CAT Lesson6

7/23/2019 CAT Lesson6

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IS102Computer as an Analysis ToolWeek 6: It’s About Time

Reading:Capter !: "ro#esses and Time

Instru#tor:Asso#iate "ro$essor %uo &ilingS#ool o$ In$ormation Systems'ilingguo(smu)edu)sg

mailto:[email protected]

mailto:[email protected]



Agenda Today

• Simulating *ore +ata "oints

– Using Frequency Bins – Using Re-sampling

– Using Inverse Distribution

• ,esson -ut#ome – Date and Time Management in !cel

– Modeling "ueuing #ystem using #imulations

– Macro Recording

• ./er#ises – $%&' Timer(li)er*!ls

– $%+' $DBban)*!ls



Simulating *ore +ata "oints

• *etod 1: sing reuen#y 3ins

– Build (RF table and use R,D./ 0unction to matc1 (RF by

,--4"5 and returns t1e simulated data $2'

.i/ 0requency count or .ii/ percentage o0 occurrence

.iii/ distribution 0unctions

• *etod 2: sing Re7sampling

– Discrete Data' S*A,,.array3 RA8+3.TW..85198/

– (ontinuous Data' ".RC.8TI,..array3 RA8+5/

• *etod : sing In;erse +istribution – Discrete distribution .Uni0orm3 4oisson3 Binomial/

– (ontinuous distribution .Uni0orm3 !ponential3 ormal/



*etod 1: reuen#y 3ins

• 5e 0irst compute t1e cumulative relative 0requency .(RF/ o0

data $ and build t1e (RF data• 5e t1en use R,D./ to generate a random number

bet6een 7 and 8

• T1is number is compared 6it1 t1e (RF table using

9oo)up./ and return t1e simulated data $2

#ince a bigger range o0 values 0romR,D./ 6ill 0all 6it1in t1is interval3 7 1ast1e 1ig1est probability o0 turning up



*etod 2: Resampling

• Resampling dis#rete data

– Use Randbet6een.83/ to generate a position number )* – T1is number is used to return t1e )t1 value in t1e ra6

data collection as i0 t1e ra6 data is already sorted inascending order*

– T1is ensures t1at 1ig1er 0requency results occur moreli)ely t1an t1e lo6er 0requency results*

$2:#M,99.array3)/$2:#M,99.ra6 data3 R,DBT5.83//



An ./ample: Resampling +is#rete +ata

8umber reuen#y

8 ;

; <= =

< 8

8

8

;;

;

;

=

=

=

<

Sorted +ata Randbet<een51910

8

;

=<

%

>

&

+

?

87

Because t1e positionnumber is generatedrandomly3 1ig1er

0requency result .;/6ill occur more o0tent1an lo6er 0requencyresult .</*

Result ; 1as t1e1ig1est probability o0turning up*



*etod 2: Resampling

• Resampling #ontinuous data

– Use Rand./ to generate a random number bet6een 7and 83 to represent t1e percentile value )*

– T1is percentile value ) is used to return t1ecorresponding percentile number in t1e ra6 data

collection*

– 4R(TI9./ sorts and interpolates among t1e ra6data using t1e number returned by R,D./*

– T1e ne6ly generated data $2 may be +I.R.8T 0romt1e ra6 data due to interpolation*

$2:4R(TI9.array3)/$2:4R(TI9.ra6 data3 R,D.//



*etod : Simulating +ata $rom +istribution

• ni$orm

– $2 : R,DBT5.min3 ma!/ – $2 : min @ R,D./A.ma! – min/

• 8ormal

– $2 : RMIC.R,D./3 mean3 std/

returns t1e $2 0or a given cumulative probability R,D./

– 2 : RM#IC.R,D.//

returns t1e 2 0or a given cumulative probability R,D./

• ./ponential – $2 : .-Mean/A9.R,D.//

– or $2 : .-Mean/A9.8-R,D.//



• 8-R*+IST5/9 mean9 standard=de;9 #umulati;e – !' value o0 interest

– cumulative : true returns (DF3 0alse returns 4DF

– $2 : RMIC.R,D./3 mean3 std/

• 8-R*S+IST5' > standard normal – mean : 73 standardEdev:8

– ' value o0 interestG only returns (DF

– 2 : RM#IC.R,D.//

8ormal +istribution

z



+i$$erent +istribution un#tions"robability *ass un#tion 5"* Cumulati;e +istribution un#tion 5C+

Cumulati;e +istribution un#tion 5C+"robability +ensity un#tion 5"+

"oisson+istribution

./ponential+istribution



+istribution un#tions

• "oisson

– 4I##.!3 mean3 cumulative/• !' number o0 eventsG mean' e!pected value

• cumulative : true returns (DF3 0alse returns 4MF

– !ample' number o0 customers 61o arrive in a store

every 1ourG number o0 emails you receive everyday• ./ponential +istribution

– $4DI#T.!3 lambda3 cumulative/• !' value o0 interestG lamda' 8Hmean

• cumulative : true returns (DF3 0alse returns 4DF• $2 : .-Mean/A9.R,D.// or $2 : .-Mean/A9.8-R,D.//

– !ample' customer inter-arrival timeG email inter-arrivaltimeG 0is1Hbus inter-arrival time



+ate and Time *anagement



+ate ? Time *anagement in ./#el

• 2 date systems in ./#el 5./#el -ptions @ Ad;an#ed

– 8?77 date system .de0ault/ – 8?7< date system

8?77 date system

8st an 8?77 : 8 ;?t1 Feb 8?77 : >7 8st Mar 8?77 : >8

8?7< date system

8st an 8?7< : 7 ;?t1 Feb 8?7< : %? 8st Mar 8?7< : >7

T1is date does not e!istJ >7



+ate+ay un#tions• T-+AB5

– returns t1e current date• B.AR5serial=number

– returns t1e year corresponding to t1e serial number

– !amples'

• 5rong' K,R.8<-an-7%/• L' K,R.8<-an-7%N/

• L' K,R.B8%/ 61ere B8% 1as value 8<-an-7%

• L' K,R.=?78</ : ;77>

• *-8T5serial=number – returns t1e mont1 corresponding to t1e serial number

– Oo6 many serialEnumber 6ill return you t1e same yearP#ame mont1P #ame dayP



+ate+ay un#tions• +AB5serial=number

– returns t1e day corresponding to t1e serial number – !amples'

• MTO.=?78</ : 873 D,K.=?78</ : ;<

• #o3 in 0act3 =?78< is ;<t1 ct ;77>

• +AT.5year9 mont9 day – returns a serial number

• W..4+AB5serial=number9 return=type

• Subtra#ting

• 5RQ' 8<-an-7% – ;=-#ep-7<• L' 8<-an-7%N – ;=-#ep-7<N : 88=

• L' D,T.;77%3838</ – D,T.;77<3?3;=/ : 88=



Time un#tions

• Time is stored as te $ra#tional part o$ te serial

number9 tat is9 te digits to te rigt o$ te de#imalpoint

• 8-W5

– returns t1e current date and time

– *g* I0 no6 is +'77,M3 ;%t1 Dec ;77%3 t1en t1e value o05./ is =+&88*======= 61ere

• =+&88 is t1e day ;%t1 Dec ;77%

• ======= is t1e time o0 t1e day 61ic1 is 8H= o0 t1e day

– #o3 +'77,M3 ;>t1 Dec ;77% is =+&8;*======= – 51at is t1e 0ractional part o0 noon timeP



Time un#tions• TI*.5our9 minute9 se#ond

– returns t1e serial number to t1e rig1t o0 t1e decimal point int1e 0ormat 7*$$$$$

• -R5serial=number

• *I8T.5serial=number• S.C-8+5serial=number

– returns t1e 1our3 minute and second o0 a serial numberrespectively

• OUR.=?<>8*+<&/ : ;7

• MIUT.=?<>8*+<&/ : 8?

• #(D.=?<>8*+<&/ : <8

7*+<& is in 0act +'8?'<8pm on any day



*anagement o$ Waiting ,ines

• Dueues arise <en te sort term demand $or ser;i#e

e/#eeds te #apa#ity – Most o0ten caused by random variation in service times and t1etimes bet6een customer arrivals

• Dueuing models are used to: – Describe t1e be1avior o0 queuing systems

– Determine t1e level o0 service to provide – valuate alternate con0igurations 0or providing service

• Simulation is o$ten used to analy'e more #omple/ueuing system

Interarrivaltime

Interarrivaltime



-bser;ing Dueues E Re#ording Arri;als

• 5e construct simple macros and assign to buttons to convenientlyrecord arrival time3 service start time and service end time*

• T1en 6e compute t1e inter-arrival time3 6ait time and service time*

TimerCli#ker)/ls

,rrival time

#ervice#tart time

#ervicend time

Inter-arrivaltime

server 5ait time

#ervicetime

http://timerclicker.xls/

http://timerclicker.xls/



• Timer

– designed 0or "ueue observation and analysis'• records times

– customer arrival time

– service-start time

– service-end time• tabulates intermediate variables

– inter-arrival time

– #ervice time

– 6aiting time – system times :service @ 6aitingS




Timer E *a#ro to re#ord arri;al time

#teps 8 ;

#tep 87

#tep +

#tep &

#tep 8= - FF

#tep 8<

8*D= : o6./3 c1ange to time 0ormat

;*Fill ,rray (+'+ 6it1 lin) to D=

=*Fill ,rray F+'I+ 6it1 0ormulas

<*Format cells

%*ToolsHMacroHRecord e6 Macro

>*Ley F? (to activate Calculate)

#tep ? -

8%* (reate buttons assign macros tot1em

&* #elect (& and copy

+* #elect (> and )ey (trl-Do6n,rro6

?* #elect Rel* Re0 in Macro Record (ontrol 4anel

87* Ley Do6n,rro6

88* 4aste#pecial CalueumberFormat

8;* Ley sc

8=* Unselect Rel* Re0 in Macro Record #top8<* #top Macro Record



• Cli#ker

– Timer 1as limitations' First-(ome-First-#erve3 #ingle #erver – (lic)er is an adaptation o0 Timer

– (ounts arrivals

• records arrival times o0 up to = types o0 customers

•by clic)ing an appropriate button3 one 0or eac1 type o0 customer • tabulates t1eir cumulative 0requency counts 0or given timeintervals .bins/

• c1ange t1e time bins to t1e correct date to capture time stamps

– #ample ,pplications'

• (ount number o0 ve1icles using a stretc1 o0 road

– *g* Motorcars3 Motocycles3 Buses




Simulating Dueues

• %i;en obser;edistori#alra< data9 o< #an <e

model and analyse <aiting linesF

• se o$ Re7sampling – #imulate data 0or inter-arrival and service times via re-

sampling o0 ra6 data t1roug1 observed distributions e*g*• Inverse o0 !ponential Distribution' 7A;erageG,n5Rand5

• Inverse o0 mpirical Distribution' "er#entile5+ataArray9Rand5

• Single Ser;er Dueues ;s *ulti Ser;er Dueues – c1ec)out lines3 0ast 0ood outlets



Simulating Dueues

• Some de$initions 51 Ser;er

– Inter-,rrival #ervice ,rrival 5ait #ystem #ystemTime Time Time #tart nd Time Time 9engt1

#ervice

,rrival Time @Inter-,rrival Time

I0 no one in queue3 : ,rrival Timelse : nd Time o0 last customer

#ervice #tart Time @#ervice Time

btainedusing

Inverse

!ponentialDistribution

#tart Time – ,rrival Time

nd Time – ,rrival Time

o* in queue :o* o0 #ervice ndTime V ,rrival Time

Re-sampling 0rom1istorical data using4ercentile 0unction



H+3 3ank

• Inter ,rrival Time : – meanA9.R,D.// – simulate using the

Exponential Function

• #ervice Time : 4R(TI9 .service time array3 R,D.//

• ,rrival Time : ,rrival Time o0 previous customer @ Inter ,rrival Time

• #ervice #tart Time : M,$ .previous customer service end time3 arrivaltime/

• #ervice nd Time : #ervice #tart Time @ #ervice Time

• 5ait Time : #ervice #tart Time – ,rrival Time

• #ystem Time : 5ait Time @ #ervice Time or nd Time – ,rrival Time• #ystem queue lengt1 .number o0 customer in t1e system at arrival time/

: (UTIF .all previous customer nd Time V ,rrival Time/

• Tra00ic intensity : service timeHinter arrival time

(ustomer Inter-,rrival #ervice ,rrival 5ait #ystem #ystem

Time Time Time #tart nd Time Time 9engt1

#ervice



Con#atenate5 or ?

• 5e can concatenate te!t toget1er to 0orm longer te!t by

using t1e 0unction concatenate./ or t1e sign• (oncatenating te!t is necessary 61en you need to enter

criteria as te!t

• !ample 8'

(oncatenate.Microso0tN3 N3 !celN/ : Microso0t !celN Microso0tN N !celN : Microso0t !celN

• !ample ;'

Qiven t1at cell ,; stores t1e number ;7 and cell ,= stores

t1e te!t ,pplesN (oncatenate.,;3 N3 ,=/ : ;7 ,pplesN

,; N ,= : ;7 ,pplesN

• !cel automatically converts numbers to te!t 61enconcatenating



Counti$5

• Counti$5range9 #riteria

– Returns t1e number o0 cells t1at satis0y t1e evaluationcriteria

– Range is t1e range o0 cells 0rom 61ic1 you 6ant to count

– (riteria is input as te!t .e*g*3 W:D;/

criteria

range

Return =



H+3 3ank E #7Ser;er • 51en t1ere are more t1an 8 servers

• Model same as be0ore e!cept customer service start time can beearlier

• I0 t1ere are cN number o0 servers3 t1e customer start time 6ill bet1e ct1 largest customer service end time o0 all previous customerservice end times*

87*77am

87*7%am

87*8%am

#erver 8

#erver ;

#erver =

rd largest

I0 0 l i 0



-bser;ing Dueues

• Some de$initions 5*ultiple Ser;ers

–

"ro#essing Dueues

:IF.20@>J.JK39,RQ.J%J1K:%1L3XX</3.20/

I0 no* o0 people in queue W no* o0 servers3#ervice #tart Time : ,rrival Time

lse i0 no o0 people in queue V: no* o0 servers3#ervice #tart Time : Time any #erver becomes available

: nt1 largest nd Time 61ere n : no* o0 servers



Takea<ays

• Timer ? Cli#ker

– Time-based #imulations – 5ays to count arrivals

– ,pplication o0 Time 0unctions

– ,pplication o0 Macro Recording

• H+3 3ank

– Use o0 observed distribution .!ponential3 mpirical/0rom ra6H1istorical data to generate simulation o0 0uturetrials



Reminders

• "roMe#t S#ope Con$irmation <it "ro$) be$ore te

Re#ess <eek• Start <orking on your proMe#t

• 8e/t #lass

– Revie6 o0 5ee) 8 to 5ee) & lessons

CAT Lesson6

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