03 MN1790 Capacity Planning WW FH

7/31/2019 03 MN1790 Capacity Planning WW FH

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Consulting

Fundamentals of Traffic TheoryFundamentals of Traffic Theory

General remarks to traffic theory:

The traffic theory in general uses mathematical models to describe and to optimise traffic systems.In telecommunication traffic theory (also called teletraffic theory) it is a telecommunication system

which is considered with the help of appropriate mathematical models. Since real systems are quite

complex systems, simplifications and assumptions have to be performed to not deal with too

complicated and sophisticated mathematics. Later on these assumptions and simplifications have tobe justified.

Since a bad model can never lead to good results, the problem is to find a good and easy modelto get reliable results. Some mathematical ideas, models and formulas which are used in traffic

theory are presented now on the following pages.


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Definitions and TermsDefinitions and Terms

General:

Each telephone system must be dimensioned in such a way that even during periods of high traffic(offered), the subscribers still have a good chance of success in making calls. Those subscriberswho do not succeed in making a call will either be lost (in a pure lost-call telephone system) orthe calls will be delayed (in a waiting-call telephone system). Usually, real telephone systems arecombined lost-/ waiting-call systems.

Even during the so called busy hour the percentage of non successful subscribers should notexceed a predefined value. This means for the network operator that the dimensioning of his

telephone system must be driven on the one hand by guaranteeing some Quality of service (QOS)and on the other hand by economical aspects.

From economical point of view, the amount of necessary equipment (switches, base stations,

multiplexers, cross-connectors, ...) and also the number of links between this equipment should be

kept to a minimum.

From QOS point of view, the more trunks are offered by the telephone system, the higher theprobability for the subscribers to succeed in making calls.


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Consulting


Traffic OfferedTraffic Offered Traffic CarriedTraffic Carried

TrafficTraffic LostLost

TelephoneTelephone systemsystem::

n =n = number ofnumber of

devicesdevices ((trunkstrunks))

KK

KK

KK

KK

KK

KK

KK

LL

JJJJ

JJJJ

JJJJ

N =N = number ofnumber of

traffic sourcestraffic sources

KKKK

KKJJ

JJJJ


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Consulting


Traffic flow units:

In honour of A. K. Erlang (1878-1929), a Danish mathematician who was the founder of traffictheory, the unit of the traffic flow (or traffic intensity) is called Erlang (Erl).

The traffic flow is a measure of the size of the traffic. Although the traffic flow is a dimensionless

quantity, the Erlang was assigned as unit of the traffic flow in traffic theory.

By definition:

1 trunk occupied for a duration t of a considered period T carries t / T Erlang.

From this definition it follows already that the traffic carried in Erlang cannot exceed the number

of trunks.


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Consulting


Several definitions can be given for the traffic flow:

Especially for traffic measurements it is useful to consider the traffic flow as averaged number of

trunks which are occupied (busy) during a specified time period:

Traffic intensity = Mean number of busy trunks in a time period

If this is a long time period, ongoing calls at the beginning and at the end of this period can be

neglected. The traffic flow then can be considered as call intensity (number of trunk occupations per

time unit) times the mean holding time (which is the average holding time per trunk occupation):

Traffic intensity = Call intensity x Mean holding time


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Consulting

Erlang-B FormulaErlang-B Formula

Assumptions:

Pure loss system Infinite number of traffic sources

Finite number of devices (trunks) n

Full availability of all trunks

Exponentially distributed holding times

Constant call intensity, independent of the number of occupations

Time and call congestion are equal:

This formula is called Erlang`s formula of the first kind (or also Erlang loss formula or ErlangB formula).

=

===n

i

i

n

n

i

A

n

A

AEBE

0

,1

!

!)(


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Erlang-B Look-up TableErlang-B Look-up Table

The Erlang B formula describes the congestion as function of the Traffic Offered and the numberof available trunks.

In real life the situation is mostly different. People often want to calculate the number of neededtrunks for a certain amount of traffic offered and a maximum defined congestion.

That means the Erlang B formula must be rearranged:

n = function of (B and A)

This rearrangement cannot be done analytically but only numerically and will be performed mosteasily with the help of a computer. Another possibility is the usage of special tables, namely so

called Erlang B look-up tables. On the following page an example of such an Erlang B look-up

table is presented.


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Consulting


0.080.471.061.752.503.304.145.005.886.787.698.619.5410.4811.43

12.3913.3514.3215.2916.2717.2518.2419.2320.2221.21

0.050.380.901.532.222.963.744.545.376.227.087.958.849.3710.63

11.5412.4613.3914.3115.2516.1917.1318.0819.0319.99

0.030.280.721.261.882.543.253.994.755.536.337.147.978.809.65

10.5111.3712.2413.1114.0014.8915.7816.6817.5818.48

0.010.150.460.871.361.912.503.133.784.465.165.886.617.358.11

8.889.6510.4411.2312.0312.8413.6514.4715.2916.13

123456789101112131415

16171819202122232425

Offered Traffic Afor

B=E=0.07

7 % blocking)


B=E=0.05

5 % blocking)


B=E=0.03

(3 % blocking)


B=E=0.01

(1 % blocking)

Number oftrunks n

Erlang B look-up table for an infinite number of traffic sources and full availability:


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22.2123.2124.2225.2226.2327.2428.2529.2630.2831.2932.3133.3334.3535.3736.4037.4238.4539.4740.5041.5342.5643.5944.6245.6546.69

20.9421.9022.8723.8324.8025.7726.7527.7228.7029.6830.6631.6432.6233.6134.6035.5836.5737.5738.5639.5540.5441.5442.5443.5344.53

19.3920.3121.2222.1423.0623.9924.9125.8426.7827.7128.6529.5930.5331.4732.4133.3634.3035.2536.2037.1738.1139.0640.0240.9841.93

16.9617.8018.6419.4920.3421.1922.0522.9123.7724.6425.5126.3827.2528.1329.0129.8930.7731.6632.5433.4334.3235.2236.1137.0037.90

26272829303132333435363738394041424344454647484950


B=E=0.07

7 % blocking)


B=E=0.05

5 % blocking)


B=E=0.03

(3 % blocking)


B=E=0.01

(1 % blocking)

Number oftrunks n


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Erlang-C FormulaErlang-C Formula

Assumptions:

Pure delay system Infinite number of traffic sources N

Finite number of devices (trunks) n

Full availability of all trunks

Exponentially distributed inter-arrival times between calls which corresponds to a

constant call intensity y, i.e. the probability of a new offered call is the same at all time

points, independent of the number of occupations

Exponentially distributed holding times (s)

Time congestion is defined as the probability that all devices are used:

This formula is called Erlang`s formula of the second kind (or Erlang delay formula or ErlangC formula).

= +

==1

0

,2

!!

!)(n

i

ni

n

n

An

n

n

A

i

A

An

n

n

A

AEE


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Erlang-C FormulaErlang-C Formula

Call congestion is defined as the probability that a call has to wait:

The traffic carried and traffic offered are:The mean number of waiting calls is:

The mean waiting time for calls, which have to wait is:

The mean waiting time for all the calls is:

The waiting time distribution depends on the queue discipline, whereas the mean waiting time is in

general independent of the queue discipline.

EB =

An

stwait

=

An

s

An

n

n

A

i

A

An

n

n

A

Tn

i

ni

n

wait

+

=

=

1

0 !!

!

An

A

An

n

n

A

i

A

An

n

n

A

Nn

i

ni

n

wait

+

=

=

1

0 !!

!

syAAAofferedcarried

===


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Trunking GainTrunking Gain

Exercise: Use the Erlang B look-up table to find out the meaning of trunking gain:Which traffic offered can be handled by an Erlang B system assuming 32 trunks

and 1 % blocking?

Which traffic offered can be handled by 2 Erlang B systems for each assuming

16 trunks and 1 % blocking?

Which traffic offered can be handled by 4 Erlang B systems for each of them

assuming 8 trunks and 1 % blocking?


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Traffic DistributionTraffic Distribution

Time Dependency:

The traffic in a telecommunication network as a function of time will not be constant but will showsignificant fluctuations. Variations of the traffic during a single day, from day to day, for differentweekdays, or even for different seasons can be observed. Also on a long time scale the averaged

traffic will not remain constant but will increase in most telecommunication networks.

0 12 24 hours

0 %

100 %

50 %


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Traffic DistributionTraffic Distribution

Location Dependency:

The traffic in a telecommunication network will not be location independent but will showsignificant location dependencies. For example, in rural areas there will be less traffic compared tocity areas.


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Traffic ForecastingTraffic Forecasting

An important aspect in dimensioning a telecommunication network is the expected traffic in the

future. Therefore, an analysis of the expected traffic is of great interest. Even in case that the

penetration (number of traffic sources) saturates, the amount of traffic does not necessarilysaturates too. Traffic forecasts are not easy and may be influenced by many aspects: e.g. price

politics, offered services,

The more the important dependencies are realised and taken into account, the more precise the

forecasts will be.

For a detailed analysis it is useful to:

Split the total PLMN into subareas

Categorise the subscribers: e.g. into business, residential,

Analyse: e.g. the number of subscribers per area, the development of the penetration

depth, the expected penetration depth

Analyse also economic dependencies like e.g. any correlation between the demand oftelephone service and e.g. the economic activities in a special region, the economic

situation in general (measured e.g. by the economic growth), the income of the people,


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Traffic MeasurementsTraffic Measurements

It is of great interest for the network operator to measure the real traffic situation in his network.

To perform such measurements, in former telecommunication systems special traffic

measurement equipment (e.g. the so called electromechanical meter) was needed. Since in themeantime most telecommunication systems are digital, this kind of equipment is not needed any

more: The call and device concerning data are stored in the memory of the system processor. It isonly a question of software to read them out.

The traffic measurements are usually part of the so called Performance Data Measurements.

Performance Data Measurements can be run continuously, periodically or sporadically, for a long

time or a short time, observing smaller or greater parts of the network.

Concerning the traffic measurements, either special events are counted (e.g. the number of

successful calls, the number of lost calls, ...) or special time intervals are recorded (e.g. holdingtimes, waiting times,...).

The corresponding counters could in principle be actualised continuously during the observationperiod, but mostly a scanning method is used. Scanning method means that the system counts

the number of events not continuously but only at particular times. This leads to some uncertaintyfor the measurement results. Nevertheless, the error performed can be estimated using statistical

methods. In general, the smaller the scanning interval the higher the precision of the

measurement. Typical scanning intervals are 100 ms or 500 ms.


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Dimensioning TRXsDimensioning TRXs

The dimensioning of the number of TRXs per cell should be based on traffic estimations for this

area and should be performed for the busy hour.

Using:

the number of subscribers in the corresponding area (for the busy hour)

the expected averaged traffic per subscriber (for the busy hour)

the offered traffic A results from:

A = No of subscribers x traffic load per subscriber

Using the Erlang B look up table the number of TRXs can be derived.

Hint:

This number also depends on the amount of half rate being used in the cell


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Dimensioning Control ChannelsDimensioning Control Channels

Initial signaling sequence for MTC, MOC, LOCUPD, SMS,...

Paging Request (PCH)

Channel Request (RACH)

Immediate Assignment (AGCH)

SDCCH-Signaling


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Dimensioning Control ChannelsDimensioning Control Channels

combined BCCH: includes 4 SDCCH subchannels

uncombined BCCH: requires additional SDCCH timeslot(each one containing 8 SDCCH subchannels)

SACCH multiframe (containing 2 BCCH multiframes)

S

11

S

1

F

10

F

0

BCCH

2 3 4 5

CCCH

6 7 8 9

CCCH

1 2 1 3 1 4 1 5

CCCH

1 6 1 7 1 8 1 9

S

21

S

31

F

30

F

20

SDCCH0

2 2 2 3 2 4 2 5

SDCCH1

2 6 2 7 2 8 2 9

SDCCH2

3 2 3 3 3 4 3 5

SDCCH3

3 6 3 7 3 8 3 9

S

41

I

50

F

40

SACCH0

42 43 4 4 4 5

SACCH1

46 47 48 4 9

1.

1.

S11

S1

F10

F0

BCCH2 3 4 5

CCCH6 7 8 9

CCCH1 2 1 3 1 4 1 5

CCCH1 6 1 7 1 8 1 9

S21

S31

F30

F20

SDCCH02 2 2 3 2 4 2 5

SDCCH12 6 2 7 2 8 2 9

SDCCH23 2 3 3 3 4 3 5

SDCCH33 6 3 7 3 8 3 9

S41

I50

F40

SACCH242 43 4 4 4 5

SACCH346 47 48 4 92.

uplink R = RACH + SDCCH / 4

downlink BCCH + CCCH + 4 SDCCH / 4, F = FCCH, S = SCH

R

5

R

4

SDCCH3

0 1 2 3

SACCH2

6 7 8 9

SACCH3

1011 1213

R

15

R

14

R

17

R

16

R

19

R

18

R

21

R

20

R

23

R

22

R

25

R

24

R

27

R

26

R

29

R

28

R

31

R

30

R

33

R

32

R

36

R

35

R

34

SDCCH0

3 7 3 8 3 9 4 0

SDCCH1

4 1 4 2 4 3 4 4

R

46

R

45

SDCCH2

4 7 4 8 4 9 5 0

2.R5

R4

SDCCH30 1 2 3

SACCH06 7 8 9

SACCH11011 1213

R15

R14

R17

R16

R19

R18

R21

R20

R23

R22

R25

R24

R27

R26

R29

R28

R31

R30

R33

R32

R36

R35

R34

SDCCH03 7 3 8 3 9 4 0

SDCCH14 1 4 2 4 3 4 4

R46

R45

SDCCH24 7 4 8 4 9 5 0


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Dimensioning Control and Traffic ChannelsDimensioning Control and Traffic Channels

Exercise:

Consider 1 BTS with 2 TRXs and full rate channels. Assume 1% blocking.Assume a typical TCH load of 25 mErl per subscriber per hour.

Furthermore, assume a typical SDCCH load of 10 mErl per subscriber per hour.

Compare configurations A and B: Which one offers the higher capacity?

BTS

Combined BCCH15 TCH full

Configuration A

TRX-0

TRX-1

BTS

Uncombined BCCH1 SDCCH/814 TCH full

Configuration B

TRX-0

TRX-1


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Dimensioning Control and Traffic ChannelsDimensioning Control and Traffic Channels

Total blocking probability:

SDCCH

TCH

A*

Y

B1 (A*+A) B2 (1-B1)A

Y=(1-B1)(1-B2)A

A

Y*=A*(1-B1)

B1 (A*+A)+B2(1-B1)A


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Capacity and Cell RadiusCapacity and Cell Radius

In capacity limited areas of the network:

Cell radius is smaller than would be for coverage limited situation to satisfy the traffic demand.

Coverage limited area

Capacity limited area


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Dimensioning terrestrial interfacesDimensioning terrestrial interfaces

Um

Abis Asub/Ater A

LAPD for O&MLAPD for TRX

LAPDfor O&M

CCSS7

Base

Station

ControllerTranscoder MSC

SGSN

Gb

BSSGP

MS

Signalling links: overview


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LAPD signalling links:

O&M signalling for BTSM: LPDLMTRX signalling: LPDLR

Signalling for TRAU: LPDLS

Rules of thumb:

1. LPDLM and LPDLR are counted as ONE LAPD-link

2. In case of 1 or 2 TRX 16 kbit/s are sufficient for LPDLM+LPDLR

3. Otherwise 64 kbit/s are required

4. LPDLS always uses 64 kbit/s


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Processor capacity:

Traditional BSC: One PPLD processor handles up to 8 LAPD linksOne PPCC processor handles up to 4 CCSS7 links

High cap. BSC: Two PPXX processors handle 248 signalling linksload sharing (LAPD and CCSS7)


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BTSE0

TRX-0-0TRX-0-1TRX-0-2TRX-1-0

BTSE1

TRX-2-0TRX-2-1

BTSE2

TRX-3-0TRX-3-1

Um

Signaling channel on Um

Traffic channel

LAPD = LPDLM + LPDLR

empty

31

Abis

5 1 5 1 5 1 5 14 0 4 4 0 4

7 3 7 3 7 3 7 36 2 6 2 6 2 6 2

5 1 5 1 5 1 5 14 4 0 4 0 4

7 3 7 3 7 3 7 36 2 6 2 6 2 6 2

LAPD

LAPD

FAW BSC

7 6 5 4 3 2 1 7 6 5 4 3 2 1 7 6 5 4 3 2 1

TRX-3-0 TRX-2-0 TRX-0-0

7 6 5 4 3 2 1 0 7 6 5 4 3 2 1 0 7 6 5 4 3 2 1 0

TRX-3-1 TRX-2-1 TRX-0-1

7 6 5 4 3 2 1 0

TRX-0-1

7 6 5 4 3 2 1

TRX-1-0

1817

16 14

LAPD

10 2 01

TRX-3-1

TRX-3-0

TRX-2-1

TRX-2-0

TRX-1-0

TRX-0-2

TRX-0-1

TRX-0-0

LAPD signalling on Abis


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01630

31

TRAUBSC

01630

31

TRA

U

MSC

Asub

A

empty

CCSS7

LPDLS

OMAL

CCSS7

FAW

FAW

OMAL

LPDLS

LAPD signalling on Asub


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CCSS7 dimensioning:

Traffic Model with following assumptions for busy hour (standard subscriber):

2%SMS

0.025Erlang per subscr.

1 (65% MOC; 33% MTC; 2% MtMC)Busy Hour Call Attempts

0.7Attach/Detach

1Location registration/updates

0.6Handovers

AssumptionParameter


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CCSS7 dimensioning:

Traffic Model with following assumptions for busy hour (highly mobile subscriber):

2%SMS

0.025Erlang per subscr.

1 (65% MOC; 33% MTC; 2% MtMC)Busy Hour Call Attempts

0.9Attach/Detach

3.5Location registration/updates

1.6Handovers

AssumptionParameter


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SS7 Signalling load per subscriber

600 byteStandard profile

1100 byteHigh mobility profile

Signalling LoadProfile

Signalling load per BSC

Number of subscr. = Traffic capacity / Traffic per subscriber

Example: 2000 Erlang / (0.025 mErlang/subscriber) = 80 000 subscribers

Total Signalling load = Number of subscribers * Signalling load per subscriber

Example 1: 80 000 subscribers * 600 byte / 3600 sec = 13.3 kbyte/sec

Example 2: 80 000 subscribers * 1100 byte / 3600 sec = 24.5 kbyte/sec


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CCSS7 links per BSC

Example 1:

Required CCSS7 link capacity: 13.4 kbyte/sec

CCSS7 link single capacity 64 kbit/s = 8 kbyte/sec

Consequence: 2 CCSS7 links required

Example 2:

Required CCSS7 link capacity: 24.5 kbyte/sec

CCSS7 link single capacity 64 kbit/s = 8 kbyte/sec

Consequence: 4 CCSS7 links required


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CCSS7 dimensioning: Message transfer delay

Message transfer

delay

Load on link

(in Erlang)0.4 0.8


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01630

31

TRAUBSC

01630

31

TRA

U

MSC

Asub

A

empty

CCSS7

LPDLS

OMAL

CCSS7

FAW

FAW

OMAL

LPDLS

CCSS7 signalling on A


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Transcoder capacity: depends on cell sizes

13151275.6291201220240

12133633.434540640240

32502.5071001100100

Trans-

coders

Erlang /

BSC

Erlang / cell

(1% blocking)

TCH /

cell

SitesTRX /

cell

Cells /

BSC

TRX /

BSC

Assumption: 120 traffic channels per Transcoder

Blocking of A interface has to be taken into account


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ExercisesExercises

1) Consider a call rate of 1000 calls per hour. The mean holding time is 90 sec. What is the

Traffic Offered in Erlang?

2) Consider a Traffic Offered of 30 Erlang and a mean holding time of 120 sec. How many callsper hour do you expect?

3) Consider a telephone system with N=6 trunks and a time period of 10 time units (0,1,...,10).

Subscriber 1 makes a call from t1 to t3. Subscriber 2 makes a call from t2 to t4.




a) Draw the number of used trunks as function of time.

b) Draw the number p of simultaneous occupations in the trunk group as function of

the total time with exactly p occupations.c) What is the traffic offered in Erlang?

d) What is the traffic carried in Erlang?

e) What is the lost traffic in Erlang?


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ExercisesExercises

4) Consider a pure delay system and a group of 10 trunks belonging to a trunk group. Assume

that all these trunks are available (full availability). Assume a traffic offered of 4 Erlangs and

a mean holding time of 100 seconds. The queue discipline shall be first come, first served(ordered queue).

a) What is the probability to be queued?

b) What is the mean waiting time of queued calls?

c) What is the mean waiting time of offered calls?

d) What is the probability that call are queued for longer than 1 minute?

5) Consider a pure loss system and a group of 10 trunks belonging to a trunk group. Assumefull availability. What is the traffic in Erlangs which can be offered to this system if the

probability to be blocked should be maximum 1%, 3%, 5% and 7% ?


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Consulting

ExerciseExercise

Nominal Cell Plan

Consider a suburban area (clutter correction term = 5 dB) of 1000 km

2

with an expected traffic of20 Erlang/km2. The standard deviation 1 sigma in building was measured as 9 dB. The planningtarget was decided as 99% cell area probability.

Consider also an adjacent rural area (dense forest, clutter correction term = 9 dB) of 5000 km 2

with an expected traffic of 1 Erlang/km2. The standard deviation 1 sigma for outdoor coverage was

measured as 6 dB. The planning target was decided as 95% cell edge probability.

The blocking rate for both areas was defined as maximum 1%.

Assume that in total 60 RF channels are available. Assume also a typical antenna height of 30 m,

a C/I>21dB being required for the BCCH and a C/I>15 dB being required for the TCH. No tower

mounted amplifier is used. The antenna gain is 15 dBi / 17 dBi for 900 / 1800 MHz.

Assume 1 SDCCH is required for up to 2 TRX per cell, 2 SDCCH are required for up to 4 TRX per

cell, 3 SDCCH are required for up to 6 TRX per cell and 4 SDCCH in further cases.

How many sites are needed for a 900 / 1800 MHz system in case frequency hopping is used / notused?

03 MN1790 Capacity Planning WW FH

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