aLZa: >->< _l00 UJLUXZ 2: —"<2:2! oorOf-t*^ LU 1—4
o:zo:«< > LUUJ2LL0 UJ »—
1
^ ^uu • ».(\i •^
o:«-'< QT2'-' LU2IO <2!_j U.ZO to »»m • 2: 2:< c£2Tlu:Oc*: O <ZooD r— oo<rai mr^-ro Z aoc" 2:won- a: a: < 2: 00 id 00 cc uj 00 2: C^O 2! • • z> a: OHUJZ5h-C^2:UJ< 00 ID 00 c^ UJ UJO LU -lOOt— UJ DVSvO a: LU LLk ctzuji-'c^cx: 00 a: lu lu 2: ct:< Z3 OOO Q- ocmcMO^zlumq: uj ujujsict: 00 O Oh »-Q. • • «o h- 2: 2!—>0C LL'LUh- 2:ac" U-iLUOO UJ —II ' 1- -r-tV^ • 00 r> r>
>->-t-h-Z >->-r-r--LU QC 000 _J>- ooco »>oco a£ oi a:LULUr— -<<•-' lu luk r- <r< 2: !-«<XCO c^LOr-o •- »-«4 UJ UJZZ'-'whw ~z? ~Z •—<— —"—
<
-y 01- 1—
'
>—« rsj • «r*~ LL a: a:OO •—holq:gqi >-> >— a: a:Oc X UJ Z<CoO U- •^<N(JN
LU 1— 1— OOluujoo 1——OO UJ LU O") UJ <l-H-C0 —v^—1 •"0" 2! 2! 2:O ZDZ>>—• -«2'5:<t 33 -«>-' 2: 2: < C£ 00 »o 00 cnj ino O O CDt—
<
ooo^orsisj aa cl or 2: 2: _j z:_i UJCNjOslO^ • 00 00 00c£ a:ci£:Q.Q-t-.HHU. CL at; Q- Q_ 1—
"—
1 LL. 00 s:>-3^ 2Nrfl »>v < < <h- •-•-jctro H-l •\0 >>»O< 2!CirLU<. y— *. »-h • O O O2: O WDcCCO f\i>vcor>- UJ UJ UJ
O vO <—1 r—t•—
• 1—< •> H CLO <t »m • •• £ a: a:O •-•r-»r\l<\jc\jr\JO CNJ OX -•V..—((\JO O- CL a.z. f-t_1 1—1 r-1 ,—( t—1 ,—
|
•* ino> ••c>
< OOOOOOOOOOOOO—i
C\J(\Jt\l(\l(M(\|f\| OO
•-1 •^000 1—1 r—4 r-4 r-^ f-W rH •• OOOOOOO r-H »-vD »>s»
UJ UN LO LOLO LO LO in «• CNJ r-ICT> •V^CNJ_l OOOOOOO O rvi»—
1
rOrO^vfM • <t-r- 4-t^- >ti^-CO OOOOOOO OOOOOOO O »~ •« CJ<—ICOLOvO O »•
< 1—1H <—4 r—) 1—1 ~-t rH in 10mm in in in 1—
1
OI^- •^ * « • t- •-1—
«
••f—
1
•t—
1
t- »» CNJO CNJ^V •"<\JC0 ro^. ro*v. r<-|^.
<<<<<<< 1—I r-t r—1 1—( 1—« —4 r-t < • «~ 2; •4- «—• -& ZLO 2:0 2TLO
a. a. cl a. o. a. ex »—
1
XX 00 ctroLOfMo dc: »• a: •» ar ••
t—
1
z: rHLnc> • LO LO in1- • • «>^ CO CO CO00 *—
1
•^^ro c* 0>1—
I
i- 2!rHC7Nm 1 2! t 2: • 2: •
1- O »o «m a-v. a^ o^>< XX 2: 1—<^s •(%) »• -iro — <*- r-tfT)
»- UJIUIU LULU LULU LU LU LU UJ LU LU LU LU »—<I-H z> h- LO * »-LO l- •- r— •• H- ••
00 _J_J_J-J_I_J_J 1 1 ) 1 t r 1 _J cccc LL OOLOOCX* 00 uo OOCO CO CO CO CO CC CO CD CO CO CO CO XI CO CO \-\- 2: • • »o 2!v0 2:0 ZvO
UJ <<<<<<< <<<<<<< < << LU 3 »->Wv • 3r*~ DN :or^2: h-t— 1— t-h~ i~t— 1— 1— h- r- h- h- h- y- 2ZX 2! u_C>'-ir\J^ LL. • u. • LL •—
1
—
t
-4-n0i—IvQ >». ^ ^.LL U. • • • r-l !NJ rHUJ LU • CM-t » 9» fe
O O N^^-l ». *. ro ro nO--<c\Jr0-4- LO OLOCOC> O
r-«(\JrovtLOsor- COO •—•»—«•—lrHt-4 r-l •-<rH rH ^-tCOO^ CNJvt ro>t <i-v)-
# # * # # ##*#--!* O • • •* * •«••« • # # • •}(• •»
151
—
»
—. >• —» —«mcocovOO.-iin>OOOominuMnoo r<iinininoif\oo^ooinin Mnoomoin —« o •
msoc^c\iino>o<\lo^o co r--o ror-o in —tcocMn <-«(*- cmp- cMcoroco>o c\i cMr-coinmr»-vOc\j• ••••••••• «...•«...*»•« *•••• •mm HmCMnHfio^
cm .-i,-iCMCMcor*-0 r*» r-i.-i,HCMCMroco^sOOcM in «-« r-t cm c\i co Oh-O II r-iCMcMrorOco cm in rH_t st co • • x>-l CM CM II 2111 cocMinr-rooooo 11 OvO—<o-i- -too mining 11 in cocoomo Dcoin I 0000000Z3 CM CO r^- CM COO CM inO IDr-r0'^Oina>C0<Mv0Cr>Crs CM Z)«d-CMn—4r-c0 simo noooocoo^ >t 0^ r-l CM CM r-t v£> !*-<?* S^CJ^r-t.MOcOsOrOCOCMvOCO ST CM r- CO vfO vO I
—<co X in in CM COO CM in
I cm ro ino !* co co o^cr> 1 r-tcM-tinvOvOr-cocoo^o^o I cMromvOr»-cr* a.ror— LucMinr-cocochcr*• •••• • ....... 2: • •
I/) l/) (/) LU h- CO cm in CO >t coo•inininooominm oooommminooooo .ommooo -^ u. • . • • •
oiinco^-iino^in^fOvO c£r-orOvoo,, -tor--co>tcMino ar:r— 'Hrs-cor-r- x xcr*>or--cor»-corM
I•••....•. 1 ••.......*••. 1 • • • • . . 1—mm oocMcostomcMn
o. r-ir-tr-tcMcoinin a. i-h-h—ir-i cm coco vj-\0 00 cmo ex •h-hcmcm.'- or*-cr< • r-tcMcMCMcoX —1 X .-icm x -J • • h-LU LU LU or.
cco—tr^o—»ocoino ct:Ln>tcMvO'-^OLn>OsO^Ovj_ cMc^ cc 00 •& no -o co cm o<mco -0000000lu cm inO cr> f-i ro >t coo LuO'-<cn^irOrHr>jLn(Mr--rO'-ia' LUvt-j-sj-cMcOvO ooro-o ooooommo_ ^1 r—ooo cMn >t cr> CLrxir^-oococo^ocMcocMincoo Q-OsOcMmoin si^aco >ooocMcciH>tVCMco-tvOr-r-cooo >- —< cm ro -J-m -o r- co co sO cr> a* >cMcoinvOvOCr> cm I
s- < <M in r- co co o^ 0^
X. ••.••»•• X******* •»»••• X ***** * •^ • • _J**.**.*«-» —
«
«— m Luinr-Or-tooOvoOOomoomoo inininmooinoooinoin inooommo — o ••X in co —1 4- co ^-o cm cr« XvOO^cMinOvj-or^r^—iroh-o x>oomcMvO-oo in cM^sOvOr-c\ioI— ••••••••• t— •....»•.•«... 1— ..,••• • —.00^0 oOCMr-cOC>vJ-Q>>*-O —1—<—.cMcoin>t O i-tF-^r-^cMCMro^^Or-rHin o r-tr-tcMcMino cor— Cr> • 2 r-trHcMCMco_J f—I I r-tr-t _i cm 51 • *»h <
O cco--<oc\icooin.-HrOrH oomvOorovOt-HO'in^—<coo oiaiahm^oo oincMO \—000000000 —to—» in —<o r-o r— oocmco>±o —tcMrH—too —tror—o </> sf ir\ <f in >ooo —a-to 0000000scoinaoococo^vfo srcj'.d-r— r-r— r-incMr*-cM>d-r>-a> s:co--hvO'Hcooon r-tcocr> Q"ininp-or--<-<<i"
.-tcOsj-invOr-coocr' ocMro^"in or-cocoo^oo^O r-tcoNj-vOvOCT'O ocm-00>> ujr-iNi-vOcococ7,,
CF>-—......... •—>••.......*... —.«»•«»»• oo... oc * ......a: o_ 02: vOrovOi^-CMnowinininooommin —-oooominooooomin woinininomo u_ 2! • •
»tr-Ovt-r- coco .-icm oo^cMincocMr-st or-cMOO 00^ <*"•-• in vt--t I m Luin^m>tcoin.-<3. *......• 2 • • • • • ,,....,. 3: •••••• • 2o^N lu r-i vQ cm co rn co rn1/) ^-1 r-i ^-t cm cm ino 1/) r-i^^HCMcMm»tinr^"-t>d- 00 r-tcMcMincM i/ir—co • a: r-ir-icMCMco<t t-t <t hh <i r-t <r • ••—< oU_ LL LL LL . 00
or^-com^-i^-iocMcn vtr-in^-icMr-CMn^-tcooh-cM omONcooo rOvO^t 0000000co in r-4 r-*o r- o^ cr> co r\j-4-in.-iOincot^-4''-^f-i<J->o roco>-tvO>t'-^o in^nh- ooooomm^cMvOcoin-ocMroco ocMinvQinvt'-tof'-'-ivj-r'-co \OCMnOvOOc> orn^j" oo^covuocot-< ro >tm r»- cooo ocMro^tinvor-r^-cooo^oo^ <-<cM<i- v0^oc>0^ i-inOo r^^vOf-oocM^
vJ-.» ....... (*<-............. 0»«*»»«» sO • • • CM*******in r*« -4- >-* incMf^-Oror^-rOr-toooomminooo ominininoinoinooininin oooinoininm o o*******»-4"r—O ro vO cm co co cm •-incOrH^cOr-(vOroO>J- i-fOco ••roa^roo<t-Oo •> m "Ovt^O^-oocMin.******** m************* vO******* >ooio^ f- in>—irrnt^-cMZ ^H^-I^CMCMvj-O 2 r-|i-tr-lCM(Mrn>tinf^-OrO 2: r-tCMCMCMCM 2>i-C0 • Z rHi-ICMCMr<1oC iH cc i-<r-H a: i-t ct: • •«-• c£.
inroLnininos
>cM<f'-< coOvOOsOroino^tinrO'Hi'- ^->oh-vO'-«cMO o-^r*- 0000000roo «h vO 1^ s ino co r-10 in in ^00 4- cm cm coo -tin inoror-r^soo cm-h-J- 0000000
Z--«o>t>0vf incMroco ZroorOvJ-^cMOa>sj-o>tr^co 2' fMcocMrs-inc\jco 2TincMO> zmin^-tvcmoroOrHcMvj-ms&r"- cooo QOcMro^-invor-r^-coo^ocM^ oocMv3-mvor*-c7< oo-j-co ooroor-cooo*—«•••••••»• 1—1. ...... ...... —••»•.#• 1—1 • . . 1—1 .••«»••h- I— \- \— \- OCO-HvOC^mCOoinininooinouoo ooooomoir.ooooino oiAOinoomo o o*******ZcMOOrOvO'-tf^-coco zm co rH ^t h- -( in cm CTtO <-hmO 2: cm co cmO vt" co s 2! in 2! rO in h- >t cm ro ro!D«. ....... 3 • • • • .....*••• 3....... 3QOO 3 vfOOCMr— —
<
LL i-H r-l CM CM rOO LL ^Hr-«rHCMCM.-OfOinr^-OrO LL —I r-t CM CM <-< LLsJ-CO • LL -Hr-iCMCMrO
o h- co c> >j- co ro -J-o ' oinoromooino^inr-o of- coco .-11^. .4- ^r-« 000000OHOomtin-oo 0vt<j-cocov0socov0oooro o ro >tts- s ro co cocm ooooinmO »* <M in ro >t —t c> co o r— r-t cm ro •--< s f^- coo ro r— co o -t CMn -t r-t co v£>>4- oco^^o^cm
mo cm -tm vO r- co co cr^ oo r-< ro <J- in -c o r~- co or cr* 0^ 0^ r-ocMroinor— a> co roco oo co in r— cocoes......... .•••»••••. ,..-x- •..,...-; o • •-;; •••••••
152
•4- —• r- ooooooooo v.
CM r-OO ••••••••• sOr— • • .,-trH^r-ic^HOH^ V.CO r^oiricgo^oocMr>mi-t<-i«-iOfMr-i>$ co t-i _i in .-tr-r^ cm •-••*} cor*- o • -^roincO'-«>ti--trs-r--cocooor~incjNcM
mcT)oo.-«r\jc\jrovHr\vor»-o> Or-iv* o_ cm <j- 1*- r- r- cm >t <r <r com •>!- cm c\j cmmr-* in -& ll! oooooooooooooo
o i! o^vOOinoocNjoomiTivO <-» ••* • ooooooooooooooooooo r>vOcxDomoo-4r^>t>troiv- --< »«ooco oooooooooooooooooo soinsOr-coorM^^or^-co u <f- • ». v00oco<j-Ov0^jco<j-o-£>cmcov)-OvOcj» I cm 4- vO r- 00 o^cr>o 0^ cr> cr> 3 • v.oo r-isOr\jO>too^-nr\co<\iv0^rOvoO>i-r^• •••••••••••• SZv.sOO"1
I co f*- "* r-t r-4 cm cm <\j cOcoco^" -J- inin inr— 00 1 >t • • ro• • ooooooooo a. »r-i>v r-i
in o^oo ••••••••• x •» »-in
vf 1 • iho^vOvO-ivomo ujcOco • 3rcOcoHeo>tf->tf-o<t''--«r«-^-$- ^ininco•4
1 Q.CMCM>to>Oin.-tOCMrMsO «— co »co oOr-«,-icMincO'-<vtNOO-HcocoincM>-^oX cm r-—1 cm cm co >J- in vO I
s- CT> iv •« <cM.-HLnr*-Nj-cOcgsi-Ntr-icOcOcococOinID (— V»cor*- LL OOOOOOOOOOOOOOc£>t<-<oe>Nj-ror-cosOO>t oomcoo ^oooooooooooooooo
in ixjco^Hvor^^^co-^cMrof*- win • • oooooooooooooooor- Q. vf cm ^- in ro (^ --^ >t vO I
s- 00 DcO-h^. I— OOCMco<)-OOCMcOvJ-OsOc\ioo^acj» >- <-* >}•o r- co 00o o o^o a* o* • *cm oovOOcor,~rH»3-oo.--<inON cMvocncor>-• x*********** uj »-m • Zm^-—ir-^r-icMcMCMrOrom^-4-Ntmin000 >— o oifor^m o• • >- ooooooooo • t • »• LL
coin <roo • t ...... .0 z^^nOcm.~i _j • tH—<ococococoror-o ujcocmct* _jvf^cncM^tc>ooaN
rs-cM'-icOvOrom
•^•o ujocMrncMn^ocooocMNj- lu * • »o <cor^ooinr--mOsO'-<inoinr-<i-»cor-i orMvO^^cMrn^-vj-vor-cOr-H ac hs • 2rcMj-^"inin<t-coinsCc\jinN}-v)-vi-coin
oco *cr>eo a: 000000000000000* i/'>h-co.-i.-i.-4r-.oa^omo^ oomh-cr* •» ^oooooooooooooooo00 >- <nn r-t *&m r-m coo —1o cr> cm • »r*- »-iooOr>oooooooooooor-o coror^-cMvtfMco^Hromr-coo a: • vvCmct> oooocMco<t-OsOcMco<foocMco<f00 i-trn-or^cocooc^CMX^cA uj^rH »-cr> sj-o^cn^o^i^r-isj-coMin^tMvO• • <£••••••••••• a.cM rncr* t^OcM-OO^r-i^cMcMCMmrorO^'vt-^inm
coco 00 o cmcmct> • _)• • lu ooooooooo • oocvco »v» <
inco 000 •••••••• »vO 2 «»o\o >Oro • t —t—< cm r-t ino ro co cm co o * •—* • -• cj^cooinoo> -4- c\iin'—'cocoininco>to oOrHCMco^oo^cooo^cMcM occM^oor- ar:in^-omo x m'-nNOincom.-»^0o^rv-<"r>
>^-4inrHr-icMv-orO^ins0cOt-i uj «in • • ac ococOvt <-*<-* cOvf in coco inm enroot00 Qc:
,N.--tcMO < 000000000000000 vO'HO^mo»cM--»ocMmcMm tnc> »-o ooooooooooooooooLnm CMr-ICOr-OCM-Hr-COOO^ <-* •<tOy' oooooooooooooooovOa- vO cm a> cm >-• so >-( com r^ coo • »cr> • ooovOc\ico>4-oocm'Xi-<)-Ovocmco&o* ocomr*-cococ>o^o>'cr>o>'C^ »-sO »>s co^tocMOo^cor^-o4-r~^-<incocMin• • 0*«****««***« i—<c> • v^cm ^ir>ONrHHr-^ cm cm rococo ^-^"xj-LnLn
COnO r- O cOcov^cm • O• • o ooooooooo • <_>»-icomvo cj>
cj>m •• o*t«*«*«« •\0 •»••••« oCOin r-O ir-lHOo^t^O^O^O CO>^ »-CMCO *-CO-^-fJ>OOcOOC>rMCMh-vOCMNOCO^-com "z. • -4" i-h r- co o> c> vO 00 co r-io "Z-tr-t -o\ HocOvOOinrjMnvOoo^coOr^oo
c^ cm -i" 1-1 »h cm cm co nj- in sO co -< oiomcMo o^-cMincoror-"-4inr^inr-i4-rs-vt-cMO^Hino> • 000000000000000 *-*>tcoNOincMOco<-4vtinr- • • •*>* oooooooooooooooo00 coco^-or^-vj-Ovtr~a>a>o ••^.v.co oooooooooooooooo
voa^ 2ocosooa>m'-<coinv0is-o>> ^--ioco • zoooo^o^covJ-oonco^o-ocnjcj>o^ oocMLnr-r^coo^o^c^c^o^o o «^o »m ocmotnj- cMinocMNOOcor-Oxtco.-tin• • )-H*t»«*«»*»*«t m\ #f\i » •-irHsj-cO'-H<-tt-(CMCMcococO'4'4- >}-inin—iO i— o 1—us - »-in t—• t o 00000000 • uomoo o
inr- ~z. 00 ••••••• «m 2«« »a> 2f~~0 30 • •f-iOOror*c\jinmO o »»^%. • zd co 1—1 00 cm >j-o <f vt co 0^ co in co co co 0"^
COLO U- • 00 CM ^O CM CO CO CO ->t <t-OO U_0--«rM\ U-rH-OO^H.O^vJ-HHvQrriCOHCON(McooNr-i(\ir\jrONfinvOcO'-< ^-^Or-tsO CMcMcororOin<lTOror~-cM4'OrOr-<cM
O • • t 0000000000000OO OcM-O^COvt^-^-C^O^—<<X> • *CM>J- OOOOOOOOOOOOOOOmm oc^oomvOvomoNvtooo ^^ » ». oooooooooooooooomco ooNj-oa>coNtocM>t vOr~oo holacoo cMOoo<}"OsOCMcovtOvOcMco<)-OvO0^<7> t-io cm in Nor- co0^0^ 0^0^ 1-1 •>-4-coo> f-tocMco'-<mcocMinorOsOOror^rH>?-• •4t ••••••••••••# o • • •# N0-tr-<-t--«r-4CMcMcMrOcONt^"<fmm-^ !:- •-•« -K-
0.UJ
I/)*—
*
V0 0-»H LU
1 </>
mr-» O
r-4
2 1
CO ro< r-l
LL<B« 3> 1/)
< <Q LL^^ >—
«
(>0
_J >< <> O—
1
^or 00orTO Q'
<Q0 LUCOst" coco
OO h-Ol/)0 OTOSO UO
vO 00 vOZN Dh-z>m "Dinor 00
t- LLooco OQCQn O>-«m aC<tLLO ZO
OO
CM CMCO co<t- •t
>4* 4-
OCO *«
r-tvO HOOO o<f-O OO OO O
zoo ZCO000 Ocoi—CM »-«rM
l- HO O2! 2Z>cM OU.CM LLCO
vt COOOO
CO-t >t>d-r-<^- ^•4-
153
* OUliJ X> fOUJ— LUUJ O -SI-* .-I
<UJXUJ Z OT X O-Z -HCL Zi^wZfr OOOlh-OO Z 13 LL! 00>-OLL) h- Q. <Q^h-< ~-IUJ
ooa_ z> z x> a: a: <co a. a: uj x zt—a* UJ ~» 3 CC oO\ 00 _J rvlO OQ1— Q^QIZO —<<UJ
oo2:>-roz a: whzz xoo iliz h-z>- clo-o ooxoi—* it) cqq.0 oov-zooro h-x i— <u. <o "-«S ujo y-
01 —•-< h-zoozJororo: oh- <oi« o uj aroooo 2: <yi>—T.8- <o^ l— ooX)ct:a:t-'Uj zO ZO- ooq:h- ujujI— i>ia: wzzsuj
oo<uur<")< or o: •-' lu u_ or t— ujz ouj 2:2:1— 1 00 >-<U- h-o<root—* cou-12: _i <-<uju-af. 00 _jlu 1— _i^c\j »— —1 <oo02: xzoo
uj t-iarr? u_crr lulucc: _j oz Dq.5: ujooooo rouuoo* 2:01— ujcd >->ki— -. uj a:_» < zooo oo_J2:zoo *-h- or.00
h- h-< luuj(— H-<r<u_ oujuj uj<ox uj z o <s: luoi~fr h- Z _JUJh- ZZwhmh <OD Ql— I—O o0|—< J<Oa: UJO—IZ 2:
Z ZDuj<T2: 1—«a:a:oQX oo<uj <0 0:0: u_ tui— -Oooo.<ooa2! uj 0:0x0' i-h-ooujujw 00000 00 uj(— ujo: z<t- 1 u-H- luqj2:2: 00:< 2: z*-»oiuj d^m >-i2:2:< ujooo uj x z>a uji— +oq.oq;d o-hoou.ar. z h-ujar.<h- ooiiiiHJ 2iuj 2: >lu a.oouj sz^-aiozs:O o wD^a< q!:iv:q.q.mmu. 2:uj «- djdh o co ^uj>—>uj 00 < oo -< ocuj< _j X O h- otcloz 1— hjzujz>i<ziq:iocc 00 h-ioocz uj oox< o»-i < ^oo ^^t-owjoozxo. 00 u_ujuj>-ho: 00 t— a: <ioooo rr> 3t—XX mzh Dia<r<LLM
< a:h- o uj <q _j<oo _jooo »-o 2:uj_i oo^ujujz ujclZOU- ujo —<u_ u__jlu z iro<r <\iu,o o o:uja:u_t— 00.--X1—o uj h- >— uj 1—ov-<oor u.2: :r> <nj2:_j»— z^—oo j-uja: •• *-*-< <r 1— <r•— o <z acr- orzDooha^ z cc u_q_ < ^s: ooa.u_ oi-ess zh- Z oToujql 0<0o0 OUJ Oujx uj < •> y Xuj O2"ooujr-4n:oooo t— *-*
< uj ujn-i_j a 00 or.uj aro >-_joo or. oh-uj 00:0 jnizci:a<zzzz5:j o Zoocoh-o 2: Q-uj ooco< Ooooouj cz u_lu<o c.<<ujDo:Z> UJ Lui/XXX OO 00<_J Q 02ZLUC*: LLaTUJ Qi^l-ZLLiaiaaDLU2: o o<rt-o. <c? <i— u_ z < 1— a. •~<v-oo oo.t—oo«cki-ouh*-> UJ < ^vo o: 3
a. 00 ++ + + + 1 + + + + +uj o *«*»<* * ***«xx — 00K- h- UJ 21 (NJ UJ
»-h z z a:U. 3 HH X X »O »- 00 (NO O
Oi Z3 < XCL ^h- o ^-tf\jmvj-uavo o _j o •a: 1- zzzzzz a: u. ^-» or< < 000000 oz a:K a: oooooooooooo i— o »-x uj x00 uj <<<<<< ceo j— vto ujo: a: ••
z »h .•.»•.» r^- 2: •• ^-icl otsiuj a. r-i--H
•k- uj z -HcNjro-tinsOz uj vt ac tn z* cxi-o: •• ^2;o a. orr- ^^^i^^^o uj x uj cv-j-xn 0:0.0. cc -on
K- *-(N a. •• •>•.•.»•. -iS) cc x a > !- I-Oli a +LUuj nza: ••+ en cc cc cc cc cc< a to < + *-r~o •> -\- - cc-* 01—
* O XLLQ-rOfO Q.Q.Q.Q.Q.Q. •< >— <—tQ-h- UJ i-H—IC?CD C\|r-( •• ^-4 Q.O.i-l^((NI »•
< X* 00 00
OO UJ Q UJ* uj uj>-uj cc O uj cc cc cc "Dec
2: i— i— i
—
uj < i— o ujarujH- uj o:_juj* <.~<Z^ OOOOOOLL 00 Z< JE ZZ-JU. _) U_ Q. hUZ <U_
z a:a:_ioo oo oo o_iuj oo oo t— oo 2: a:zo:o>ooM- 3 UJCO •"-"-« I— h- 1— I— I— I— Z UJ hDo m —•>-(!—Z UJh-Z uj «DwUJZ
o: Z>-<CDo0oO O0o0o0o0o0v0< 5! OOCDUJ <\1 00o000< t— _J< UJ OH-OX•«• ujoKoooo ujujujujujuja: oo<3 ooooujet: <a.a: o: luqujo<ot
i— oo-i—<< t— h-t— i— i— i— h- x <*—o < <<t— i— oooi— a. o<a:_jooi—« oo oo
CC < f^ O UJ (NJ rH* -• z k _iZQ a:xzu-z> o: u.o< aox* cc o oo a: ^ o
u. oo < i— o a.
154
Z< zX f\J wLUo ZD<oO
• —»<lu2!'-«LU ooxt- 3:UJ ujOKza:00 s: <-iajujs:
t-zsaiujLU hOi^OI-l-
1 z 000h-< rOLU<z >Q. ^-t— C£LU »-O0
2Too UUKXOLUOUJO-J t— 005!lu_j3oocloo 5:0qT'xujxsoz a:a. » :D OOOLUh-LL+oiozaxz 00 OHIOluu-'X<zo' zooa. wjozv) 2:oq<ilm -a:
»•._J OOLU OLUC\JO LL \~ OOX <M U_KZ t-n-nh-Z <r<oOt— 2:2! <m2XOaToOoOH-X —
•
oj<zzzum^:LLCL<<3 h-Q^
LL IJJQia:OLL<LL»-•OD 1— h-O—O t—
XKI IZo»- z X z KLU z z Xoo zzo h-X O-J a X t-XLUZ 1—
1
Ol- l—l z M t-x l—l OH- -*_ILU t- zo h- LULU h- 01- 1— ZO h-
-J < LUZ < -JO < zu < LUZ <O > _ILU > <x > LUZ > _)LU >00O 1—
I
-J l-H Ooo l-H _)LU l-H _J l-H
21 OO 1— LU K 0000 M" 2: H- O H-51 Olu 21 LU LU 000
z < <ro < 2: < OLU < 5:00 <DZLL1 00 <r z <rO 5:a:33<\| 0000 rg 3ZLU<NJ 00< C\| Z CVJ
LUQiLUZ LUOO z c£33Z 00 00 z 3ZLUZC£LU3< 21 LU < LUcfLU< LUOO < c£33<ctOI 2: X o£UJ3X 2:lu X LUctTLUX
LU LU r^OO 5: 0CUJ3OH-LUZ 1— LULU > >- o£C?<i— 3a: <H-3a: (->-Z^ H->LUoi lu a:•-xtaio >-,<ujo >-H3CJ —H30 ZujZOQ'-HLL'LL Oh-OLL C£>-«OiLL ^-•UJLL >-«Z3U_lUOtt LUQO Oo:lu 00:3 HHCt21 LU h- 2TLU 1— mooch MOOt- X>t- tut-21 21 LU 00 s s: luoo Q£l-l 00 «:•-« 00 or) a: 00—SHLU ws:i- lu Q-ar>LU q_c£>-lu <XO LU
—<ri— .-.<l- Q_»--»— Q.H-J- OTLUh-z ~> z >— Z »-i z <-< z zOLUOO OluQO OLU C^O oluqco Ow—<0•-"-JLUt— HH_JLUt— MJOH i-_JOI- HjhhOOCOS 00 cos: OOcOhh OOCO«-h 00 CD IDoo<2ZO 00<2IO oo<c£0 oo<a:o 00<OO<)-wO <»--< CJ) <K-Q-cjj <h-CLO <i— q:o
+ I + + + + + +# -tt * •« * «
LUa:
on •
a: 00 •
LU X LU OO •
CC -04 O r- h- UJ sO 00 ina. —12: (\J < *• l—l » T-i O ^ !—t «• t-H LU •» ^H- ^.a: 5: to ro h- ro h- < f\J h- (NJ 1- O r-l K
CL »-LU DC 00 X 00 X 00 OO X 00 X OO < X 00Q- +t- LU LU X LU • X LU 00 X LU X LU OO X LU-CC t-t O •» 1— 21 ••m H OO •TO h- LU ••CO h- • •TO t- 00 ro H-
(\J(NQ_CL(\Jf\J(M^-< •• rHQ_vO » LU 1-HQ.LO •- 21 '-fQL.<t - OO —to.ro •• LU r-ta.r\J *z O LU 21z> < z O
LU oi 00 z> < z3 Of LU LU DC 00 LU CC oi LU CL 00 IU al 3 lu ct:
001— lu _jooo:lu a: \- LU LU K LU LU h- LU 00 K LU a: h- IU-JQ-l-OZ<_l LL z< LL s: z< LL CC z< LL LU Z< LL LU Z< LL
5lcirZci:> ooo LU O—JLU00 O-JLUOO O—iujoo 21 O_)LU00 a: O—ILU00LULU<<Z5LULU^Z H- -T)X»Z LU — Z)Z)Z > — Z)Z)Z hDDZ hDDZh-LUCL>t->l—0< < 00CQLU< 1— O0CQLU< (— OO CQ I.U <Z >- OOCQLLX LU 00CQLU<< C£ LU Quj<<O OC t—t 00<Z)Qi < oo<x>oi l-H ooOaC 1— 0O<Z)C!i z oO<3Cr^OQ-Q<ct:oOO.-l>— Q <l-OI- >-H <l-Ol- a: <l— Ot— 1—
1
<hOh l-H <l— Ot-LU O CC t-
(NJ s: LU in •—
t
vt rO 3 (NJ
z 3: z 21 z oc z —
»
Z O •zX y—< ST Q. a: O a:
00 1—
(
00 00 CL 00 00Q. < < < < <*** *# * *-M-^ # ^* #-** «#*
155
<MH- UJ zee QilU O0
z OOCMCL hq: OI UJ»— UJ -JUJo ujzO O h- 2<wcc UJK
Xoo >—
1
f-< OT > ooa_.-i •—0<0 -• Z< >-*
l-X h- ILUS —I-H IJJOLL h- a. oo ZaTOK < OOCDh- Z _l o LL ooZUJ UJ < UJ XZO > z a. OZUJ OoOO ZUJLUCO 1- X<S •-•
LUZ »—
4
3ZJO <z k-CQ —'O0Q- O O*-"-1 cC_JUJ h- OUJ—
I
UJIZ Oa: OOQ Z 1- H-_j o o:x«-m>- C£0< oo<0 K-_J Z Ml/)IO <
UJ < <h-3:co 3 X STK-t- <_>o-J< sruji-uj^: oos:OUJ -— OOOO oo 1 < -I iai OOcrlOcOO<o (\J XrHfNJrO ZK 1— Q XH-<-<oOUJO<cQ CjX«—z »—oo< z O-^ •—••—! UJ —1 ZOUi uj3:3:u_cnoo zj ii-m ooooo < ZIII CT—
'
UJZh- —too OLL OOZoiO—<oO <UJOO X <xxx .-tUJ< CC*-*O C\J^J3H-UJ00 x>—uj X5IUJ o cC o> <c£0 soZ-Jtous: ooz \— s:n CQUJUJUJ LUO< a. a. a: _)_.<< < r-* ou_<>-iujac:
UJ a: uoo h- on 1 ZOI 1y)Xa:ujo»-'OH-l— H-ujZLUUJO z <UJO tU-00 OOOCtTLU OH XI— 00 <5IwZ3U- LUCM^vO OSh I— ll —
<
J UJ>00LL<O<00 CDO"--H->-«UJ CL + + + »—i •-a 1 oo 05!<0 O —ILUUJZ \-Z>H-Oh- 0>-i rOLn Dh-Q _j •o 3: «o0i—'IJJ_J(M ZOOO'-'O^OOOoO Z UJ a. oooo ouj i— _iozzujs:_iujz:rujoro UJ (MLULULU <<h- oozs: -isa: X<C'-'0-'-h<ouj|-H
oclui— ZOOO O <r _J>~<Q.00LU^-X<O00>OQ-Q.<z z <UJUJUJ aCI—
O
OOQCt— <H- <0 U2 OOZOliiwO xooo UJ<ai •-•t—z LU <a: cMi-i— l- —>
MJKh oooo u_ UJ UJ<ooZooujZZZZZZUJZZ00COO LLOO <S>c£cC \— *—o oo s: uj uj <r >-i »-. 1-.> uj a:00<OO LLLLLLLL OoOoO 00O< <l—<Oijj nhclo. x cr:a:Qc:<Q.uj<v-aro
•
zat—
(
MMMM COSTS 5IU-CL 0<OC 00 5"HOOU CL CL O. 00O 1—
•
c\J
< z> <r • r-l
i—
i
Hr-lH X CM Oh- K-h-l- o Z •*
O -J-J-J •» < rH< Q.Q.Q.
oooooo zXo eg
r\j •* •» •» < 00in z *-!.-« CM CO X a: LL CO O•• .—
)
< ItHr^H o s: •-H O s: oi-i h- X U-XXX •» h- LL CC —t xat-iX 00 o oxxx X Cl LL z UJ O i—i •» •»•«£
X UJ m •* •* •* H o O o h- O >ocor~-ZCO H or rHCNJrO a •» CO »-H •• 1-t
• -tan •» o c\J>>> i—ico 1—
t
•» K CO CO CM COCMr-lCM t.-tHr-IfOOoo LL <UJ > UJo 00 t-H UJ ID LU< UJ cC UJ a: a: 1- > O -J h-00 H- UJ >—
t
CC OiLU LU o a:ooK- UJOOQi^) <Qi<OO z< u_ a: _J_J_J-I a: _iu_ u. < -J •-" o < > zUJ O—iujoo UJ UJ 00 H- 00 <_><* ZOOX-KI-UJO'-'s: •-OOZ oo UJHI-h- U-UJ2 1—4 z a: UJi—O <hhujzzz>ms:
00 CD UJ< t— OOoOOO U-h-
<
_J < o 1— (Jw >00>'-iw*-|<Oc^UJ oo<oa: o <UJUJUJ o<a: Cl a: u. <oct: QOO<o:cc^oooujZ <KOh- z Ohh(- coot— OO — O-JCL <_j_iooq.clq-5:_)>—t-4 »—
1
cC»- ^( 1- r-l i—
i
.—1 UJ cc oj cO3 z oo h- u, h- s; 2! oo 51o o UJ 00 LL _J »—
i
1- o orcc 00 h- UJ O a. h- CL O LU
< H CO 00 O _J K
> UJLUh- O0UJ—
1
ZJcOp-^_J •x: <-*
»—
t
oooo:o <a.< oxLL H O
Ol-—
<
Oooz oso<t oX^ZLLo LUt-iO
LUCL O0OOKOKUJ<
: OOLLrMOOOIUi—h-
4
i-H-LUZ •
OOhhCM—(D< MU.I
ujsru'oci—o 1— O-Cl<uj< i s:00000 + LUO0O LULU_|LL—ICC5ID«->>CL
o<11
a:a
luooo
^: *oo<cmcl
00 CC-JUJ
LUONmUJI-wOh-l/1UJO<LU00_JOh-
«••«•}> *•** *• «• }( ««
z<Xo
< O0
X UJ
a t-
156
UJ CC i-l (M —LU(/> LUCMZ> lucl mu_ > > zz>lu oozUJ -* XI— mQ O Q Oluoo CMI-O 0<Z> Z>-< UJ 1-00 II — < < t-OO ZOoO JIC? OZO LU O OUJ OCCjm Z >• hOJZ<Z oo0'—<<^ OO Q. Zh Q-<LL O C LU I— < UDI O
luoooox2! z> oa < lull i— i— a. •— zlu m«ooo cmmI— 2IoOO O h- O ZID i-H c\J O a! _i <l— cnjoO O O cnjcnj
< m I-LU2I Z OoO 31- O CD zo 2:0 C ~ -J<ZoO_j lulus: XXMU.2ZXI-11J *-* I— LU O <—\— «— <(J5 <0 00 LL O Q- mj< -« LUQ 00 h- LU XXoioooouji— 1— i— _ioo oo< x-* x« — < xdis:a:uj>-Hi-Q. Z Zm<oO I— O _JLU 00 cC OO 00^ Z LL luCLO^ o03mhoO Z!2Toz<uj s:>- o 00 <o <qlu a. q. cm lu a zluoots::*- <<a:oa:i— cdoooo z 1— o lulull 2: 11 2: 11 2: cl cm mc£ll<i— _iluoooo IIawi-tuoz lu o o:i-ll >-+cc ^-.a: < o 2: zaw^^oiz 1— i—
CLI— _JLL<2: 00 00O I—O Q-Z3 O. Q. X < <CL I— _J H<2!<<o0CL cdO >-h 30 <S) ZZCD O*— 0« O CMOX^X<ri— clzocx:o 0000aairH^-a: .-12: lulu 00a: 00a: 1 z—<o o oolusilu h- a: c/>oo
OOOI—O LL CM ZLU + XLULU 2ZQ. SQ. (M <LL LU 00LUOOLU •« LL LULUI—O<OLU00 Z —00 LUZ hQil 00 XU-C^I-LUI— I— <UCQLUO0 JJCC _J I—OO < 3 I— UJ HI- OO DO -J 0<LU<LUOi 00 I—OO<£ IDZ< 00 00 X h- <tX O LU<-< LU"-< QitvJOOO<o>3002roO<IOOoO ^ (Maosoois o oz oi— • a.ooi— 1— at h-a: ll lli——• — a. luO<'J>2:2: + +LULL— m* Z;"-1 2! h-< CLO 0-0 >-< "h LUZ LUl—ImI COm:D oOOO^OtTLU Q 2! • 3 213 2! 5T ZOO»-iCMO(_) O0 P'CLLUO l/)t-iZ:i— Z CMCM m*Z> a: m*Q_LU LUZ LU2r Q 00Z> <m-« <LU00CM'-'ZI— LUIJJ
luoo t_< < < 2:2: <a: lu 2! luo luO 2: ja:LU2a:ujX(-i-1z< <r r>3usirj^z << 2ix a: cc —> a:-* cc>-* < o o a.o <s:<soiz lulu< I— 00 m- m* 2: XX I— CLX—I Q-00 CLOO OCl— <LU I <(— _JOOX I— >-h DDWDOZZZS lu i^<j> 21 CC U 00 00 O I— 00 00 00 + 00 .-02: 02: 2! SI GO00_jz<lu Oct: a. luO a »—.•-LU ar< a:< lu Zaiooo 00—isi< luOo:LUOLUq:Q.OLU O LLLL Q-OO LL DII OLU OUJ OO Ow LL'_jCMLUO.>-ia:LLCLQLU LLLLSIJkDUf- «-••-• Or Q.3K LLC£ LLC*: UlL5:U>5-WoO|-MOOh- mm
OO LU _J Q•— z o <M + + + ++ ++ I
CsJ -J 00 * •- M* Z
LU U_ 3h- O CM a< ZO
<<X
1-SIS
2! LU CM X eta:LU X 1
t-4 00 LULUX CM CC Kl-
X 3 1- C£ a. X CM . •»
•> 1—
t
< _J •> CM CM « Z CM»-<•-4 2: LUO. Q. 1-1 1- 2: f-) < CMCM*r LU Oh 1- 1- LL r-4 CM LL *: 00 CC >«i X XX
CL O-OO 00 x> a: LL > > MH *• UJ LU •k XX+ O OLU LU a. a. Z) O O V- H- + »» •*
aL~4 ••H- 1- «Nr\CQ C^< cr>< • • ^hq: t.^1 * O ct: CMr-lCLO. 1—li—ICMO OO CM •• r-4 •> 00 (JNH •« Q. •• Q. »• LU CM CM <-H CL Q.m Q. CM CM r-t CMO >>
»—
1
t—
1
1-O
LL
LULU r-t O z LULU 00XJh- DC DC 00 >-Qrr >-CC >-a: Dt- LU
LU LUQd_J< LU LU Ct!LU 2:1i-LU KLU l-LU 00 00 LULU00Ct:_J< t—
1
KU 00 <z I- Z)LL LL 2: -<LL mhLL mhLL • _J LUH O00_l <Z a: -J_Jc£z: <o>«-< < OO OoO OQiOO QioO 0^00 CM LUO CCh-Z< 0>'-' LU<< LU—'LU5I O lu2: — 2! LU h-4|OZ OZ OZ LU Mn-th-< ;
•-< <I LU LL1 >—< 1 U 21 00 l-h-Q-> _jo>ct: i-< o< 1— 001M«< HH< M^<J _J 1— •-"CDoocl_j>_j>— 0>aT 0O0OluCj LUO<LU LU <.QC oa: a. OOQ^Di CCCC CCCC LU < LUOLULUClQLU<0<ILU O LULUQ< a:_joot— cC I9h _ji— 2: <CLH- CLI- CLI— ^ CD 00_J|— OoO<QiO_J^I— z l-K
3 LU z H-
1
i-4 00 LU 1—
1
LU cc < CM CM 1— CMi-« s: 2! 00 UJ CC CC 1—
t
CM X Z CM 2: 00 H-> c^ LU 3 O a. LU MH —
1
< > CC LU 00a LU ^ Q. CC cc CC X Q LU r- LU< 1- O a. a. CL < H- K
M- «••«•«••}<••»«»• #«*-**# # * -Jt
157
LUcCuj cmcm (— oLUh- Z2 < oo2I< <<00qC 00i-«0 IIU ^t—
O
r-i lilUUW< uzooooo 2Z>—lu X<wQ
zluo »Z 2: mXW•"•OOjWmZOw of oujOOaC 3UJ|— 1— 1— -JO0
^_i Luooia: <XO—
"
OO-H-00 *i 002ILU 3< Jzs:i~zorou zi- a:XI-h uj oOaiOXmZ <LUf—
a LUc£ «-» O 3a. oo r- -^ LU
1- 00 32: z 00 K CLU LU z 2:t— 2: < LU DOO 2: a: 2: l—>- o 1— 2:00 o o Q
z o LU:*i < t—i z00 1— o < olu 00 o y- 1—
1
a z r- 00 OO—
1
3 2 00o < 1—
<
<> LU00 LU LU LU 00
00 1— LU t—
1
< w < O0h- 1 _J •— zoO 1 3 1 3H- A y
1 CC3 - -* A LUo— 00- -(V
oo < zLU r- I— h- OUJ LU21 00 LU h-ioO LUXUJ 21•-•zo 2if-4_juj a:>— oo —hOZ -.^Q.rD'-* Q- 3 h- OO
•-" h-CLOOO -< O_jooc*r luk oo>-coz o co<oolu oZcdacOLUcao-Ouj>«I Z>-<0 O wh-oHH^|- HH U_LUpH<.00 t— LUc£ooo ooO H- r-tooujc0<t3
mccz ooLuoo<ra.oo5: 30O<<or uja:zz uji—.at: i
ooc£c£0 o r>—>u_5:(— lucqolus u_a:o_i i h-H-af id 5ZLUI— ooar^'-i r-<i—
^oo oOmwu^v) olui—< i— oo ail— luo: Z—Ilui—cnjoo u_ x>-iluu-ooox ozzo a. o:luooz)<5: o
>-UZSI OZ h-2" 3 •- LUhhhicCI 00 I— c DC
X
CC LU_Ji-h< Ko:ioll<muj —ic£ c£ IZZ 00 LU r-i CC LUZzoi^ooumghhi-z uj o>-o Luz)oas:oia:<i-ooooluzu. i— oo <»—lu5: zlu<i— \-clcc ii ocq.<»-h
_j xlu o<oo oo I— •-< ccar_j ooluu_oozo< _jooCO Ol ICNJUJ-JLiJlUZ 00<|— (_) LUh- >-cC ZZ>\-CCZ 003E •ooO Zo0333—'oi'—O 00ZOZ oo ^ZDa: LU»-<cr:<Olu zcd<05:jluoo5: lu a: lu cc cC\ucc\- o_i2:cr:<oox_j>-'<30r-r-iZr- ujoluoo ^zkili^clzuu.^_J»-iQ_ 2!OO00>CT_J_jZLU< f— OOr- O0 UOC —LU HH<r- LUH 00<Q-Z < <</) LUZ< LUZ c£l*-
lud;cc:lu(m»— t— i— ioh q;lu_j>-i ooorrorrt— Oluq_ zLU<oODUJOOZZZZUJ2ro 5" LU UJ_l3 i-tt— Z<"-'_J QDh- mLL20<w>-| w>ljj H-oi Z ZcqSO ooocQ LuooaDt— C>(X<h-< lu H-. _j x a: a: a:< Q. u_o lu •-! ll, <'-, lu >o03U-c£oo<3<.luo<ra:coi—uoaanoooMZi- t— Or-ooa: oo<oo»-iO<i— a. c£
Z)oa:
q.o t-O 00
o z> 5: s:•• >^ O cC at
rg o •» uj lu•• < < ^-1 (— rH i—
• (\J CD H- i-i ».i-h i-t »-(\j
Z cc Q oo o •• loo o •• ino3 >t O ^" LU CT»Z r-IO <-ILU r-^O r-*VJ O02: o 2: lu ^n z.-< zh xa: zh la: zo a: o xo-J cc ll 2 u. llihxq. i- ilihxo. ll \-
J— LU cH •• -*fi> LU LL. ••CO »"X •-•••- Qir»-Qi »-x ••••. •• CO-CCZD \— >Orot^-Z t— Q •• inx <£) • 1 —ir-iro a. »-o h- »•
I—«f-<>to^ a. »-o
X ••O'H •.»•.» S CNJLOXX X--»-^-H>-tZQi "+00 IhhhhZIq: »>+ooO0 ^-4*<NJ CLCOCNJ ^ r-(i-lrHst'-<'-<0 < Xr-tX • X r-l r-t Q. Q_ LL Q. CO fO »• X f-H r-l Q. Q_ U_X Cl CO CO ••
<\J LU h-Z LU Z) LU 00< > 3 -J h- LU LULU CC >-LU Oi >- LU OlX QiOOJ— LUOi_J <Qi 00< 3 I— h-LULU <U Hh- LU LU |— LU (— LU0-J^-<0< >3ZC? «Ull OZZO —<ZZli. ozzo ^-<o<zzll.
OQC: ZO>l— I— (— LUO O^ LU a:_JZo0 ZOO I— c£_JOO00 ZOO I— Q^ZJOO'/la: luk-hO <>HLiizzz>'-"iiHS a: luz><2: <mh|-modmhz <>-h—<i— ^-oowmzO H-O'-" >0>>-">-'»-.<oi— Oai ZcQX > oo oo oo _l •-< cQ oo oo< >oOoOoO_I'-h>cCoOoo<u. <tocc QO<cCo:a:ooo<OLU Z LU<Qoi QooooajQ-oi<ooooQ: Oooooluclo:'0<^/>ooc£
O-JQ- <_JoOQ-Ci.a.5:_JO—it— LU Ot— <H- <<<l— oOQ-f— <<l— <<<t— 00O-<l— <<h-CC LUlu cc cm ^ a: <21 2: CC 2! O I-i-» I— o a: «/> 00I— —I O • LU Z
o -J I- >-
r-l 1— CMO 00 OLU r- LUa: 3 a:a. O a.
158
I/) 00zz33ccccU-IUJ
oca:
oo
arc?LULUa: a:
cccc
oooo
LULUh-K<<ZZi—ii—
i
35: s:
LULU
OO
LULUhh<<
SSICCcCLULU
LOvOSIS:
LULU
1 cc cCLUO 3 0:3CCZ z O 10LU< t—i X XX 00 1-l-LU (- CC LU 001-
2: 3 LU X <oo^^-l Q-C* (- K -J<Jh > LU 00 _Ja: ro 21 _J O z3< HO < < h- ~z 000-" ZZ cc > *—
<
_JX LL —
1
< I—
1
00 00 <z 00 a. cc _l _J00 >
o<t 2:3 cc < <_J 1—
1
vt-
ZLU LL LU < > CC >< at CC (M<2I < > >- t-H 3 _> cc 3 LU XOm >—
1
_j oo cC O Qil-I < O O »
*-<Z 00 t— < mcc X a: a: X z 00OD 2TZ 1- cc o< <CC LL LU a: fH• a: < LU O 3 z LU < O t- O 3 X
ZUJ a. l- O mz X z 00 LU 00UUK 32: 00 X 03 (— DZ a: < O X LU axoo oc LU LL Luac 0:3 LU _J LU 3 z1— a: LU cc O LU O l-ai CO CC LU _J <
Z 1— i-»O0 h-K X LUh- h- OO LU 2! LU a. X <O LL-O O0< LU a: K- 0:00 HOi 3 X LU 1— > h-»—
1
_J i-i a:_j X LU Q-O: 00 Z 1- >~ > LU X1— <LUI— 1-3 h- CO O 1—.LL 1 LLLL CO 1—4 > y< LU2 00 u-o 2: I- LLC< OO LU z t- »- <-J c£>—ih-t _j z 3 > 1— 1—
1
O 00 X3 EK cC< NH Z CCCC'M CCcC < LU 00O »-a:< zo LULU QT ZZ _l CL _l z
LU _J <LUh- LU LU cOajoi 3 00 < t—
1
Z < »-<-0 UJZ a: X 22< LULU O LU h-1—
t
O OLU 2LU O 1— 3r1 h-l- —1 a:I- ZOh »-»X H zz:z << < h-3 LU hH O Sl- 00 3 _J_J O LU
a:
2! t-a:Luc£lu_j
otLUnO
33OO
LLI
ccX1—<<ILU
\- <(-_j H-.-I a: cc 1:£ 1— -a: _I_J CC CC cc OO l-LLO LUX a: c£ i3i OC1 << cc cc CC h-z _J oo<o QX cC a: 0. a.OOmh t- <~J<^> afa:o.o-OCjrvJ 001—
1
<cd > h- C\J
LU hH O X rH<Njrovj-mNor*- <-hj>
X a: •* •» zzzzz:ZZ'ZOUJK o£ 1—
1
m 00000003U-lai< < •» 1—
i
000000000000000:0:0. (\imvj-inor--coO a: ^ Z <<<<<<<LLO.-tf» OO r—)•—(1r-4 r~i r~1 1—t ,—
1
<-> <\i ro Nf- oa so r^-
Olu OOO
LLQn-> y -^ ~^ -^ -z? Z7 -?r -zr -^ ».
r-IC\J
>> >>>>>>> 0000-0-0.0.0.0-0.
v> •» ..»,»»-f- rHCMrOvj-LOvor^ toa^OHMf^v}-
1—4 vO f-4i-t --•CNr^-J-LnvO^-COOO •4-Ln 1—Ir^lM r-1 r—( 1—1 1—
1
vOr^f-Hf-tCNJCMCNJCNJCNJ
h- z00 < LULU LULU LULULLILUIULULU LULULULULULULULULU—
1
LU LU 33 33 3333333 333333333h- 2T 1- _J_I zzz;Z.Z.TLZZ^.:z -J_l —
1
t r —
1
1 1 —
1
_l_l_l._J —
1
( 1—i_J< < << 0000000000 << <<<<<<< <<<<<<<<<t- z CC >> >> >>>>>>> >>>>>>>>>00 3 LU LULU O0O0'V)O0O000o0o0O0o0 LULU LU LU LU LU 1 U LU LU UJLUIUUJLUIULUUJLU
a: Z >> OOOOOOOOOOOOOOOOOOOO >> >>>>>>> >>>>>>>>>> LU << <<<<<<<<<< << <<<<<<< <<<<<<<<<-J h- O 0O 00 00 00 00 00 00 00 00 00 00 O0o0o0o000o0o0^)o0a: 003 cc
O t—1 LUX LL 2:
•
•**#«••»•«-•«# Vr* # -^ ^ ^
159
.-1 t/J CC <K X >-z t—4
X z ^ <« --»
t-i LU CMLL z z Q 00
DC 1— IOZ > »—
I
_) < LU ~»Z- z X a _) l-< LUOOO ZO
< o Q*-" LU t—
t
LU Xl- s:>-)0 Lut-.
s: o ZZki-HLUO
<2:
a> LUO
Zl->-J 2:0.1-
O OQiOOoOLULU LU <Q.cc h- ac
CC X 001—00 LU a: oz CC OO CM h- CM00Oxara: o z<z Z O < zo :DZ ZZHXXI- o < 3 z 1—1 1—
1
z <0<<o0D- oo • —. _l >-*V~>CC a: < O >o0 ttQIKICCooi— t— <h- oooo c£:*; 00OI— X h- Q.00 OLUO UhZ<oooo_jZlu>—OUjOOO 00 .— z 0--. OOoO—00—_j<< lu3z_jo:zo< MhO O-^02 (Z> LU LO>-(
_j—i oo a: lu lum a. lux cd 2:001-1 •—
<
CM OOfO 00 LU_l<0< 1—or: 2a:3l-U 00 >—<h- 1- O 2:-iooz I-UhO«Z<ct:a:a:ocz<>h-LL_j Zl-00 < • cc<. < LU—
1
<a:c£:a:o ocqco<o< <<_ _J II <ZZLU(X -JCMZI-ZX3<<l- O— h- a:t-l— =3 LU|— 3Oc0f-O DZ<U<3S
z o t-00< 5: 2:<q^>-<»-> 11 0<LU<LU -«3z_»_j h- t— —i mQ 1— C£00O JIZXZKoOon3<i< _JLU00 00 1- h-l_)0>-CM <o O\-cc\- i— en a. cc <3 h-ooZoO<X O C3fOO<LUOOLUOO CC CC DC KLULU _J _JZ)afr)2DQX IJ.LULULUXX•-* CC h- 1— ivj3O 0- a. CC CC 031- <_l <o.hhu_3 Z'— CCiSlCC H-1 1 1 1 1 1 1 4 1 1 1 1 t-Qf< cC UJZU- oOoOl— II LU O >1 1 1 1 1 1 1 1 1 Or-nrg Z h- a:.-. LU Z)LUvt- d^ZjZJQ•—•C\|rn-4-mvOh-00CT'<—lr-(rH LUI— HH Z c^LualOoocM O —t QiO Qim LU
a:Z2 O h"—Zoo;;>o o<i-
_l O*-. a: O <oo -- >ZX 00 0000OOD<Io Ko:lu :lu LULULU MlJ M Zo 00 a. 1— O o-z>-zq;ii- ,ZUJ LULUt-H
z ZZm<m Q_|_ LU CM'— H- CMI-H-2:< HH IDS 00 zoo<z<<a:
X hoa: OTLUfO <3_J<-JZLUXX XX 00 a£^LUh- u_ia:(NJQ X 3X3— 1-xx mil - m h- <^-t_X(-OXZ OLU0002:•« *t—(CM •«•»»•« »»C\Jr—<CM z H- 1-lUJLULUf—X< :s:_i —iciLu»tLorNj(\ir--vDLr\^mc?a> LU 00--QZQoo ILi—'<ll<luq:XX>>C?C?O0'C? «••••• 2:
LU
CM•*
Ml^UHOH<i-icMc<^NtirtNOr~cocT>—*—i—
<
X X XXLULbLULUUjUJUJLUUJUJUJLiJ 32:2:5:5:2:2:5:5:2:2:2:2:
r\l
13LUCC
*•
OO z
•4-oxx1—(CM »• »•
zxooCM<t-H
2:Oar—
(
1— h- 1— f- l~ t— 1— 1— 1— H- h- h-*/* V) *^ V-: -fc^ tA «} v • •«* *f- *«• ««• X •• O u_ llx^:^: Qi 1—ILU—
1
2ZZZZZZZZZZZ *r- V- •4" •a 9- •• »» ^ 00 >!->^ 3 -4" sO f*-r0Ovfr Pi •«•»•CMrHO a
z1—4
<-t t—
t
H CM CM CM CM CM CM CM"-! in
LU LU LU LU LU LU LU LU LU LU LU LU
DDDDDDDDDD3D UJ LU LU LULU LULU LU LULU—
•
t I—1—»—I —
t
I I » I 1 3 1- >- LU 3 3333 3 31-<<<<<<<<<<<< -1 < _j h- -J —
1
1 —1—
1
CC _J00_J<>>>>>>>>>>>> < Z »—
1
< < <<<< _J <_J<ZLULULULUUJLUUJLUUJUJUJUJ >l——
1
< aC > >>>> > >H-^>>>>>>>>>>>> luzz LU LU LULU LULU UJ LULULUSOi<<<<<<<<<<<< >»-«a: z > >>>> 1- >i->a:<QOOoOoOOOoOOOOOOOoOOOoOoO <q:uj LU LU < <<<< < <<< uj 1—Z2:2:5:5:2:2:2:2:2:5:2:2: OOQ-I—
z<X
o- 00 00 00 'S) 00 oOOoOh- oOJJ
CM<s*-CCccvu00 1—^** * * * # * # »
160
LIST OF REFERENCES
Operations Evaluation Group Memorandum to CommandingOfficer, Naval Communications Station, San Francisco,(OEG) 0652-71, Subject: Preliminary Analysis ofBroadcast Communications during ROPEVAL 3-71 (U) ,
by W. C. Hardy, and others, 12 October 1971.(CONFIDENTIAL document)
Operations Evaluation Group Memorandum for the Director,Operations Evaluation Group, (OEG) 0485-71, Subject:Description of MODCAST-1 and its Application to theBacklog Problem on the K-Broadcast (U) , by W. C. Hardy,and others, 5 October 19 71. (CONFIDENTIAL document)
Brownlee, K. A., Statistical Theory and Methodology inScience and Engineering , pp. 334-396, Wiley, 1967.
International Business Machines Corporation, GeneralPurpose Simulation System/360 Introductory User'sManual , (GH20-0 30404) , 1969.
International Business Machines Corporation, GeneralPurpose Simulation System/360 User's Manual ,
(H20-0326-3) , 1970.
Hillier, F. S. and Lieberman, G. J., Introduction toOperations Research , Holden-Day, 1968.
Newell, G. F., Application of Queueing Theory , Chapmanand Hall, 1971.
10
11 Naylor, T. H, , and others, Computer Simulation Tech-niques , p. 85, Wiley, 1968.
161
12. Epstein, B. , "Tests for the Validity of the Assumptionthat the Underlying Distribution of Life is Exponen-tial, Part I," Technometrics , v. 2, No. 1, pp. 83-85,February 19 60.
13. Lindgren, B. W. , Statistical Theory , pp. 296-304,MacMillan, 1962.
14. Cochran, W. G. , "The Chi-square Test of Goodness of Fit,"The Annals of Mathematical Statistics , v. 23, pp. 315-345, September 1952.
15. Larson, H. G. , Introduction to Probability Theory andStatistical Inference, pp. 280-287, Wiley, 1969.
162
INITIAL DISTRIBUTION LIST
No. Copies
1. Defense Documentation Center 2
Cameron StationAlexandria, Virginia 22314
2. Library, Code 0212 2
Naval Postgraduate SchoolMonterey, Californi 9 3940
3. Chief of Naval Personnel 1
Pers-llbDepartment of the NavyWashington, D.C. 20370
4. Naval Postgraduate School 1
Department of Operations Researchand Administrative Sciences (Code 55)
Monterey, California 93940
5. Assoc. Professor K. T. Marshall, Code 55Mt 3
Department of Operations Researchand Administrative Sciences
Naval Postgraduate SchoolMonterey, California 93940
6. Asst. Professor R. W. Butterworth, Code 55Bd 1
Department of Operations Researchand Administrative Sciences
Naval Postgraduate SchoolMonterey, California 939 40
7. LCDR D. A. Spaugy, USN , Code 52Zs 1
Department of Electrical EngineeringNaval Postgraduate SchoolMonterey, California 93940
8. Commander, Naval Communications Command 3
Naval Communications Command Headquarters4401 Massachusetts Ave., N.W.Washington, D.C. 20390
9. Commanding Officer 3
Naval Communications Station San FranciscoRough and Ready IslandStockton, California 95203
163
10. Commanding OfficerNaval Communications Station HonoluluFPO San Francisco 96613
11. Commanding OfficerNaval Communications Station San Diego9 37 N Harbor DriveSan Diego, California 92132
12. Naval Electronics Laboratory Center, Code 230271 Catalina Blvd.San Diego, California 92152
13. Dr. S. B. SchneidermanOEG Representative, Code 302Staff, CINCPACFLT, Box 11FPO San Francisco 96610
14. Dr. W. C. HardyOperations Evaluation Group1401 Wilson Blvd.Arlington, Virginia 22209
15. CAPT F. M. Snyder, USNStaff, CINCUSNAVEUR, Box 6
FPO New York 9 501
16. LCDR Harlan D. OelmannUSS Holder (DD-819)FPO New York 09501
164
UNCLASSIFIEDSecurity Classification
DOCUMENT CONTROL DATA -R&D,Secunty classification of title, body ol abstract and indexing annotation must be entered when the overall report is classified)
originating ACTIVITY (Corporate author)
Naval Postgraduate SchoolMonterey, California 93940
21. REPORT SECURITY CLASSIFICATION
Unclassified26. GROUP
3 REPORT TITLE
FLEET MULTI-CHANNEL BROADCAST TRAFFIC INTENSITY STUDY
4 DESCRIPTIVE NOTES (Type of report and,inclusive dates)
Master's Thesis, June 19725. AUTHORISI (First name, middle initial, last name)
Harlan Daryl Oelmann; Lieutenant Commander, United States Navy
6 REPOR T DATE
June 1972
7«. TOTAL NO. OF PAGES
166
7b. NO. OF REFS
158a. CONTRACT OR GRANT NO.
6. PROJEC T NO.
9a. ORIGINATOR'S REPORT NUMBER(S(
9b. OTHER REPORT NOISI (Any other numbers thai may be assignedthis report)
10. DISTRIBUTION STATEMENT
Approved for public release; distribution unlimited.
II. SUPPLEMENTARY NOTES 12. SPONSORING MILITARY ACTIVITY
Naval Postgraduate SchoolMonterey, California 93940
13. ABSTR AC T
This thesis contains the analysis of data of messagetraffic loads on the Naval Communications Fleet Multi-channelBroadcast System and results of a simulation model of thesystem under various channel alignments. Distributions ofinterarrival times, message lengths and requests for screensand reruns are determined from the data. These distributionsare used in a simulation model of the Broadcast System. Themodel is used to compare the average delays caused by back-logs of messages when two channels devoted to a given ship-type are a) used in series with the second channel used torebroadcast messages from the first channel after a one hourdelay, and b) both channels are used in parallel to transmitfirst-run messages. The results of the simulation showthat backlogs are reduced considerably by running the twochannels in parallel at all times.
DD FORM I47OI NOV 65 I *T / +J
S/N 01 01 -807-681 1
(PAGE 1)
UNCLASSIFIED165
Security Classification1-31*08
UNCLASSIFIEDSecurity Classification
key wo RDS
COMMUNICATIONS
NAVAL COMMUNICATIONS
FLEET BROADCAST
FLEET MULTI-CHANNEL BROADCAST
SIMULATION
QUEUEING
LINK A
FORM« NOV 65
101-807-68?!
1473 (BACK UNCLASSIFIED166 Security Classification A-3 t 409
Thesis 135769024715 Oelmannc.l Fleet multi-channel
broadcast traffic in-
tensity study.
16 AUG 90 3 6 108
Thesis T35769024715 Oelmannc.l Fleet multi-channel
broadcast traffic in-
tensity study.
thes024715
Fleet multi-channel broadcast traffic in
3 2768 000 99929 6DUDLEY KNOX LIBRARY
