Throughput and Buffer Analysis for GSM General Packet Radio Service (GPRS)

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1 Throughput and Buffr Analysis for GSM Gnral Packt Radio Srvic (GPRS) Josph Ho, Yixin Zhu, and Sshu Madhavapddy Nortl Ntorks 221 Laksid Blvd. Richardson, TX Abstract - Th Global Systm for Mobil Communications (GSM) Phas 2+ standard spcifis a n typ of packt data srvic calld Gnral Packt Radio Srvic (GPRS). GPRS allos th dynamic allocation of bandidth rsourcs. Wirlss channls ar allocatd to a mobil trminal basd on its traffic dmands. Thus rsults in bttr rsourc utilization compard to th circuit-basd data srvics. In gnral, packt-basd communication has mor bursty traffic and longr connction tim compard to its circuit-basd countrpart. A communication sssion may last for an xtndd priod of tim ith intrmittnt packt transmissions. This traffic bhavior coupld ith flxibl bandidth allocation in a GPRS ntork rsult in multiplxing gain that is not availabl in circuit sitchd data ntorks. This papr valuats th throughput and buffr utilization in a GPRS ntork undr Intrnt traffic modls, such as WWW and . Th prformanc of GPRS is thn compard ith circuit basd GSM ntork to dmonstrat th improvmnt du to multiplxing gain. 1. Introduction Th popularity of th Intrnt has rsultd in a larg numbr of srvics that ar availabl onlin. Ths includ, , World- Wid-Wb (WWW) brosing, and straming audio/vido dlivry. Ths applications ar radily availabl to vry hom ith a prsonal computr and a connction to th Public Sitchd Tlphon Ntork (PSTN). Th id accptanc of th Intrnt has rsultd in an xponntial groth of data traffic load in th PTSN. Hovr, irlss tlcommunication ntorks, such as th Global Systm for Mobil communications (GSM), hav bn usd primarily for voic communications. With th xcption of Short Mssag Srvic (SMS), thr ar vry f xampls of idly accptd data applications for irlss ntorks. On factor that hindrs th groth of irlss data communication is th infficincy of circuit sitchd irlss ntorks for transporting packtizd data. Intrnt traffic is charactrizd by th ON/OFF bhavior. Each communication sssion gnrally lasts for an xtndd tim priod. For xampl, a WWW brosing sssion may last for an hour or longr. During th sssion, a burst of packt arrivals (ON) is follod by a silnt priod (OFF). This ON/OFF pattrn continus until th sssion trminats. Whn circuit basd tchniqu is usd for carrying Intrnt traffic, th bandidth of th ddicatd circuit is astd during th OFF priod. Hovr, th usr must pay for th circuit connction for th duration of th sssion vn though bandidth is rquird only ithin th ON priods. This rsults in rlativly high cost for data communication through xisting irlss ntorks. To allo for mor fficint transportation of packt data traffic through th irlss ntork, an xtnsion to th GSM standard calld Gnral Packt Radio Srvic (GPRS) has bn dvlopd. GPRS allos for th dynamic sharing of th irlss bandidth among activ Mobil Trminals (MTs). No ddicatd channl is assignd to a MT for th duration of th communication sssion. A MT is allocatd radio bandidth only hn packts ar availabl for immdiat transmission. This rsults in bttr bandidth utilization and lor communication cost. This papr prsnts a study of th ffctiv throughput and data fram drop rat of th GPRS ntork undr various traffic paramtrs and availabl buffr sizs. Our rsults dmonstratd that, dpnding on th traffic paramtrs, th GPRS ntork provids similar ffctiv throughput as compard to th circuit-basd GSM ntork hil rquiring significantly smallr numbr of air channls. This papr is organizd as follos. Sction 2 givs a dscription of th GPRS ntork and a brif introduction of GPRS multipl accss mthod. Sction 3 dscribs a packt data traffic modl. Sction 4 prsnts th throughput and buffr analysis and Sction 5 conclusions th papr. 2. Gnral Packt Radio Srvic GPRS is dsignd as an xtnsion to th GSM ntork, hich provids an fficint ay for transporting packt data through th irlss channls. Figur 1 shos th GPRS ntork architctur. A GPRS ntork consists of to typs of GPRS Support Nods (GSNs), th Gatay GSN (GGSN) and th Srving GSN (SGSN). GPRS supports to typs of xtrnal Packt Data Ntorks (PDNs): Intrnt Protocol (IP) and X.25 ntorks. Ths xtrnal PDNs intrfac ith th GPRS ntork through th GGSN. Whn a Ntork Layr Packt Data Unit (N-PDU) from on of th support PDNs arrivs at th GPRS ntork, th GGSN forards ths N- PDUs to th srving SGSN through an Intra-PLMN (Public Land Mobil Ntork) IP Backbon Ntork. Th SGSN is th cntral componnt of a GPRS ntork, hich is rsponsibl for dlivring th N-PDUs to th targt MTs as ll as othr functions such as mobility managmnt and sssion control. An N-PDU arriving at th SGSN ill first b comprssd and partitiond into smallr Logical Link control (LLC) frams. Ths LLC frams ar thn forardd to th Bas Station Subsystm (BSS) using th BSS GPRS Protocol (BSSGP). In addition, th SGSN is rsponsibl for handovr, QoS managmnt, and flo control, among othrs. Th dtaild dscription of th GPRS ntork and protocol architctur can b found in [1].

2 Mobil Trminal Fram Rlay SGSN Intra PLMN IP backbon GGSN IP X.25 Unusd tim-slots 4 tim slots B B1 B2 B3 B4 B5 B6 B7 B8 B9 B1 B11 52 tim slots Figur 2: GPRS 52-Tim-Slot Multi-Fram BSS Figur 1: GPRS Ntork Architctur Each SGSN is connctd to a numbr of Bas Station Controllrs (BSCs). Th BSCs ar rsponsibl for partitioning th LLC frams into fixd siz Radio Link Control (RLC) blocks and to schdul th transmission of ths RLC blocks through th irlss channls. Each BSC controls on or mor Bas Transcivr Stations (BTSs), hich intrfacs ith th MTs through th Radio channls. Th BSCs ar connctd to th SGSN through a Fram Rlay ntork. In traditional circuit-sitchd GSM ntorks, ach 2 KHz RF channl is partitiond into ight logical channls using Tim division Multipl Accss (TDMA) [2] tchniqu. Whn a MT stablishs a call, th BSC assigns a logical channl to th MT for th duration of th call. This tchniqu is infficint for carrying packt data traffic that xhibits th ON/OFF. In GSM ntorks that support GPRS, on or mor logical channls ar prmanntly or dynamically allocatd for carrying packt data traffic. Ths logical channls ar calld Packt Data Channls (PDCHs). Th basic unit of transmission in a PDCH is a radio block. Each radio block composs of four conscutiv GSM tim slots and can b usd to carry on RLC block. Th tim slots of ach PDCH ar groupd into 52-tim-slot multi-frams. Each multifram contains 12 radio blocks and 4 unusd tim. Figur 2 shos th structur of a 52 tim-slot GPRS multi-fram. Mobil originatd packt transfr is achivd by a to-phas procdur. During th first phas, th MT snds a packt-channlrqust mssag to th BSC through th Packt Random Accss Channl. On rciving this mssag, th BSC rplis ith a packtimmdiat-assignmnt mssag that allocats a numbr of uplink radio blocks to th MT in a PDCH. During th scond phas, th MT snds a packt-rsourc-rqust mssag to th BSC ths radio blocks. This mssag includs th dscription of th uplink rsourc rquirmnt. Th BSC than rsponss ith a packt-rsourcassignmnt mssag. Th packt-rsourc-assignmnt mssag includs a list of PDCHs that th MT may us for data transmission, and an Uplink Stat Flags (USFs) for ach PDCH. Th USF is a thr-bit valu that is usd to indicat th availability of radio block to th MT. Th MT thn constantly monitors th donlink radio blocks of th allocatd PDCHs. If th MT dtcts its USF in th donlink radio block hadr of th corrsponding PDCH, it may us th nxt uplink radio block in this PDCH for data transfr. Thr ar to options for rsourc assignmnt. In th first cas, th MT is allod to usd th assignd PDCHs as long as it has quud RLC blocks for transmission. Th channl rsourc may b rlasd ithr by th MT or by th ntork hn thr is no mor quud data packts. In th scond cas, a limitd numbr of radio blocks ar allocatd to th MT. Th MT must initiat anothr rsourc rqust procdur if additional rsourc is rquird. Mobil trminatd packt transfr is initiatd by th BSC using a packt-rsourc-assignmnt mssag through th Packt Accss Grant Channl. This mssag includs a list of PDCHs that ill b usd for donlink data transfr. It also assigns a Tmporary Flo ID (TFI) to th MT. Th MT thn monitors ths PDCHs and rcivs all radio blocks hich contains its TFI in th hadr. For MTs not activly transmitting and rciving data (i.. in th standby stat), th ntork dos not kp track of its xact cll location. As a rsult, a paging procdur is rquird to locat th MT bfor th packtrsourc-assignmnt mssag can b dlivrd. For both mobil originatd or trminatd packt data transfr, onc th rsourc assignmnt is complt, a schduling algorithm is usd to allocat th availabl radio blocks to th MTs. A numbr of such schduling algorithms xist in th litratur [3]. Ths includ FIFO, Round Robin, Fair Quuing, and Wightd Fair Quuing, among othrs. In th analysis givn in this papr, assum that th Fair Quuing schduling algorithm is usd. 3. Intrnt Traffic Modl Poisson procss [4] and Markov Modulatd Poisson Procss (MMPP) [5] as prviously proposd for modling of packt data traffic. Hovr, rcnt rsarch [6] dmonstratd that ths modls do not captur som of th important charactristic of packt data traffic. For xampl, th duration of th ON and/or OFF priods ar found to b havy-tail distributd [6] hich dos not xhibit th mmorylss proprty of xponntial distribution. Th havy-tail distribution of th ON and/or OFF priods lads to th slf-similar [7] bhavior of th aggrgatd traffic. Slfsimilarity has rsultd in a numbr of major issus in th provisioning and nginring of packt data ntorks. To accuratly prdict th arrival pattrn of packt data traffic and to corrctly provision ntork rsourcs, th undrlying traffic modl must b abl to captur this uniqu charactristic of packt data traffic. For th analyss givn in th papr, assum that a GPRS subscribr must st up a sssion bfor h/sh can start transmitting and rciving data. Onc a sssion has bn stablishd, th subscribr may ngag in various srvics, such as WWW brosing and donload. W assum that sssion arrival is a Poisson procss ith arrival rat λ sssions/hour and th duration of ach sssion is xponntially distributd. It is dmonstratd in [6] that usr-initiatd sssions ar ll modld by Poisson procsss. Th packt arrival pattrn ithin a sssion dpnds on th typ of srvic. To of th most popular Intrnt applications ar and WWW brosing. In th folloing, ill dscrib th and WWW traffic arrival modls for an individual usr.

3 Activ ON Activ OFF Inactiv OFF ON OFF ON OFF ON OFF ON Finish mssag donload Usr bgins rading mssag Bgin mssag donload (a) Usr click Activ priod Srvic Complt Inactiv priod (b) Usr click Figur 3: (a) and (b) WWW Traffic Arrivals ithin a Usr Sssion 3.1 Traffic Arrival Modl W assum that incoming mssags of a usr ar stord at a ddicatd srvr. This srvr saf-kps all mssags for th usr in a mailbox until h/sh logs on to th ntork and rtrivs th mssags. In gnral, hn th usr runs th application, th hadrs of th availabl mssags ar donloadd to th computr from th srvr. Th usr ill thn scan through th hadrs and donload th rquird mssags on aftr anothr. Aftr donloading ach mssag, th usr may rad th mssag and compos a rply to th sndr. Whn th usr finishs ith th currnt mssag, h/sh ill donload th nxt mssag, and so on. In [8], it is dmonstratd that th arrival of mssags to th mailbox can b approximatd by a Poisson procss. Individual E- mail usr gnrats th ON/OFF traffic pattrn in th donlink during an sssion as shon in Figur 3(a). An ON priod rprsnts th intrval during a mssag donloadd. Th OFF priod is th intrval btn th nd and th bginning of to conscutiv mssag donloads. It rprsnts usr rading tim. Lt x and t to b iid (indpndnt and idntically distributd) random variabls rprsnting mssag siz and lngth of OFF priod, rspctivly. Basd on mpirical analysis of actual E- Mail mssag [8], th probability distribution function of x is: 1 F( x ) = 1 k1 x c1 k 2 x c2 Whr c 1 =1.2~3.2, ith man 2.4, c 2 =.31~.46 ith man.37, k 1 =.~21. ith man 17.64, and k 2 =2.8~3.4 ith man Th lngth of ON priod is a function of mssag siz and instantanous throughput availabl to th usr. W assum th lngth of OFF priod, t, follos th Parto distribution ith th probability distribution function: k Γ ( t) = 1 t According to th Parto distribution, th paramtr k is th minimum duration of th OFF priod. Th paramtr α rlats to th dgr of th havy-tail bhavior (or th havy-taildnss) of th OFF priod. Basd on this modl [8], k = 3 ~ 6 sconds and α =.5 ~ WWW Traffic Arrival Modl if F( x ).5 if F( x ) >.5 In gnral, ach usr slctabl link in a Wb pag involvs on or mor Univrsal Rsourc Locator (URL) rqusts. Whn a usr submits an URL rqust, th WWW srvr xcuts a clint program that gnrats rspons to th usr. Dpnding on th contnt of th b pag, additional rqusts may b gnratd by th clint α program. For xampl, th clint program may initiat a sparat rqust for ach inlin imag. Each of ths rqusts stablishs a n TCP connction to th MT. Ths TCP connctions may ovrlap ach othr or thy may b in squntial ordr. Whn all th rqusts rlatd to th URL ar complt, it ill tak th usr som tim to rad th information bfor initiating th nxt rqust. Thus, may captur th WWW traffic by a modl hich consists of activ and inactiv priods. Whr th activ priod corrsponds to th duration from th submission of th rqust by th usr to srvic compltion. This activ priod consists of th transmission tim of th individual fils and th activ OFF tim. Th activ OFF tim is th rlativly short tim intrval btn to fil rcptions hn th MT is procssing th rcivd Wb pag componnt. Th inactiv OFF tim is th tim intrval hn th usr is rading th rcivd information. It is th duration btn th compltion of a srvic rqust and th bginning of th nxt srvic rqust. Figur 3(b) shos th WWW traffic arrival pattrn. Th WWW traffic modl as dscribd abov follos th ON and OFF pattrn. Th ON priod rprsnts th fil transmission tim on th donlink. Th OFF priod rprsnts th intrval hn thr is no data transmission. Thr ar a numbr of studis [9] hich invstigat th distribution of th donload fil siz and th lngth of th OFF priods. Th ON tim is a function of th fil siz and th availabl donlink bandidth. Lt x b an iid random variabl that rprsnts th WWW fil siz. It as dmonstratd that x follos a Parto distribution ith th probability distribution function [9]: k F ( x ) = 1 x Whr th minimum fil siz is k = 1 byts or largr, and th havy-taildnss is α = 1.1 ~ 1.5. Th OFF priod consists of to sgmnts: activ and inactiv OFF tims. W considr an OFF priod to b activ if its duration is lss than a thrshold valu and inactiv, othris. Lt t and t to b iid random variabls that rprsnt th activ and inactiv OFF tims, rspctivly, of a WWW sssion. As shon in [9], t follos th Wibull distribution ith th probability distribution function: b t a Γ ( t ) = 1 Whr a =.3 and b = Th inactiv OFF tim, t, follos th Parto distribution ith th probability distribution function: k Γ ( t ) = 1 t Whr th minimum inactiv OFF tim is k = 1 scond, and th havy-taildnss is α = 1.5. To dtrmin th lngth of th activ α α

4 Effctiv Throughput (Kbps) 88 PDTCHs PDCHs 44 PDTCHs PDCHs Effctiv Throughput (Kbps) PDTCHs PDCHs 4 PDTCHs PDCHs Effctiv Throughput (Kbps) 98 8 PDTCHs PDCHs 4 PDTCHs PDCHs λ (s(sssions/hour) ur) λ λ (sssions/hour) λ λ (sssions/hour) (a) (b) (c) Figur 4: Effctiv Through for (a) WWW, (b) , and (c) Combind Traffic Modls. priod, it is important to charactriz th numbr of mbddd rfrncs in a Wb pag. This valu rprsnts th numbr of fils (in addition to th initial fil) to b donloadd during an activ priod. Basd on [9], assum th numbr of mbddd rfrncs in a Wb pag to hav th asymptotically Parto distribution ith a minimum k f = 1 fil, and havy-taildnss α f = Throughput and Buffr Analysis In this sction, prsnt th throughput and buffr analysis of th GPRS ntork basd on th WWW and traffic modls as discussd in Sction 3. Tabl 1 givs th traffic paramtrs that mployd for this analysis. In addition to th WWW and traffic modls, also considr a combind traffic modl such that 5% of th sssions carry WWW traffic and th othr 5% carry E- Mail traffic. Tabl 1: WWW and Traffic Paramtrs: Traffic modls WWW # PDTCHs 4 and 8 4 and 8 Fil siz Parto ith k =273.67, α =1.2 c 1=2.4, c 2=.37, k 1=18.36, k 2=3.33 Activ off tim Wibull ith a=.382, N/A b=1.46 Inactiv off tim Parto ith k' =1, α' =1.5 Parto ith k =3, α =1.5 Sssion lngth Exponntial ith man 15 minuts Sssion arrival Poisson ith variabl arrival rat # Embddd Parto ith k f=1 and Rfrncs α f=2.43 Exponntial ith man 5 minuts Poisson ith variabl arrival rat N/A In this analysis, assum that th maximum siz of th data fild in ach LLC fram is 124 byts. Each LLC fram has a 1 byts fram hadr. Th amount of data carrid in a LLC fram may b smallr than 124 byts if it is th last fram of a ntork layr packt. Th siz of a ntork layr packt is assumd to b 248 byts and th intr-arrival tim of ntork layr packts ithin th sam burst is 2 ms.. Th GSM coding schm CS-3 is mployd such that ach RLC block carris 36 data byts xcluding hadr and trailr. This rsults in a channl throughput of Kbps. Th airintrfac Carrir-to-Intrfrnc ratio (C/I) is assumd to b 16 db, hich rsults in a RLC Block Error Rat (BLER) of.2 [11]. Whn a RLC block is lost, it ill b rtransmittd up to 3 tims (total numbr of transmission is 4). If on or mor RLC blocks of a LLC fram ar lost, th LLC fram is considrd to b incomplt and is discardd. In this analysis, LLC fram rtransmission is disabld. If th LLC fram buffr is full hn a LLC fram arrivs, th LLC fram is droppd immdiatly. As dscribd arlir, this simulation analysis capturs to prformanc masurmnts: th ffctiv throughput and th LLC fram drop rat. Th ffctiv throughput of a sssion is th ratio of th total numbr of byts succssfully rcivd by th MT to th total duration of all ON priods. A sssion is considrd to b ON hn on or mor LLC fram dstind for th MT is in th LLC quu at th SGSN. Th LLC fram drop rat is th ratio of th total numbr droppd LLC frams to th total numbr of LLC frams arrivd at th SGSN. Figur 4 shos th ffctiv throughput for th thr traffic modls (WWW, , and Combind) for diffrnt sssion arrival rats. Whn th sssion arrival rat is lo, th numbr of simultanous sssions is small and th ffctiv throughput is high. As th sssion arrival rat incrass, th numbr of simultanous sssions incrass. Ths sssions must shars th availabl bandidth, hich rsults in a rduction in th ffctiv throughput. Hovr, sinc a sssion is mak up or cycls of ON/OFF priods. At any givn tim, only a fraction of th xisting sssions ar ON. Th multiplxing of svral ON/OFF sssions in on or mor shard PDCHs rsults in ffctiv throughput gain such that th ffctiv throughput pr sssion is highr than th avrag throughput availabl to ach sssion. Hr, th avrag throughput is dfind as th total throughput dividd by th numbr of xisting sssions. This multiplxing gain is not availabl in circuit basd GSM ntorks, such as GSM High Spd Circuit Sitchd Data (HSCSD). Tabl 2 tabulats th numbr of Kbps circuit channls in a HSCSD ntork rquird to achiv similar ffctiv throughput providd by a GPRS ntorks ith 8 PDCHs undr th WWW traffic modl. Basd on HSCSD, ach sssion is allocatd on or mor channls for th duration of th sssion. As sn in Figur 4(a), th GPRS ntork ith 8 PDCHs can provid an ffctiv throughput of about 26 Kbps to ach sssion undr WWW traffic ith a sssion arrival rat of 18 sssions/hour. To provid similar throughput undr HSCSD, to Kbps circuit channls must b allocatd to ach sssion for its hol duration. Assuming a channl blocking probability of 1%. An analysis using th Erlang B formula

5 indicats that th total numbr of HSCSD circuit channls rquird to achiv similar ffctiv throughput is 2 (s last ro in Tabl 2). This man that th GPRS ntork can achiv th rquird throughput ith lss than half of th numbr of channls. It can b sn in Tabl 2 that GPRS achivs clos to 4 tims th capacity of HSCSD undr th sam ffctiv throughput rquirmnts. Similar rsults hav bn obtaind for othr traffic modls and ar not providd hr bcaus of spac limitation. LLC Fram Drop Rat 1.E-1 1.E-2 1.E-3 1.E-4 WWW Combind MMPP Tabl 2: Channls Rquirmnt undr GPRS and HSCSD ith WWW Traffic Arrival Modl Sssion arrival Rat (λ) Throughput (Kbps) Total # GPRS PDCHs rquird Total # HSCSD circuit channls rquird Figur 5 shos th LLC fram drop rat for diffrnt traffic modls. For comparison purpos, includ a MMPP traffic modl that is similar to th traffic modl xcpt that both th fil siz and OFF duration ar xponntially distributd. For this MMPP modl, us an avrag fil siz of 36 Kbyts and an avrag OFF duration of 9 sconds. Both th WWW and modls gnrat traffic arrivals that xhibit th slf-similar bhavior [7] ith Hurst paramtr.9 and.75, rspctivly. Th Combind traffic modl has a Hurst paramtr of.9. In this analysis, assum that thr ar four availabl GPRS PDCHs. Th sssion arrival rat for WWW, , Combind, and MMPP traffic modls ar 4, 12, 4, and 4 sssions/hour, rspctivly. Ths valus ar slctd to achiv similar starting LLC fram drop rat at a buffr siz of 1 MByt. Th purpos of this analysis is to dmonstrat th impact of buffr siz on diffrnt traffic modls. In Figur 5, it is dmonstratd that th LLC fram drop rat for th MMPP traffic modl rducs significantly form abov 1.x1-2 to about 1.x1-5 by incrasing th LLC fram buffr from 1 MB to 2.2 MB. Hovr, th sam rduction is not achivd for othr traffic modls. For th WWW and th Combind traffic modls, th LLC fram drop rat rmains clos to 1.x1-2 aftr a nin tims incras in buffr siz. For th traffic modl, th LLC fram drop rat rducs to 1.x1-4 undr th sam incras in LLC fram buffr siz. This rsult dmonstrats th ffct of slf-similarity on buffr provisioning. Th highr th Hurst paramtrs, and thus th slfsimilarity lvl, of a givn traffic sourc, th highr th xpctd LLC fram drop rat. Whn th Hurst paramtr of th traffic sourc is high, th LLC fram drop rat is not vry snsitivly to incrass in buffr siz. This mans that incrasing th buffr siz is not an ffctiv solution for solving th problm of high LLC fram drop rat. To possibl solutions can b usd to addrss this problm. Th first on is to dvlop traffic shaping algorithms that rduc th slfsimilarity lvl of a givn traffic stram [12]. Anothr solution is to dvlop flo control algorithms that throttls packt dpartur from th sourc. Our currnt invstigation focuss on ths dirctions. 5. Conclusions This papr prsnts a throughput and buffr analysis GPRS. Our rsults dmonstratd that GPRS achivs significant incras in ffctiv throughout as compard to HSCSD. This is possibl du to th ON/OFF natur of packt data traffic that rsults in multiplxing gain. Whn compard to HSCSD, GPRS incrass th capacity of th GSM air channls by mor than 3%. Hovr, packt data traffic gnrats vry bursty traffic arrival. Th aggrgation of a numbr of individual packt data traffic sourcs rsults in a combind traffic that xhibits th slf-similar bhavior. Som of th ffcts of similarity includ high packt drop rat and larg buffr rquirmnt. It is dmonstratd that th packt drop rat may b rathr insnsitiv to incras in th availabl buffr spac. This mans that incrasing th buffr siz is not an ffctiv solution to rduc packt drop rat. It ill only lad to long packt quuing dlay. Mthods for rducing th similarity of th incoming traffic is ncssary to rduc th packt drop rat and, thus, incrass th quality of srvic of th GPRS ntork. Rfrncs 1.E LLC Buffr Siz (MB) Figur 5: LLC Fram Drop Rat [1] ETSI, Digital Cllular Tlcommunications Systm (Phas 2+); Gnral Packt Radio Srvic (GPRS); Srvic Dscription; Stag 2, ETSI GSM 3.6, Vrsion 6.1.1, Aug [2] ETSI, Digital Cllular Tlcommunications Systm (GSM Radio Accss Phas 3); Multiplxing and Multipl Accss on th Radio Path, ETSI GSM 5.2, Vrsion 6.., Jan [3] D. Stiliadis, Traffic Schduling in Packt Sitchd Ntorks, Ph.D. Thsis, Univrsity of California, Santa Cruz, Jun [4] L. Klinrock, Quuing Systms, Volum I: Thory, John Wily & Sons, [5] H. Hffs and D. M. Lucantoni, A Markov Modulatd charactrization of Packtizd Voic and Data Traffic and Rlatd Statistical Multiplxr Prformanc, IEEE JSAC, Vol. SAC-4, No. 6, pp , Spt [6] V. Paxson and S. Floyd, Wid Ara Traffic: Th Failur of Poisson Modling, IEEE/ACM Trans. on Ntorking, Vol. 3, No. 3, Jun [7] M. S. Taqqu, W. Willingr, and R. Shrman, Proof of a Fundamntal Rsult in Slf-Similar Traffic Modling, Proc. ACM SIGCOMM. [8] Y. Zhu, J. Ho and L. Bauchamp, Traffic Modling at th Accss Link, Nortl Ntorks Tchnical Rport, [9] P. Barford and M. Crovlla, Gnrating Rprsntativ Wb Workloads for Ntork and Srvr Prformanc Evaluation, Proc. ACM Sigmtrics 98, [1] J. C. R. Bnntt and H. Zhang, Hirarchical Packt Fair quuing Algorithm, IEEE/ACM Transactions on Ntorking, Vol. 5, No. 5, pp , Oct [11] R. Ludig and D. Turina, Link Layr Analysis of th Gnral Packt Radio Srvic for GSM, Proc. IEEE ICUPC 97, Vol. 2, pp , [12] A. Erramilli, O. Narayan, and W. Willingr, Exprimntal Quuing Analysis ith Long-rang Dpndnt Packt traffic, IEEE/ACM Transactions on Ntorking, Vol. 4, No. 2, pp , April 1996.

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