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Feb.12/Feb.24,2015

Topic4:TeletrafficEngineering

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QuickReview

Cellularconceptandfrequencyreuse

o Eachbasestationisallocatedaportionofthetotalnumber

ofchannels

o Differentcellsthatareseparatedbyadistancelargeenough

canreusethesamegroupofchannelstocovertokeep

interferencetolerable cochannelcells

o RelationshipofNwithS/Iratio: N,numberofchannelsassignedtoeachcell

Callcapacityofcell cochannelinterference

o Howmanychannelsareneededforacelltoaccommodate

userdemandsinasatisfactorymanner?

o Anyothercomplementarymethodtoincreasecellcapacity?

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Trunking

Trunking

o Eachuserisallocatedachannelonapercallbasis,andupon

terminationofthecall,theoccupiedchannelisimmediately

returnedtothepoolofavailablechannels

Trunkingexploitsthestatisticalbehaviorofuserssothata

fixednumberofchannelsorcircuitsmayaccommodatea

large,randomusercommunity.

Gradeofservice(GoS)

o Specifythelikelihoodofauserobtainingchannelaccess

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TypesofTrunkedSystems

Blockedcallscleared(ErlangBsystem)

o Ifnochannelsareavailable,therequestinguserisblocked

withoutaccessandisfreetotryagainlater.

Blockedcallsdelayed(ErlangCsystem)

o Ifachannelisnotavailableimmediately,aqueuemaybe

usedtoholdtherequestingusersuntilachannelbecomes

available

o Thecallrequestmaybedelayed

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Questions

Theprobabilitythatacallisblockedinalosssystem

Theprobabilitythatacallisdelayedinadelaysystem

Theaveragedelaytimeifacallisdelayedduetolackofresources

Theprobabilitythatadelayedcallwaitsforatimegreater

thanalimit

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6

ReviewonQueueingTheory

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7

EvaluateTrunkingSystem

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DefinitionofTrunkedSystem

Requestrate():averagenumberofcallrequestspertimeunit

per

user

o Poissonarrivals

Holdingtime(H):averagedurationofatypicalcall

o Exponentialdistribution

Trafficintensity(A):measureofchanneltimeutilizationin

Erlangso Thetrafficintensityofferedbyeachuseris Au = Ho ForasystemwithUusersandanunspecifiednumberofchannels,the

totalofferedtrafficintensityis

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A = U Au = U H

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GoS(1)

Callblockingprobability

o ModeledbyanM/M/m/mqueue

o

ErlangBformula

9

m C

A /

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GoS(2)

Calldelayedprobability

o ModeledbyanM/M/mqueue:infinitebuffersize

o

ErlangCformula

10

m C

A/C = /(m)

A m= /

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Background

BlockingprobabilityofanM/M/m/mqueueingsystem

o ErlangBformula

DelayedprobabilityofanM/M/mqueueingsystem

o ErlangCformula

11

m C

A/C = /(m)

A m= /

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GoS(3)

Ifnochannelsareimmediatelyavailablethecallisdelayed,

andtheprobabilitythatthedelayedcallisforcedtowait

morethantsecondsis

Theaveragedelayforallcallsinthequeueingsystemis

givenby

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Background

ForanM/M/mqueueingsystem,averagewaitingtimeof

customersstayinginthequeue:

ForanM/M/mqueueingsystem,waitingtimeofcustomers

stayinginthequeue*:

*W.C.ChanandY.B.Lin,WaitingtimedistributionfortheM/M/mqueue,IEEProceedings,vol.150,no.3,pp.159162,June2003.13

m C1/H

A/H

m = C/H A/H

= (C A)/H

mPW q 1 Pq = P[W > 0] Erlang-C formula

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Example:BlockedCallsCleared

SystemAhas394cellswith19channelseach.Findthenumber

ofusersthatcanbesupportedat2%blockingifeachuser

averagestwocallsperhouratanaveragecalldurationofthree

minutes.

Solution:

o Probabilityofblocking=2%=0.02

o

Numberofchannels

per

cell

used

inthe

system,

C=19

o Trafficintensityperuser,Au=H=2 (3/60)=0.1Erlangs

o ForGOS=0.02andC=19,fromtheErlangBformula,thetotalcarried

traffic,A,isobtainedas12Erlangs.

o

Therefore,thenumberofusersthatcanbesupportedpercellisU=A/Au=12/0.1=120

o Sincethereare394cells,thetotalnumberofsubscribersthatcanbe

supportedbySystemAisequalto120 394=47,280

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Example:BlockedCallsDelayed

Ahexagonalcellwithinafourcellsystemhasaradiusof

1.387km.Atotalof60channelsareusedwithintheentire

system.Iftheloadperuseris0.029Erlangs,and =1

call/hour,foranErlangCsystemthathasa5%probability

ofadelayedcall:

o Howmanyuserspersquarekilometerwillthissystem

support?o Whatistheprobabilitythatacallwillbedelayedformore

than10seconds?

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Solution:BlockedCallsDelayed(1)

Ahexagonalcellwithinafourcellsystemhasaradiusof

1.387km.Atotalof60channelsareusedwithintheentire

system.Iftheloadperuseris0.029Erlangs,and =1

call/hour,foranErlang Csystemthathasa5%probability

ofadelayedcall.

o Cellradius,R=1.387km

o Areacoveredpercellis2.598 (1.387)2 =5km2 Areaofahexagonofsidetisgivenby:

o Totalnumberofchannels=60

o Numberofcellspercluster=4

o Numberofchannelspercell=60/4=15channels

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Solution:BlockedCallsDelayed(2)

Numberofchannelspercell=60/4=15channels

FromErlangCformula,for5%probabilityofdelaywith

C=15,trafficintensityA=9.0Erlangs

Numberofusers=totaltrafficintensity/trafficperuser=

9.0/0.029=310users 310users/5km2 =62users/km2

Probabilitythatacallisdelayedmorethan10seconds:

o

o

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