Lecture 9

TrafficEngineeringforCircuitSwitchedConnections

+Traffic Engineering

nCells- deployalargenumberoflow-power basestations- eachhavingalimitedcoveragearea

nReusethespectrumseveraltimesintheareatobecoveredtoincreasecapacity

n Issues:n Capacity(trafficload)inacellnOnemeasure=numberofcommunicationchannels thatareavailable

n Performancen Callblockingprobability,handoffdroppingprobability,throughputetc.

n Interference

2

+GSM Logical Channels

nNoRFcarrierortimeslotisreservedforaparticulartaskexcepttheBCCHn Anytimeslotonanycarriercanbeusedforalmostanytaskn Framingstructurehastobemaintained

nChannelsareoftwotypes:n TrafficChannels(TCH)

n Voiceat13kbpsn Dataat9.6,4.8or2.4kbps

n ControlChannels(CCH)n Broadcast,CommonandDedicated

3

+Broadcast Control Channels (Unidirectional)nBCCH(BroadcastControlChannel)

n Usedtotransmitcellidentifier,availablefrequencieswithinandinneighbouring cells,options(likeFH)etc.

n Continuallyactive“beacon”n Hastwosub-channels

nFCCH(FrequencyCorrectionChannel)n Usesafrequencycorrectionburst

nSCH(SynchronizationChannel)n Timesynchronizationinformation

4

+ALOHA

n Transmitwheneveryouwantn Ifyouareacknowledged,everythingisfinen Otherwiseretransmitpackets

n Lowthroughput(18%)

n Slottedversionsareslightlybettern Transmissionattemptscantakeplaceonlyatdiscretepointsoftime

Computer A

Computer Btime

t t+x t+F t+x+F

collision

5

+Use of ALOHA in Cellular Networks

nTosetupacall,MSs initiallyemployslottedALOHAtosendsomeinformationtotheBSn Called“randomaccesschannel”orsomethingsimilarn InLTE,apreambleistransmitted(uniqueormaycollide)

n Ifsuccessful,theyare“assigned”afrequencychannelandtimeslotorspread-spectrumcode

n Ifunsuccessful,theytryagainnMSgivesupifrepeatedtriesfail

n Collisions(congestion),poorchannelquality,etc.

6

+Common Control Channels (Unidirectional)n Usedforallconnectionsetuppurposes

n Thepagingchannel(PCH)isusedforpagingamobilewhenitreceivesacall

n Therandomaccesschannel(RACH)isusedbytheMStosetupacalln SlottedALOHAontheRACH

n Accessgrantchannel(AGCH)isusedbytheBTStoallocateachanneltotheMSn ThiscanbeaTCH(startusingvoice)n OraSDCCH(negotiatefurtherforconnectionsetup)

SDCCH:StandalonededicatedCCH

7

+Dedicated Control Channels (Bidirectional)n AslongasaMShasnotestablishedaTCH,itwilluseastand-alonededicatedcontrolchannel(SDCCH)forsignalingandcallsetupn Authenticationn Registration,etc.

n EachTCHhasaSlowAssociatedControlChannel(SACCH)n Exchangesysteminformationlikechannelquality,powerlevels,etc.

n AFastAssociatedControlChannel(FACCH)isusedtoexchangesimilarinformationurgently(duringhandoffforinstance)

8

+Framing Scheme in GSM (Traffic Channels)1 2 3 4 2048

1 2 3 4 51

1 2 3 4 26

TB TBData(57bits) TS GPData(57bits)

1 2 3 5 6 7 8

Hyperframe:3hours28min53.76s

Superframe:6.12s

TrafficMultiframe:120ms

Frame:4.615ms

Slot:577µs

Framingschemeisimplementedforencryptionandidentifyingtimeslots

9

+Framing Scheme in GSM (Control Channels)1 2 3 4 2048

1 2 3 4 26

1 2 3 4 51

TB TBData(57bits) TS GPData(57bits)

1 2 3 5 6 7 8

Hyperframe:3hours28min53.76s

Superframe:6.12s

ControlMultiframe:235.4ms

Frame:4.615ms

Slot:577µs

Framingschemeisimplementedforencryptionandidentifyingtimeslots

10

+One Time Slot (typical)

nAtimeslotlasts577µs (546.5µs ofdataand30.5µs ofguard-time)

nBitsperslot=3+57+1+26+1+57+3+8.25=156.25

nBitrate=156.25/577µs =270.79kbps

TB TBData(57bits) TS

TB:TailBits(3bits)TS:TrainingSequence(26bits)GP:GuardPeriod(8.25bits)

GP

Flags

Data(57bits)

11

+Traffic Channel

n 20msofvoice(260bits@13kbps)isconvertedto456bitsafterCRCandconvolutional encoding

n Effectivedatarate=22.8kbps

n 456bits=8× 57bitsn (Reminder:atimeslothastwo57bitunitsseparatedbyatrainingsequence)

n VoicesamplesareinterleavedandtransmittedontheTCH

n DataandControlbitsarealsoencodedtoendupwith456bitsover20ms

12

GSM Coding for Voice Traffic

n Class1a:CRCandconvolutionalcodingn 3-biterrordetection&errorcorrection

n Class1b:convolutionalcoding

n Class2:noerrorprotection

*tailbitstoperiodicallyresetconvolutionalcoder

(2,1,5)convolution

coder

260bits/20ms

=13kb/s

50class1abits

132class1bbits

78class2bits

456bits/20ms=22.8kb/s

Channelencoder

3-bitCRC

53bits

Bitinter-leaver

378bits

4tailbits*

13

+Example: Mobile Initiated Call in 2G GSM MessageName Category

1.ChannelRequest RRM

2.ImmediateAssignment RRM

3.CallEstablishmentRequest CM

4.AuthenticationRequest MM

5.AuthenticationResponse MM

6.CipheringCommand RRM

7.CipheringReady RRM

8.SendDestinationAddress CM

9.RoutingResponse CM

10.AssignTrafficChannel RRM

11.TrafficChannel Established RRM

12.Available/BusySignal CM

13.CallAccepted CM

14.ConnectionEstablished CM

15.InformationExchange voicebits

Security

Related

TrafficChannel=Circuit

Thisisallcontrolsignaling

14

+IS-95 Forward Channel

OneForwardCDMALink,1.25MHzinthe869-894MHzbands

Pilot Synch PCH 1

PCH 7

Code 1

CodeN

CodeP

CodeS

Code55

W0 W32 W1 W7 W8 W63

Fundamental Code Channel

Data

Mobile PowerControl

Subchannel

Fundamental Code Channel

Data

Mobile PowerControl

Subchannel

SupplementaryCode Channel

Data

The1.25MHzchannelisobtainedbycombining41AMPSchannelseach

havinga30kHzbandwidth

Forward traffic channel with one code

Forward traffic channel with multiple codes

15

+The IS-95 Forward Link (I)

nTherearefourtypesoflogical channelsn TheyarecreatedbyusingorthogonalWalshcodes

nBroadcastchannelswithoutpowercontroln PilotChannel(assignedWalshcodeW0)n SynchChannel(assignedWalshcodeW32)n PagingChannel– PCH(upto7innumber)

nDedicatedchannelswithpowercontroln Forwardtrafficchannels– FTCH(many)

n Fundamentalcodechanneln Uptosevensupplementalcodechannels

16

Basic Spreading Procedure on the Forward Channel in IS-95n Symbolsaregeneratedatdifferentrates

n Forthespreadsignaltobeat1.2288Mcps,theincomingstreammustbeat:1.2288x106/64=19.2kbps

n Whathappensiftheincomingstreamisatalowerrate?n Example:Incomingstreamisat4.8kbpsn Numberofchipsperbit=1.2288x106/4.8x103 =256

BasebandFilter

BasebandFilter

IPNat1.2288Mcps

QPNat1.2288Mcps

1.2288Mcps

WalshCode

LogicalChannelDependentSymbols

WhatisthisDSSSScheme?

17

+Channelization, Scrambling, and Error Correction Codesn CDMAsystemsuseavarietyofcodesforspreadingthesignal

n ChannelizationCodesn WalshcodesandOVSFcodesn Usedtoseparateusertransmissionsinthesamecellontheforwardlink

n Usedtoseparatemultiplesignalsofsame useronreverselinksin3Gsystems

n ScramblingCodes(PNcodes)n M-sequences,Goldsequences,Kasami sequencesn Usedtoseparatesignalsonthereverselinkfrommultipleusersn Usedtoseparatesignalsfromdifferentbasestationsontheforwardlink

18

ToQPSKModulator

BasebandFilter

BasebandFilter

IPilotPNat1.2288Mcps

QPilotPNat1.2288Mcps

1.2288Mcps

WalshCodeW0

All0s

Pilot Channel

n ItiscontinuouslytransmittedbyaBSontheforwardlinkn Likea“beacon”(CompareBCCH)n ActsasthereferencesignalforallMSsn Usedindemodulationandcoherentdetection

19

+The Pilot Channel (II)

n ItcarriesNOinformationbutitisaveryimportantsignal

n Ithas4-6dBhighertransmitpowerthananyotherchannel

n Thetransmitpowerofthepilotchannelisconstant(Nopowercontrol)

n TheIandQPNsequencesn AregeneratedusingaLFSRoflengthm =15n Theperiodis215 – 1=32767

n Anextrazeroisaddedafterarunlengthof14zerosoncewithintheperiodn Intime,oneperiodis32768 × 0.8138µs =26.67msn Numberofrepetitions/second=1/26.67 × 10-3 =37.5n Numberofrepetitionsin2seconds=75

20

+PN Sequences are generated using Linear Feedback Shift Registers (LFSRs)

XORgateMultiplication

PolynomialRepresentation:ci {0,1}2

21

+Use of the PN sequences in IS-95

nThePNsequencesaredefinedbythefollowingLFSRsn PNI(X) =X15 +X13 +X9 +X7 +X5 +1n PNQ(X)=X15 +X12 +X11 +X10 +X6 +X5 +X4 +X3 +1

nAllbasestationsusethesamePNsequencesbutwithadifferent“offset”

nTheoffsetsarebymultiplesof64chipsn Totalnumberofpossibleoffsets=32768/64=512n Durationof64chips=64´ 0.8138x 10-6 =52µs

n Lighttravels3´ 108 m/s =>15630m in52µs

22

+More on the Offset

nThebasestationsinIS-95arecompletelysynchronizedusingGPSn Transmittedchipsonthedownlinkareallsynchronizedfromallbasestations

n TheBaseStation“SystemTime”issynchronizedtoa“UniversalCoordinatedTime”orUTCn UTCislooselywhatusedtobeGMTn Thetimeisspecifiedintermsofa24hourcyclen SystemtimeisnotthesameasUTCbecauseitdoesnotincludeleapseconds

nTheWalshcodesareusedwithoutanyoffsetn TheyarealignedsuchthatthefirstbitalwaysstartsattheevensecondintheIS-95system

23

+The Synch Channel

n ThesynchchannelislockedtotheoffsetofthePN-sequenceusedinthepilotchanneln Itcontainsinformationpertinenttotheassociatedbasestationn MScanretrievetheinformationforsubsequentuse

n TheveryfirstbitsdemodulatedbytheMSarefromthesynchchanneln Importantinsynchronizingtothebasestationn Example1:ReversePNcodeshavezerooffsetrelativetoevennumberedsecondsofthesystemtime

n Example2:MSmustsynchitslongcodegeneratorwiththeoneusedattheBS

24

+The Paging Channel

nTransmitscontrolinformationtotheMSn Pagemessagetoindicateincomingcalln Systeminformationandinstructions

n Handoffthresholdsn Maximumnumberofunsuccessfulaccessattemptsn Listofsurroundingcells(howaretheyidentified?)n Channelassignmentmessages

n Acknowledgmentstoaccessrequests

n Itoperatesateither4.8kbpsor9.6kbpsn Itispassedthrougharate½convolutionalencodertogoupto9.6kbpsor19.2kbps

n Iftheoutputis9.6kbps,itisrepeatedtogoupto19.2kbps

25

+The forward traffic channel

nCarriesusertrafficandcontrolmessagestospecificMSsn DedicatedexclusivelytooneMS

nCancarrytrafficatdifferentratesn RateSet1

n 1.2kbps,2.4kbps,4.8kbpsand9.6kbpsn IdealtosupportQ-CELPthatvariesthevoicecoderate(maximumof8kbps)basedonthevoiceactivity

n UsedprimarilyinIS-95n RateSet2

n 1.8kbps,3.6kbps,7.2kbpsand14.4kbpsn Idealtosupportbettervoicequalityatamaximumof13kbpsn SuggestedforPCS(butalsoallowedinIS-95)

26

+Coding of the speech signal

n Thespeechsignalsareencodedinto20ms framesn Theframescontain192bitsofspeechat9.6kbps

n Highvoiceactivityn Theframescontain24bitsat1.2kbps

n Backgroundnoiseorlowvoiceactivityn Theframescontain48&96bitsat2.4and4.8kbps

n Providesmoothtransitionbetweentheothertwodatarates

n Thereare8tailbitsintheframethatareusedtoresettheconvolutionalencoder

n At9.6kbpsand4.8kbpsthereisaCRCcodeaswelltoindicatethe“quality”oftheframen Framequalityindicator(12,10,8or6bits)n Onlydetectframeerrors

27

+Frame Quality Indicator (FQI)

nInCDMA,theframeerrorratespecifiestherequiredSIRforthesystemnTypically1%or2%(dependingonrateset)

nTheFQIintheframeallowstheBStodetectwhetherornotaframeisinerror

28

+

BBF

BBF

IPilotPNat1.2288Mcps

QPilotPNat1.2288Mcps

1.2288Mcps

WalshCodeWi

MUX

Long CodeDecimator

Long CodeGenerator

64:1

1.2288Mcps

LongCodeMask Long CodeDecimator

BlockInterleaver

SymbolRepetition

19.2ksps

ConvolutionalEncoder

VoiceTraffic

Rate1/2

24:1

PowerControlBits

800bps

19.2ksps

19.2ksps

800bps

Operation of the Forward Traffic Channel (Rate Set 1)

Uniqueforeachuser

29

+Control signals and data over FTCHs

n IS-95supportstransmissionofn Signalingdataanduserdataoverthesameframen Primaryuserdata(voice)andsecondaryuserdata(e.g.Fax)overthesameframe

n Thisisallowedonlyforthe9.6kbpsframesn Onlyspeechcanbecarriedatlowerrates

n Dimandburstn Signalingorsecondaryuserdataoccupiespartoftheframealongwithspeech

n Blankandburstn Signalingorsecondaryuserdataoccupiestheentireframe

30

ComparewithSACCHandFACCH

inGSM

+

OneReverseCDMALink,1.25MHzinthe

824– 849MHz

AccessChannel

Fundamental Code Channel

Data

SupplementaryCode Channel

Data

AccessChannel

AccessChannel

AccessChannel

TrafficChannel

1

TrafficChannel

T

SupplementaryCode Channel

Data

SupplementaryCode Channel

Data

SupplementaryCode Channel

Data

Reverse CDMA Channel

ComparewithRACHAndAGCH

31

+What is UMTS?

n UMTSstandsforUniversalMobileTelecommunicationsSystemn 3GcellularstandardintheUS,Europe,andAsia

n OutcomeofseveralresearchactivitiesinEuropen GeneratedtrialsystemsandbasicunderstandingofWCDMAn Assistedthestandardizationefforts

n Mostofthestandardizationworkwasfocusedin3GPPn 3GPPreferstothephysicallayerasUTRA– UMTSTerrestrialRadioAccessn Therearetwomodes– FDDandTDD

n UMTScansupportbothGSM-MAPandIS-41corenetworksn Anall-IPthirdalternativeis availablenow

32

+UMTS Architecture

n TheUMTSSystemn Consistsofmanylogicalnetworkelementssimilartothe2Gsystemsn Logicalnetworkelementshave“openinterfaces”

n Therearethreecomponentsn UserEquipment(UE)n UMTSTerrestrialRadioAccessNetwork(UTRAN)n CoreNetwork(CN)

n HeavilyborrowsfromGSM

UserEquipment

UMTSTerrestrial

RANCore

Network

Uu Iu

33

+Detailed Network Elements

USIM

ME

UE

Cu

Uu

NodeB

NodeB

NodeB

NodeB

RNC

RNC

MSC/VLR

SGSN

GMSC

GGSN

HLR

PLMNPSTN

Internet

Iu

IubIur

UTRAN CN

WCDMAAirInterface

34

+Summary of WCDMA

n WCDMAissomewhatdifferentcomparedtoIS-95

n Itisa“wideband”directsequencespreadspectrumsystemn Supportsupto2Mbpsusing

n Variablespreadingn Multicode connections

n Thechiprateis3.84Mcpsn Approximatebandwidthis5MHzn Carrierspacingisonarasterof200kHzn Supportshigherdatarates/capacityn Increasedmultipathdiversity(proportionaltochipduration)

35

+UTRA General Interface – II

n Higherlayerdataiscarriedintransportchannelsn Thedataiscarriedinchunkscalled“transportblocks”n Eachtransportchannelismappedtoaphysicalchannel(later)n Theframesare10mslong

n Atransportchannelhasn ATFI– TransportFormatIndicator

n Timedependentfieldn Containsparameters oftheassociatedtransportchannel

n TFI’sarecombinedintoTFCIsn TransportFormatCombinationIndicatorn TFCI’stellthereceiverwhattransportchannelsareactive

n Blindtransportformatdetection(BTFD)isalsopossiblen Usuallyhappensonlyontheforwardlink

n Therearetwotypesoftransportchannelsn Dedicatedtransportchannelsn Commontransportchannels

ControlSignaling

36

+UTRA General Interface

Transport channel 1 Transport channel 2

Transport Block

Transport Block

TFI TFITransport Block

Transport Block Higher

PHYTFCI Coding & MUXing

TFI TFITransport Block + Error

Indication

Transport Block + Error

Indication

Higher

PHYTFCI Decoding &

DeMUXing

Transmitter

Receiver

PhysicalControl Channel

PhysicalData Channel

37

+ Mapping of Transport Channels to Physical Channels

Broadcast Channel (BCH)Primary Common ControlPhysical Channel (PCCPCH)

Forward Access Channel (FACH) Secondary Common ControlPhysical Channel (SCCPCH)Paging Channel (PCH)

Random Access Channel (RACH)Physical Random AccessChannel (PRACH)

Dedicated Channel (DCH)Dedicated Physical Data Channel(DPDCH)Dedicated Physical Control Channel (DPCCH)

Downlink Shared Channel (DSCH)

Common PacketChannel (CPCH)

Physical Downlink SharedChannel (PDSCH)Physical Common PacketChannel (PCPCH)

Forward Only Reverse Only Both Reverse and Forward

38

Random Access Channel

n BasedonslottedALOHAn 15accessslotsevery20msn Preamblesaretransmittedfor4096

chipsof5120chipsinanaccessslotn Followedbytheaccessmessage

n Messagehasadataandacontrolpartn Dataparthasavariablespreading

factorn Controlparthasafixedspreading

factorof256

Slot 1 Slot 2 Slot 3 Slot 4 Slot 5 Slot 15

20 ms

Preamble

4096 chipsPreamble Preamble Message Part = 1-2 10 ms frames

5120 chips

User Data – 10,20,40, 80 bits

Pilot – 8 bits

0 1 2 3 14

TFCI

Data part

Controlpart

10ms=2560chips

39

Reverse DPCH Structure

n TheDPCCHcarriesphysicallayercontrolinformationn Ithasafixedspreadingfactorof

256

n TheDPDCHcarrieshigherlayerinformationn Spreadingfactorcanrange

between4and256

n TPC– TransmissionPowerControl

n FBI– FeedbackInformation

Data (voice bits)

Pilot

0 1 2 3 14

10 ms Frame = 38400 chips

TFCI FBI TPC

DPDCH

DPCCH

1 slot =2560 chips

Frame 1 Frame 2 Frame 72

Superframe = 720 ms

40

+ Reverse multiplexing and channel coding chain in UMTS

CRC Attachment

Transport BlockConcatenation/ CodeBlock Segmentation

Channel Coding

Radio Frame Equalization

First Interleaving(20, 40, or 80 ms)

Radio Frame Segmentation Rate matching

Transport ChannelMultiplexing

Physical ChannelSegmentation

CRC Attachment

CRC AttachmentPhysical ChannelMapping

Second interleaving(10 ms)

DPDCH1 DPDCH2 DPDCHN

Other TransportChannels

41

+More details

n Figureshowsreverselink

n Forwardlinkissimilar,butcontrolanduserdataareseparatedintime

n Includespowercontrolforsomechannels,andnotforothers

CRCEncoder

CRCEncoder Tr

ansp

ort

bloc

kCon

cate

natio

n or

se

gmen

tatio

nChannelCoder

Interleaver

RateMatcher

Tran

spor

t c

hann

elM

ultip

lexe

r

Tran

spor

t to

Ph

ysic

al c

hann

el

map

per

Interleaver

Transport Ch 1 Blk 1

Transport Ch 1 Blk 2

Transport Channel 2

Transport Channel 3

DPDCH1

DPCCH

Sepa

ratedincod

e

ReverseLinkExample

42

+Reverse chain in UMTS details –In Atransportblockisreceivedfromthehigherlayers

n ACRCisattached(0,8,12,16or24bits)n Usedtoprovideerrorindicationtohigherlayers

n Thetransportblocksareeitherconcatenatedorsegmentedbasedontheirsizeascomparedtothechannelcodingblockn Twotypesofchannelcodingareprovided

n ½and1/3rateconvolutionalcodingn 1/3rateturbocoding

n Channelcodingisperformed

43

+Reverse chain in UMTS details –IIn Radioframeequalization

n Ensuresthatdataisdividedintoequalsizedblockswhentransmittedovermany10msframes

n Dataispaddedwithzerostillitcanbedividedintoequalsizedblocksthatfitinaframe

n Firstinterleavingn Usedonlywhenthedelaybudgetisacceptablen Dependsonhowoftendataarrivesfromhigherlayers(calledthetransmissiontime

intervalorTTI)n IfdifferenttransportchannelshavedifferentTTI’s,theymustbetimealignedbefore

multiplexing

n Ratematchingn Thisissimilartothepuncturing/repetitionoperationsinIS-95n Itisusedtomatchthenumberofbitstobetransmittedtothenumberavailableona

singleframen TheTFCIcontainstheratematchingattribute

44

+Reverse chain in UMTS details –IIIn Transportchannelmultiplexing

n Differenttransportchannelsaremultiplexedheren Spreadingcodesareusedtoseparatethechannelsn Serialmultiplexingisalsopossible

n SecondInterleavingn Alsocalledintra-frameinterleavingn Lastsfor10msn Appliedseparatelyforeachphysicalchannel

n Theoutputisamappingtoaphysicalchanneln Thenumberofbitsgivenforaphysicalchannelatthisstageisexactlyequaltothenumberthatthespreadingfactorofthatframecantransmit

45

+Traffic Engineering (2)

nQuestions:n IfIwanttoplaceacall,whatistheprobabilitythatIwillNOTgetacommunicationchannel?n“Newcalladmission”

n IfIammovingfromcelltocell,whatistheprobabilitythatduringacall,IwillNOTfindacommunicationchannelinthenewcelltocontinuemycall?n“Handoffcalladmission”

46

+Grade of Service

n Gradeofservicen Usually2%blockingprobabilityduringbusyhourn Busyhourmaybe

1. Busyhouratbusiestcell2. Systembusyhour3. Systemaverageoverallhours

n Givenc =T/Nc trafficchannelspercell– whatisthegradeofservice(GoS)?n HowmanyuserscanbesupportedforaspecificGoS?

n BasicanalysiscalledTrafficEngineeringorTrunkingn Sameascircuitswitchedtelephonyn UseErlang B andErlang CModels

47

+Erlangs - 1

nLettherebec =T/Nc channelspercell

nInagiventimeperiod,supposethereareQusersmakingacalln IfQ =c,anynewcallwillbeblockedwithprobability1

n IfQ <c,thenyourcallmaygetachannel

nHowdowequantifythisbetter?nErlangs

48

+Erlangs - 2

n Howdoyouestimatetrafficdistribution?n TrafficintensityismeasuredinErlangs

n OneErlang =completelyoccupiedchannelfor60minutes

n Examplesn 30kHzvoicechanneloccupiedfor30min/hourcarries0.5Erlangs

n 100callsinonehoureachlasting3minutes=100calls/hour× 3/60=5Erlangs

n Agner Krarup Erlang

n ScientistwiththeCopenhagenTelephoneCompany

n Studieddatafromavillage’stelephonecallstoarriveathisconclusions

49

+More on Erlangs

n Lettrafficintensityperuser=Aun Au =averagecallrequestrate× averageholdingtime=l × th

n Totaltrafficintensity=trafficintensityperuser×numberofusers=Au × nu

n Example:n 100subscribersinacelln 20make1call/hourfor6min=>20× 1× 6/60=2En 20make3calls/hourfor½min=>20× 3× .5/60=0.5En 60make1call/hourfor1min=>60× 1× 1/60=1En 100usersproduce3.5Eloador35mE peruser

nu =20;l =1;th =6/60

50

+Notation associated with queues

nWrittenasP/Q/R/Sn P:Descriptionofarrivingtrafficn Q:Descriptionofserviceratesortimesn R:Numberofserversn S:Numberofusersthatcanbeinthesystem(includesthosebeingservedandthosewaiting)

nM=>Markov(Poissonarrivaltimes,exponentialservicetimes)n Commonlyusedasitistractableanditfitsvoicecalls

n Ifthenumberofusersthatcanbeinthesystem(S)isinfinite,itisdroppedfromthenotation

51

+Erlang B Model: M/M/c/c queue

n ToestimatetheperformanceofatrunkedsystemusetheErlang Bqueueing model

n Thesystemhasafinitecapacityofsize cn Customersarrivingwhenallservers(channels)busyaredropped

n Blockedcallsclearedmodel(BCC)(nobuffer)

n Assumptionsn c identicalservers(channels)processcustomersinparalleln CustomersarriveaccordingtoaPoissonprocess(averageofλ calls/s)n Customerservicetimesexponentiallydistributed(averageof1/μsecondspercall)

n Theofferedtrafficintensityisa =λ/μ inErlangs

52

+Erlang B Formula or Blocking Formulan ProbabilityofacallbeingblockedB(c,a)

n Erlang Bformulacanbecomputedfromtherecursiveformula

nUsuallydeterminedfromtableorcharts

B(c, a) =ac

c!/

cX

n=0

an

n!

B(c, a) =a⇥B(c� 1, a)

c+ a⇥B(c� 1, a)

53

+Example of Erlang B Calculation

nFor100userswithatrafficloadof3.5E,howmanychannelsareneededinacelltosupport2%callblocking?nUseErlang BtablesorchartsnWitha2%callblocking,weneed8channels

54

+Sample Erlang B table

55

+Erlang B Chart

10-1

100

101

102

10-3

10-2

10-1 1 2 3 5 7 9 15 25 35 95

Traffic load in E rlangs

prob

abilit

y of

block

ing

N: num ber of channels

8channels

56

+Example: Using Erlang B for traffic engineering

nConsiderasingleanalogcelltowerwith56trafficchannelsnWhenallchannelsarebusy,callsareblockednCallsarriveaccordingtoaPoissonprocessatanaveragerateof1callperactiveuserperhour

nDuringthebusyhour¾oftheusersareactivenThecallholdingtimeisexponentiallydistributedwithameanof120seconds

57

+Example: Continued

nWhatisthemaximumloadthecellcansupportwhileproviding2%callblocking?n FromtheErlang Btablewithc=56channelsand2%callblocking,themaximumload=45.9Erlangs

nWhatisthemaximumnumberofuserssupportedbythecellduringthebusyhour?n Loadperactiveuser=(1call/3600s)× (120s/call)=33.3mErlangs

n Numberofactiveusers=45.9/(0.0333)=1377n Totalnumberofusers=4/3numberactiveusers=1836

58

+Another Example

nConsideranAMPSsystemwith30kHzchannels,4sectors/cell,frequencyreuseofNc =9,and12.5MHzofbandwidth.n Numberofchannels=12.5× 106/30×103 =416channels

n Say20arecontrolchannels=>totalnumberofvoicechannels=396

n Numberofchannels/cell=396/9=44n Numberofchannels/sector=44/4=11

n IfanIS-136systemisused,assuming3timeslotspercarrier,thenumberofchannels/sector=33

59

+Example (Continued)

nFora2%blockingprobability,fromtheErlangBtables,themaximumtrafficloadisnForAMPS:5.84EnForIS-136:24.6E

nIftheaveragecalldurationis3minutes,andeachcallis3/60=0.05EnAMPScansupport5.84/0.05=116calls/hour/sector

n IS-136cansupport24.6/0.05=492calls/hour/sector

60

+Handoff and Mobility

nAcallwilloccupyachannelaslongasauserisinthecelln Ifweassumecellresidencetimeisexponential,thenthechanneloccupancy=min(call holdingtime,cellresidencytime)

nAlsoexponentiallydistributed

nSimilarcalculationscanbedone,butweignoremobilityandhandoffhere

61

+Traffic Engineering in CDMA

nItismorecomplicated!

nDeterminingErlangcapacityisnottrivialnOneapproximationistousethenumberofchannelsfromthe“polepoint”

nTobemoreaccurate,wehavetocharacterizetheimpactofcallarrivalsandholdingtimeontheinterference

nSeeforexample:A.M.ViterbiandA.J.Viterbi,“ErlangCapacityofaPowerControlledCDMASystem,”IEEEJSAC,Vol.11,No.6,August1993.

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