ANALYTICAL MODEL FOR TCP FILE TRANSFERS OVER UMTS. Janne Peisa Ericsson Research Jorvas, Finland. Michael Meyer Ericsson Research, Germany

Transcription

1 ANALYTICAL MODEL FOR TCP FILE TRANSFERS OVER UMTS Jae Pesa Erco Research 4 Jorvas, Flad Mchael Meyer Erco Research, Germay Abstract Ths paper proposes a farly complex model to aalyze the performace of TCP fle trasfers over UMTS. Our approach s based o the observato that the TCP performace s affected by the rado l protocol retrasmos. These protocol teractos are stroger for hgh data rate rado acce bearers. The model s the frst attempt to cosder the relevat detals of both trasport ad l layer protocols. A good match wth smulato results valdates our aalytcal model. I addto, some performace results for TCP fle dowloads are gve. It s show that the Bloc Error Rate of the wrele l has a much more sgfcat mpact tha ust the capacty reducto due to l layer retrasmos. Itroducto A ey obectve for 3 rd geerato wrele etwors le Uversal Moble Telecommucato System (UMTS) s the effcet support for data commucatos for moble users. May exstg applcatos (e.g. World Wde Web, Fle trasfer) are based o the trasport layer protocol TCP (Trasmo Cotrol Protocol). Therefore t s mportat to uderstad how TCP-based applcatos behave f a wrele acce l wth ts specal characterstcs s volved the trasmo path. I geeral t s eceary to use a l layer ARQ mechasm to hde the pacet loes o the rado l from TCP. A effcet operato of a cellular system requres a relatvely hgh pacet lo rate (of the order of several percets) o the wrele l. If o l layer ARQ mechasm s used, the TCP cogesto avodace algorthm wll treat all pacet loes o the wrele l as a sgal of a cogesto ad reduce the trasmo rate correspodgly. Ths wll result uecearly bad protocol performace. Durg smulato studes we observed that for hgh data rate rado bearers protocol teractos betwee TCP ad the rado l layer exst, whch requre careful protocol cofguratos. I ths case both TCP ad the wrele l fluece the performace. For example, rado l layer retrasmos eed to be cosdered for accurate results. Ths motvated the developmet of a aalytcal model whch allows quc performace studes for dfferet parameter sets. It has bee obvous that oly a model comprsg the relevat detals of both the rado l layer protocol ad TCP could provde accurate results for a wde parameter space. For example the model should provde accurate results for cases whe ether the Iteret or the acce l forms the bottleec of a TCP coecto. Ths paper has two obectves. Frst, a aalytcal model s derved eablg a detaled vestgato of the performace of a fle trasfer applcato wth lmted fle szes over UMTS. I a secod step, the model s appled to ga sght to the mpact of certa ey parameters. These cosderatos are baced-up wth smulato results, whch also valdate the proposed aalytcal model. I the subsequet secto the proposed aalytcal model s derved. I two steps, the models for TCP ad for RLC are descrbed. Afterwards, the model s valdated by comparg t to smulato results. I ths cotext, a few performace studes are preseted showg the mpact of certa ey parameters o the ed-to-ed performace. By studyg the effect of the l layer retrasmos we observe sgfcat protocol teractos betwee RLC ad TCP. Ths teracto ca be reduced by a correct choce of TCP ad RLC parameters. Fally, the ma coclusos are summarzed. The Model I ths secto we preset a aalytcal model for TCP fle trasfer over UMTS. The steady state performace of TCP has bee studed extesvely the lterature (see e.g. Refs []-[7]). The results of those studes show that the TCP performace ca be modeled reasoably well f the slow start phase of a TCP coecto s small compared to the total fle trasfer tme. However, a typcal UMTS system the roud trp tme ca be rather large (of the order of half a secod). I combato wth hgh data rates le 384 bps ths results a large badwdth delay product.

2 Correspodgly, the slow start phase ca be also log, ad thus the models Refs. []-[7] are oly applcable to very large fles. I order to model also the trasfer of small fles, we clude explctly the slow start phase our model, a maer smlar to Ref. [8]. I addto to cosderg the slow start ad cogesto avodace phases of a TCP coecto, we also cosder the effect of lower layer retrasmos. Frst we model explctly the rado terface, cludg the rado l cotrol (RLC) protocol [9]. The we model the rest of the path a smplfed way. Model for TCP We aume that each fle trasfer opes a ew TCP coecto. Ths s smlar to e.g. HTTP. behavor. The actual trasfer proce cossts of two perods. At the begg of the trasfer, the TCP coecto s slow start. We aume that TCP wll start by the sychrozato proce (.e. the trasmo of a SYN ad a correspodg SYN/ACK meages), whch wll tae tme T t. After that a tal wdow of W t segmets wll be trasmtted. If every secod segmet s acowledged, the sze of the TCP cogesto wdow wll be.5*w t after all acowledgemets have bee receved. After all the acowledgemets for the.5 W t have bee receved, the sze of the cogesto wdow wll be.5 W t. We ow model the umber of trasmtted bytes slow start as B( t) = W t ( MSS + MSS t Tt RTTTCP MSS) t Tt + () RTTTCP = Wt MSS, whch MSS s the TCP maxmum segmet sze, s dvded by + the umber of TCP segmets acowledged oe ACK (comparg to Ref. [8], our correspods drectly to γ) ad RTT TCP s the TCP roud trp tme. We apply Eq. () for the TCP coecto utl the slow start trasmo rate reaches the steady state trasmo rate. For steady state trasmo the TCP seder reaches ether the maxmum capacty for the WCDMA l or we have cogesto the Iteret part. The maxmum capacty of the WCDMA l ca be wrtte as MSS RUTRAN = RLCH ( ε ), MSS + H whch R LCH s the logcal chael rate of the WCDMA l, ε s the RLC pacet error probablty over the WCDMA l ad H s the sze of the TCP ad IP headers. For the Iteret capacty, we ca apply the formula from Ref. [3] R Iteret MSS =, RTT p TCP where p s the Iteret pacet lo probablty. The maxmum rate, whch TCP seder ca use to trasmt user data, s ow defed to be the mmum of the UTRAN ad Iteret rates R = m( R, R ). TCP UTRAN Iteret Usg the momet whe ths rate s reached as the ed pot for the slow start phase, oe obtas the tme spet slow start as RTCP RTTTCP log MSS T = RTTTCP + Tt. log Fally the umber of bytes trasmtted by the TCP seder at tme t ca be wrtte as t B( t) = MSS B + RTCP T RTT t TCP + ( t T ), whch we have defed B B ( T ) = MSS, t < T t > T RTCP RTTTCP MSS as the umber of bytes trasmtted at the ed of the slow start. The tme to trasmt a fle of sze F ca be obtaed by settg B(t) = F ad solvg for t. I order to use Eq. (3), we eed a estmate for the TCP roud trp tme. Aumg that every secod segmet s acowledged (.e. =.5), we tae a expreo whch descrbes the tme to trasmt two TCP segmets (tag the delayed ACK mechasm to accout) ad the tme to receve the ACK from the recever. Both the TCP segmet trasmo tme ad ACK trasmo tme cosst of both the tme to trasmt them over the ar terface ad the delay the fxed etwor. If we aume that the delay the fxed etwor does ot deped o the pacet sze, oe ca combe them to a sgle parameter D Iteret (whch () (3)

3 should also cota delay caused by the UMTS core etwor). Now oe ca wrte RTT TCP D segmets + Dac + = D. (4) Iteret The D segmets ad D ac are the tmes eeded to trasmt two TCP segmets ad oe TCP ACK over the WCDMA ar terface correspodgly. They deped mostly o l layer behavor ad wll be examed detal the ext secto. Model for l level ARQ I ths secto we preset a model for a rather geerc l layer retrasmo scheme. The maor aumpto made o the explct propertes of the l layer ARQ protocol s that t should segmet comg hgher layer pacets to small PDUs ad that the trasmtter should poll the recever after trasmttg all the pacets from the trasmtter buffer. I Fgure we show a typcal sequece eeded to trasmt a TCP segmet (or ay other hgher layer pacet), whch has bee segmeted to N PDUs. Frst all N PDUs are trasmtted, of whch are correctly receved. A status report s mmedately trggered, but ufortuately t s lost. The trasmtter evetually tmes out ad polls the recever, whch trasmts the status report for the secod tme. Ths tme t s receved correctly ad retrasmos are trggered. Ufortuately there are stll erroeous PDUs, so a secod status report s trasmtted. Whe t s receved the PDUs are retrasmtted for the secod tme. Ths tme they all are receved correctly ad the SDU ca be delvered to hgher layers. We model the l layer ARQ by two separate procees. Frst we aume that the tme to correctly trasmt a status report segmet s a costat T stat. We defe the tme whe th retrasmo has bee completed as T ad the probablty that exactly retrasmos are eeded as P. The umber of trasmo tme tervals t taes to trasmt all pacets of the th retrasmo s the umber of pacets to be retrasmtted dvded by the logcal chael rate. The tme to receve the frst pacet of ay trasmo or retrasmo s ust oe half of the roud trp tme. Fally, before we ca start the th retrasmo, we must receve a status report. Thus we obta a expreo for T Trasmtter Recever N PDUs wth errors Status report Poll Status report retrasmos, errors Status report retrasmos, o errors T T stat T Fgure : A typcal l layer ARQ sequece whe trasmttg a sgle SDU segmeted to N PDUs. + T = RTT RLC + T stat T TTI r = +, (5) whch RTT RLC s the ARQ roud trp tme, s the umber of PDUs that have to be retrasmtted for th tme, TTI s the trasmo tme terval (e.g. ms), ad r s the umber of PDUs that ca be trasmtted oe TTI. If we for smplcty aume that bloc errors are depedetly dstrbuted wth costat error rate ε, the probablty of eedg exactly retrasmos s obtaed usg elemetary probablty theory as P = B N, ) B(, ) B(, ) L B(, ) B(,), ( 3 whch B(N, ) s the bomal dstrbuto N N B( N, ) = ε ( ε ).

4 We ow ote that the oly depedecy T has to earler retrasmos s o the last term. If we approxmate each by the average umber of retrasmos, = ε = ε = K = ε N, T does ot deped o, but oly o. Ths meas that the probablty of that all N segmets have bee trasmtted tme T s a sum over all poble values of, P = N B( N, ) B(, ) L L B(,). We also approxmate the last term of Eq. (5) by ot lmtg the summato to order to obta a smpler expreo + N T RTT T ε TTI r = RLC + stat + Wth these approxmatos, the average trasmo delay of a SDU cosstg of N PDUs ca be wrtte as D( N) = T P = RTT RLC + ε N TTI r = + P + T stat P + The remag summato over P s by defto the average umber of retrasmos eeded to trasfer a SDU segmeted to N PDUs. Thus we defe ( ε ) ε N N = ReTX P, (7) whch the last approxmato s reasoably good up to error probabltes of roughly 5%. We stll eed Eq. (6) a approxmato for the tme T stat t taes to correctly receve the status report. I order to receve a status report, t s eceary that the last PDU of a trasmo s receved correctly ad that the status report tself s correctly trasmtted over the ar terface. If ether of these fals, there wll be a delay of Poll_tmer, after whch the trasmtter wll retrasmt a poll. Thus the probablty of a succeful status report trasmo s (6) q = ε )( ε ), (8) ( stat whch ε stat s the bloc error probablty o the reverse l. Usg Eq. (8), we obta the probablty of usucceful status report trasmo e = q. If the poll s receved correctly ad the status report tself s trasmtted correctly, T stat s smply oe half of the ARQ roud trp tme. If there are errors (ether poll or trasmo of the status report), we must wat for the poll tmer to expre before a ew poll s trasmtted. Thus, all errors wll troduce a delay of Poll_Tmer. The average tme to receve a status report ca ow be wrtte as Tstat = RTTRLCq + RTTRLC + Tpoll eq+ K = RTTRLCq e Tpollq e + e = + RTTRLC. ( e) I the last step we have used the aumpto that the poll tmer value s exactly equal to the RTT RLC. Collectg ow all results together we obta the followg delay for the trasmo of a SDU segmeted to N PDUs NReTX ( N) D( N) = + RTTRLC + e ε N TTI (9) r Usg equato (9), we ca calculate the D segmets ad D ACK, whch are eeded to estmate the TCP roud trp tme equato (). The UMTS Rado L Cotrol protocol RLC [8], s extremely flexble ad ca be cofgured to poll the recever ad trasmt status reports several ways. I the followg we cosder oe specal RLC toolbox settg, whch sutes well the teractve ad bacgroud rado bearers. The cofgurato cossts of a poll tmer combed wth pollg for the last PDU buffer. To further smplfy the aalyss, we have aumed that the poll tmer s set to exactly the RLC roud trp tme. Thus our RLC cofgurato ca be modeled by the l level ARQ model descrbed above. As a specfc example, cosder a stuato whe the umber of PDUs N s much smaller tha the umber of PDUS that ca be trasmtted oe TTI (.e. the trasms-

5 so rate r). I ths case we ca gore the last term Eq. (9). If we further aume that a RLC PDU sze s 3 bts so that the TCP ACK s trasmtted exactly oe RLC PDU, we ca wrte usg Eqs. (4) ad (9), ad otcg that N ReTX () s exactly ε/(-ε), oe obtas NReTX + ε /( ε ) RTTTCP = + RTTRLC + Dteret, e whch N ReTx s the average umber of retrasmos eeded to trasmt N PDUs. N ReTX ca be calculated usg Eq. (7). LCH rate Aalytcal Smulato Dfferece 64 bps 5 bps 4 bps % 8 bps 79 bps 7 bps 3 % Table : Comparso of the aalytcal calculato wth smulato results for dfferet logcal chael data rates. We have aumed that the TCP roud trp tme s accurately modeled by the tme t taes to trasmt two segmets ad oe acowledgemet. Ths s oly true f there s o queug the etwor. However, we expect that most cases ths aumpto wll ot be vald. Stll the good match obtaed wth smulato ad aalytcal results partly valdate the approxmato. I summary, we have derved a model for TCP performace of a fle trasfer. The model depeds oly o seve parameters: TCP maxmum segmet sze, the umber of TCP segmets acowledged a sgle ACK, the bloc error rato of the physcal chael, the Iteret pacet lo rate ad delay, RLC PDU sze ad the RLC roud trp tme. Comparso wth smulato results We frst compare our aalytcal model to smulato results of Byte fle trasfers for RLC data rates of 64 ad 8 bps. The fle sze was chose to be ot too small ad ot too large order to test the models for both the slow start ad the cogesto avodace. The other parameters were chose so that the RLC PDU sze was 3 bts ad the RLC roud trp tme was ms. The TCP Maxmum Segmet Sze was 5 bytes ad the combed core etwor ad Iteret delay was 6 ms. The Iteret lo rate was % ad the BLER o the rado l was aumed to be %. The performace measure used s pacet bt rate, whch s defed as the fle sze dvded by the fle trasfer tme. Table shows the comparso of aalytcal results wth smulated values. The aalytcal calculato agrees wth smulato values rather well (maxmum dfferece s % for 64 bps bearer). For hgher data rates the match s eve better. I tedecy, our model seems to be slghtly too Bytes bps, RTT=ms BLER=% BLER=% (aalytcal) BLER=% BLER=% (aalytcal) Tme [ms] Fgure : Comparso of a smulated average trace wth aalytcal model for 64 bps l rate. Bytes bps, RTT= ms BLER=% BLER=% (aalytcal) 5 BLER=% BLER=% (aalytcal) Tme [ms] Fgure 3: Comparso of a smulated average trace wth aalytcal model for 8 bps l rate. optmstc. It should be oted that the uderlyg parameters for the results Table are arbtrarly chose ad should be cosdered as examples. They do ot ecearly reflect a real UMTS system. I order to further test the model, several average TCP traces were geerated by smulatg several trasfers of a 35 byte fle ad the calculatg the average tme t too to receve each TCP segmet. We preset results for 64 bps ad 8 bps bearers for RLC bloc error rates of % ad %. It s aumed that there are o pacet loes the Iteret, order to test our models for the slow start ad the RLC. The RLC roud trp tme was ms, ad the TCP maxmum segmet sze ad tal wdow sze were 46 bytes ad three tmes the MSS correspodgly. The comparsos of smulato results wth aalytcal calculatos are show Fgures ad 3.

6 PBR / PBR(BLER=) bps, aalytcal Smple reducto 64 bps, aalytcal BLER Fgure 4: Per pacet bt rate dvded by the per pacet bt rate obtaed at BLER= for the full aalytcal model ad Eq. (). The match for the 64 bps bearer s good. However, for BLER=% the slope s slghtly correct. If the traces were cotued further (.e. to larger fle szes), ths msmatch trasmo rate would cause the dfferece observed Table. Fgure 3 shows that the case of 8 bps the basc shape of the aalytcal curve s correct ad the match s stll good. I addto, the smooth curve maes t obvous that the model predcts the average trasmo tme of TCP segmets stead of predctg each partcular segmet the complex patter of a TCP flow. Fgures ad 3 have dcated that the RLC bloc error rate s a terestg parameter, whch sgfcatly mpacts the performace. Therefore, some more detals are studed the followg. The obvous effect of l layer errors s to reduce the data rate avalable for user data by the amout of retrasmos requred. If the average error rate s ε, ths effect would correspod to a reducto of R = = ε. () + ε + ε L I order to separate the protocol teractos from the TCP slow start effect, we have plotted per pacet bt rate ormalzed to the per pacet bt rate at BLER= Fgure 4 for 64 ad 8 bps. It ca be see clearly that the trasmo rate for the full aalytcal model decreases faster tha Eq. () predcts for both 64 ad 8 bps l rates. The effect s more proouced for hgher data rates. Coclusos The paper has proposed a farly complex, but easy to use aalytcal model, whch allows performace vestgatos of TCP-based fle trasfers over a wrele l cludg l layer retrasmos, partcular for UMTS. Sce the performace of fle dowloads over wrele terfaces s characterzed by both the performace of the rado l ad by teractos betwee RLC ad TCP, our model comprses the relevat detals of both TCP ad RLC. Due to the fact that the effects of the TCP slow start caot be eglected scearos wth large badwdth delay products, our model cludes two phases, TCP slow start ad TCP cogesto avodace. The model allows a aalytcal vestgato of RLC desg parameters the cotext of a wde rage of etwor codtos ad TCP parameters. Cosderg the complex problem the model s descrbg, t provdes results wth a relatvely small umber of put parameters ad computatoally ot too complex formulae. The aalytcal results have bee compared to smulato results. The comparso verfes that the aalytcal model s accurate for a wde rage of parameter values. As a example of the questos that ca be aswered usg the aalytcal model, we have show that the l layer bloc error rate has a cosderable effect o the ed-to-ed performace, ad that the effect of the l layer retrasmos caot be accouted by ust reducg the umber of requred retrasmos from the l data rate. Refereces [] T. Lasma, U. Madhow, The performace of TCP/IP for etwors wth hgh badwdth-delay products ad radom lo, IEEE/ACM Tras. Networg, v. 5 (997),. 3, pp [] H. Chasar, T. V. Lasma, U. Madhow, TCP Over Wrele wth L Level Error Cotrol: Aalyss ad Desg Methodology, IEEE/ACM Tras. Networg, v. 7 (999),. 5, p [3] M. Maths, J. Seme, J. Madhav, T. Ott, The macroscopc behavor of the TCP cogesto avodace algorthm, Comp. Comm. Rev., v. 7 (997),. 3, pp [4] J. Padhye, V. Frou, D. F. Towsley ad J. F. Kurose, Modelg TCP Reo performace: a smple model ad ts emprcal valdato, Comp. Comm. Rev, v. 8 (),., pp [5] Kumar, Comparatve performace aalyss of versos of TCP a local etwor wth a loy l, IEEE/ACM Tras. Networg, v. 6 (998),. 4, pp [6] M. Zorz, R.R. Rao, The effect of correlated errors o the performace of TCP, IEEE Commucatos Letters, vol., pp. 7-9, Sep. 997 [7] Chocalgam, M. Zorz, V. Trall, Wrele TCP Performace wth L Layer FEC/ARQ,, Proc. IEEE ICC 99, Jue 999

7 [8] N. Cardwell, S. Savage, T. Aderso, Modelg TCP Latecy, Proceedgs of Ifocom. [9] 3GPP Techcal Specfcato Group Rado Acce Networs, RLC Protocol Specfcato, 3G TS 5.3.