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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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ReviewonQueueingTheory
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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
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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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