Modelling the Performance of a Cross-Layer TCP NewReno-HARQ System

Transcription

1 In. J. Communicaions, Nework and Sysem Sciences, 00, 3, 9-3 doi:0.436/ijcns Published Online January 00 (hp:// 4 Modelling he Performance of a Cross-Layer TCP NewReno-HARQ Sysem Absrac Nimbe L. EWALD-AROSTEGUI, Andrew H. KEMP School of Elecronic and Elecrical Engineering, Universiy of Leeds, Leeds, LS 9JT, UK nimbe@erg.abdn.ac.uk, a.h.kemp@leeds.ac.uk Received Ocober, 009; revised November, 009; acceped December 5, 009 This paper presens an analyical model of a cross-layer communicaion sysem o enable improvemen in he Transmission Conrol Proocol (TCP) over mixed wired and wireless Inerne. The focus is on he quaniaive performance evaluaion of he ineracions beween TCP NewReno and a hybrid Auomaic Repea re- Ques proocol (HARQ) in he link layer (LL) wih a finie buffer size. The significan improvemen in TCP NewReno hroughpu when HARQ adapively selecs is opimal seings according o explici cross-layer informaion is shown. Through ns- simulaions, i is demonsraed ha his proposed analyical model accuraely predics he TCP-HARQ sysem performance. Keywords: HARQ, TCP, Markov Chains, M/G//K Processes. Inroducion This paper presens an analyical model which can be used o replace simulaed esing (which ypically gives inconsisen resuls and is laborious o carry ou) for assessing he performance of mixed wired and wireless neworks using TCP. As ubiquious Inerne access grows his is increasingly imporan o aid design of fuure neworks. TCP is he mos widely used ranspor proocol in radiional wired Inerne. However i shows poor performance over wireless channels which is relaed o is design principle: TCP was designed o provide reliable end-oend communicaion beween wo hoss in wired neworks where losses are due o congesion. As soon as congesion is deeced, TCP sending bi rae is halved o alleviae i. Since radio channels exhibi ime-varying error raes, he halving of TCP sending bi rae under hese condiions is no an opimal measure given ha if he fading condiions elapsed, scarce wireless bandwidh would be wased. Oherwise, if he link s poor qualiy ransmission coninues, halving he bi rae has no impac on he SNR and channel errors will coninue o occur. Since he inegraion and ineracion of wireless and wired neworks in a smooh and efficien manner is one of he mos imporan challenges for nex generaion all-ip neworks, he enhancemen of TCP performance over wired-wireless links will resul in a more efficien use of nework resources. This will provide beer qualiy of service from he user s perspecive and higher revenue o service providers. There have been several approaches o addressing his problem [ 5]. The echniques o enhance TCP performance over wired-wireless links have predominanly used he Reno version [6]. Though his version was previously widely deployed, more efficien versions, such as NewReno [7], are nowadays exensively insalled in web servers [8]. In line wih his, he NewReno version is modelled in his paper. The performance of TCP connecions over wiredwireless links have been modelled mosly hrough wo differen approaches, direcly over he wireless link [9 ] or considering LL error conrol echniques [ 8]. ARQ proocols are used in works such as [ 5], he impac of Forward Error Correcion (FEC) codes is analysed in [8] whils TCP ineracions wih HARQ sysems are sudied in [6,7,9]. In none of hese works is TCP NewReno analyical modelling developed, all hese menioned works bu [] have used he Reno version. In addiion, [5,6,8,9] used known hroughpu equaions o predic TCP performance insead of developing an analyical model as in he res of he papers. Furhermore, an infinie buffer size is considered in he TCP analysis over HARQ presened by [6,7] and in he cross-layer TCP-ARQ sysems proposed by [4,5]. The line followed in his work is o consider LL error conrol echniques hrough developing a heoreical model of a cross-layer communicaion sysem wih opdown explici noificaions, from TCP o he LL of a base saion (BS) in a las-hop wireless link opology. I is Copyrigh 00 SciRes.

2 0 N. L. EWALD-AROSTEGUI ET AL. considered ha a hybrid ARQ mechanism is implemened in he LL. Emphasis is given o he impac of a finie LL buffer size, a condiion ha is commonly assumed o be infinie. The operaion of he HARQ scheme comprising Forward Error Correcion (FEC) convoluional codes and a Selecive Repea (SR) ARQ proocol is characerised by a Discree-Time Markov Chain (DTMC). Corrupion losses occur in a radio channel and are modelled by a wo-sae DTMC whils congesive losses are due o o he finie buffer size. HARQ performance parameers are compued hrough he wo-momen approximaion of an M/G//K analysis. Similar approaches o his work have been proposed by [4,6,7], however hey consider an infinie buffer size. Thus, he original conribuions presened in his work are: ) A heoreical model of a cross-layer TCP NewReno-HARQ communicaion sysem which comprises a novel HARQ analyical model wih a finie LL buffer size and a new TCP NewReno mahemaical characerisaion developed from an exising Reno model, ) I is demonsraed ha he proposed cross-layer sysem significanly improves TCP performance when he opimal HARQ parameers are adapively seleced a he beginning of he connecion and 3) I is also demonsraed ha he LL buffer size can be reduced wihou derimen o TCP performance. This work is divided as follows: he TCP- HARQ cross layer sysem is described in Secion. HARQ analyical model is developed in Secion 3 whils he NewReno version is modelled in Secion 4. Assessmen of he accuracy of he cross-layer sysem is presened in Secion 5. Finally, Secion 6 concludes he work.. TCP-HARQ Cross-Layer Sysem Descripion The schemaic diagram of he cross-layer sysem o be modelled is shown in Figure. The scenario used is ha of a TCP connecion beween a server in he wired secion of he Inerne, as mos of he curren servers are locaed, and a mobile clien on a wireless link. A he beginning of he connecion, when he server receives he reques for a TCP connecion, i sends op-down explici noificaions o he LL of a base saion (BS), which is in communicaion wih he mobile saion (MS) where he TCP clien is locaed. The ransmission and form of hese explici noificaions are ou-of-scope of his work. The explici noificaions indicae he maximum congesion window (cwnd), he imeou (TO) duraion and he delay in he wired secion of he nework. An LL HARQ mechanism, which implemens error deecion and correcion hrough runcaed Selecive Repea (SR) ARQ and FEC convoluional codes, is used in he BS. Then, he LL eniy compues and predics TCP performance considering he explici noificaion informaion, he dif- Figure. TCP NewReno-HARQ sysem schemaic diagram. Figure. HARQ sysem a he LL. feren code raes, R c, he variable number of reransmissions, M, he buffer size and he MS's moniored E b /N 0 (called SNR hroughou his work). Finally, i selecs he opimal HARQ parameers, (R c, M ), which provide he bes TCP NewReno performance. The TCP receiver side does no suffer any changes in his proposed sysem. Furhermore, cross-layer communicaion beween he physical and link layers and, he ranspor and nework layer is needed in order o know he wireless channel SNR and he delay in he wired secion of he Inerne, respecively. The HARQ sysem modelled in his work is validaed in deail in [0] and shown in Figure. Service Daa Unis (SDUs) arrive wih normalised rae a he LL where, afer being fragmened and encoded, form a flow of Proocol Daa Unis (PDUs). In addiion, a LL header is appended o each PDU. The PDU size is he same regardless of R c, hence he amoun of applicaion daa per PDU varies according o he amoun of redundancy added. So, PDU size =b a +b r, where b a is he number of applicaion bis, including he LL header, and b r is he number of redundan bis needed o implemen FEC. The pariy bis o perform he Cyclic Redundancy Check (CRC) are also conained in b a. The code rae is defined as R c =b a /(b a +b r ). The resuling fixed-size PDUs are passed o he LL ransmission buffer, which has a finie capaciy of K-SDU and a firs-in firs-ou ransmission policy. The CxxRc buffer capaciy is fixed and equal o C [ ] SDU size where C is he link capaciy in bps, SDU size is given in Copyrigh 00 SciRes.

3 N. L. EWALD-AROSTEGUI ET AL. Figure 3. SDU ransmission process by a SR-ARQ proocol. bis and is he average round-rip ime in seconds. The number of sored SDUs varies according o heir respecive code rae R c. If he number of SDUs queueing and being ransmied is K+, addiional arriving SDUs will be discarded unil a buffer posiion becomes available. I is imporan o realise ha he inpu raffic o he buffer will be in he order of because of he encoding process R c causing a significan increase in he raffic inensiy. The SR-ARQ eniy on he server side keeps ransmiing PDUs, while on he receiver side, i verifies which PDUs (afer decoding) sill conain errors and asks for heir reransmission. The PDU is reransmied as many imes as allowed by he SR-ARQ parameers. If i sill presens unrecoverable errors, he complee SDU is discarded. Then, TCP will deec he discarded segmen and will reransmi i by eiher Fas Reransmis or TOs. 3. HARQ Analyical Model In his secion HARQ analyical model is described. Firs, he mahemaical procedure followed o obain he mean PDU error probabiliies afer FEC decoding when ransmied over a Rayleigh channel is presened. Second, he SDU ransmission process by a SR-ARQ proocol is represened by a Discree-Time Markov Chain (DTMC). A new heoreical approach based on he fundamenal marix is developed o calculae he SDU wireless loss probabiliy, p W, afer SR-ARQ implemenaion. Nex, he SDU loss probabiliy due o congesion, p K, is compued wih he wo-momen approximaion mehod o solve M/G//K processes. Finally, performance parameers such as he oal SDU loss probabiliy, p oal, and LL delay, E HARQ [D], are derived. 3.. Radio Channel and FEC Model I is assumed ha he ransmission power keeps he SNR, E b db, o an average level, arge. Then, N0 arg e a/ a, where a is he square of he Rayleigh fading envelope and a is is expeced value. The wireless channel error process is modelled by a wo-sae DTMC wih ime uni, which represens he PDU ransmission ime. The channel induces fewer errors in he Good sae when is higher han a cerain hreshold, h, and is in he Bad sae oherwise. a h is he value of a when = h. PDUs are encoded wih convoluional codes and decoded by sof-decision Vierbi decoding. Hence, he residual bi error probabiliies afer decoding, f()s, assuming QPSK modulaion, are compued numerically by he generaors described in []. The analyical procedure developed in [7] is followed in order o relae physical parameers such as and Doppler shif o he DTMC ransiion probabiliies. Therefore, he mean PDU error probabiliies in he Good and Bad sae, p G and p B, are compued as: ah a G arg e ah RcPDUsize p e e f a da () Copyrigh 00 SciRes.

4 ah a B a arg e h e 0 RcPDU size p e f a da Unlike [7], losses due o congesion in he LL buffer are also considered as well as he NewReno version and he adapive selecion of HARQ parameers according o he explici cross-layer informaion. 3.. HARQ Analyical Model In order o develop he analyical model for he SR-ARQ mechanism i is assumed ha: ) he SDU arrival process a he LL is Poisson. Alhough some have saed ha he Inerne packe arrival process is no Poisson [], recen research has shown evidence in favour of Poisson Inerne raffic models [3,5] ) The LL buffer implemens a generic SR-ARQ proocol for SDU ransmission. 3) The process in he LL buffer is considered as a M/G//K process. 4) The number of PDUs per SDU is N PDU and he number of reransmissions allowed per PDU is M -. 5) ACKs & NACKs are always correcly received righ afer he PDU ransmission ime. Even when he assumpion of Poisson arrivals can be challenged, he validaion resuls in Secion 5 show good agreemen wih he analyical characerisaion, under he given simulaion condiions. Furhermore, his assumpion is necessary in order o solve he M/G//K process in he finie size buffer. The ransmission of one SDU by he SR-ARQ proocol is represened by a DTMC which is shown in Figure 3. A Markov chain sae is defined by: s=(c,n PDU,M ), where C(G,B) is he channel sae referred o as Good or Bad, N PDU (0,N PDU ) is he number of PDUs, belonging o he same SDU, waiing in he LL buffer o be ransmied and M (0,M ) is he number of ransmission aemps available. The saes (G,0,0) & (B,0,0) are absorbing saes which represen he success or failure of a SDU ransmission afer aemping o reransmi a PDU M - imes. The fundamenal marix is used o find he probabiliy ha he process goes o (B,0,0). The number of ransien saes for he SDU ransmission process is m=(n PDU xm )+. So, he marix M is: P 0 M (3) R Q where P is he [x] marix of absorbing saes, 0 is he [xq] marix of zeros where q=m-, R is he [rx] marix of ransiions beween he ransien saes ino hose absorbing (r=q) and Q is he one sep ransiions probabiliy marix [qxq]. If he chain is in s i, he probabiliies ha a PDU is (un)successfully ransmied o s j are given by Equaions 4, 5 and 6: P ij, for s C,0,0 i and if s j C,0,0, C GorCB 0, oherwise N. L. EWALD-AROSTEGUI ET AL. () (4) p G, for s i G,, M and if s j G,0,0 p B, for s i B,,m and if s j G,0,0, m M R ij p G, for s i G,n,and if s j B,0,0, n N PDU p B, for s i (B,n,) and if s j B,0,0, n N PDU 0, oherwise (5) pg, for si G, n, M and if sj B, n, M n NPDUand if M pg, for si G, n, M and if s j Gn,, Mn NPDU Qij (6) pb, for si B, n, mand if sj B, n, m n NPDU and if m M pb, for si ( B, n, m) and if s j Gn,, M n NPDU and if m M 0, oherwise Thus, Q n ends o 0 (zero marix) when n ends o infiniy and, n N I Q Q is he fundamenal k 0 marix which gives he oal number of ime slos during which he process is in a cerain sae. The R marix is formed by wo column vecors, each one corresponding o an absorbing sae. If he column vecor of he failure sae is called p f, hen Np f is a vecor which conains he probabiliies of going o s (B,0,0) given i sars in any ransien sae. However, as he channel is modelled by a wo-sae DTMC, he SDU ransmission iniiaes from eiher s (G,NPDU,M) or s (B,NPDU,M). Then, he absorpion probabiliies corresponding o hese wo iniial saes are aken from Np f and form he -elemen column vecor Np f. Consequenly, p W is given by: pw Np f (7) where =[ G B ] is a row vecor wih he radio channel seady-sae probabiliies of being in he Good or Bad sae. Now, expecaion of he SDU service ime, E[], o ransmi an SDU successfully over he wireless link is calculaed. In he R marix, he column vecor of he success absorbing sae is called p s. Then Np s gives he SDU probabiliy of being successfully ransmied. D s is defined as a diagonal marix wih Np s as diagonal elemens. The SDU service ime when he process sars from any ransien sae is calculaed as E s []=D - s ND s, where is a column vecor of ones [q,]. As he SDU ransmission process only sars from eiher s (G,NPDU,M) or s (B,NPDU,M) : E E s n (8) where E s '[] is he -elemen column vecor conaining he mean service imes of he iniial saes. The average number of ransmissions per PDU, E PDU [M ]=E s '[], is calculaed considering ha he SDU is formed by one Copyrigh 00 SciRes.

5 N. L. EWALD-AROSTEGUI ET AL. 3 PDU, N PDU = Congesive Loss Analysis An M/G//K analysis is carried ou o find he SDU wired loss probabiliy, p K. The wo-momen approximaion approach is used insead of he embedded Markov chain because of is reduced compuaional complexiy and is closed-form expressions. In order o use his approach, i is necessary o calculae he coefficien of variaion of he service ime, C C, such ha, E if is he variance of he service ime: Nˆ Nˆ Nˆ (9) where ˆ N Ds NDs, and is he [x] vecor which conains he variance of he wo iniial saes from he vecor. The LL buffer capaciy is, as menioned, K-SDU. p K is calculaed by he following expression developed in [6] using he wo-momen approximaion approach: p K C K/ C C K/ C ESDU [ ] C (0) 3.4. Performance Parameers HARQ Toal SDU Loss Probabiliy If i is considered ha he probabiliies of an SDU no being discarded by he buffer and of being successfully received by he MS are independen, he oal SDU loss probabiliy is: p p p () oal K W HARQ Delay The expeced oal delay experienced by a SDU, E HARQ [D], in he LL buffer, including queueing and server processing, is obained hrough Lile's formula: E HARQ ESDU [ ] [ D] p R c C K () where ESDU [ ] is he expeced number of SDUs in C he LL buffer which is derived in [6] and defined in Equaion 3. Delays due o he wireless channel propagaion, processing a he receiver and encoding/decoding are no included: C C ln / pk ln pk / pk pk ln / e C / e ln ln / K ln K / K K ln / / ln ifc p p p p ec e oherwise HARQ Energy Efficiency The Coninuous-Time Markov Chain (CTMC) represening he TCP NewReno ransmier dynamics convey- The energy efficiency of he radio link due o HARQ, E HARQ [M ], can be obained as he raio of he SDU applicaion bis o he acual number of bis sen: where a maximum cwnd equal o 0 Maximum Segmen ing daa from a bursy applicaion is shown in Figure 4 Sizes (MSS) is considered. To clarify he figure, ransiions from all saes o s OFF are no oally represened as ba NPDU Rc E HARQ M (4) ba EPDU M N well as some ransiions from S CA o S FR. The CTMC ransiion raes are shown in Table for a generic cwnd PDU EPDU M R value. c The pariy bis, conained in b a, are also considered because hey are used for ARQ CRC. 4. TCP NewReno Analyical Model In his secion, he mahemaical procedure of [4] o develop he TCP Reno version is exended in order o analyically represen he NewReno Fas Recovery algorihm. This analyical characerisaion is validaed in deail in [7]. I is assumed ha he reader is familiar wih TCP algorihms. (3) In he Reno model of [4] i is assumed ha he sysem goes o S TO if more han one segmen is los during Slow Sar (SS) or Congesion Avoidance (CA), or if one loss occurs during Fas Recovery (FR). In conras, in he NewReno exension presened here, muliple losses can occur in he SS, CA or FR phases, which can be recovered during FR. 4.. Relaions beween TCP Algorihms and Transiion Raes As soon as he applicaion sars passing daa o TCP, i divides he daa in MSS and begins he connecion by Copyrigh 00 SciRes.

6 4 N. L. EWALD-AROSTEGUI ET AL. Table. Q TCP ransiion raes. From Sae To Sae Transiion rae Condiions (OFF)S OFF (, Th )S SS cwnd Th' (cwnd,th)s SS (cwnd,th)s SS p NL (cwnd) cwndmax cwnd =cwnd and cwnd ' (cwnd,th)s SS (cwnd,)s CA p NL (cwnd) cwnd =cwnd and cwnd=th ss SS S CA (Th )S TO [-p NL (cwnd)] ss SS S CA (cwnd )S FR p NL (cwnd) (cwnd,)s CA (cwnd,)s CA p NL (cwnd) ss SS S CA (Th )S TO [-p NL (cwnd)-p L (cwnd)] max cwnd Th' max, if cwnd 4 ' cwnd ' cwnd ifcwnd ' 4 TO and if losses cwnd =(cwnd+) if cwnd<cwnd max cwnd Th' if cwnd 4 TO and if losses TO (cwnd)s FR (cwnd,)s CA [p NL (cwnd)+p L (cwnd)] cwnd ' cwnd if losses (cwnd)s FR (Th )S TO pnl cwnd pl ( cwnd) TO cwnd TO Th' if losses (Th)S TO (,Th )S SS Th =Th ss SS S CA S FR (OFF)S OFF _ cwnd' is equal o double he previous cwnd value whils is he parameer of he exponenial disribuion governing he occupancy ime of he saes and is equal o. p NL (cwnd) is he embedded Markov chain probabiliy of no having losses during he ransmission of a cer- ain cwnd and is calculaed as: Figure 4. CTMC represening TCP algorihms. seing is hreshold o he neares lower ineger power of cwndmax of. The chain ransiion from s OFF o s (,Th) S SS represens he beginning of he TCP ransfer. The ime duraions spen in s ON and s OFF are random variables, and, wih negaive exponenial disribuions. Once he sysem is in SS mode, if here is no segmen loss, s (cwnd,th) goes o s (cwnd',th) wih rae p NL (cwnd). p ( cwnd) ( p ) cwnd (5) NL where p oal is he TCP segmen loss probabiliy deeced a he ranspor layer and is defined in Equaion, considering ha MSS=SDU size. In case he cwnd of a sae in S SS reaches he hreshold value, i will ener (cwnd',)s CA wih a ransiion rae of p NL (cwnd). If no losses ake place in he CA mode, s (cwnd,) will move o s (cwnd+,) wih a rae of p NL (cwnd). TCP deecs losses hrough he recepion of riple-duplicae (TD) ACKs herefore, cwnd 4 is he condiion o recover losses by FR. If a leas one loss occurs and if cwnd<4, saes in S SS S CA will ineviably ener a corresponding sae in S TO. In he TO phase, saes will ake a value of Th where Th' represens he neares lower ineger power of of cwnd. The ransiion rae o S TO is equal o [-p NL (cwnd)] for cwnd 4. oal Copyrigh 00 SciRes.

7 N. L. EWALD-AROSTEGUI ET AL. 5 In conras, TCP eners FR as soon as i deecs a los segmen hrough TD ACKs. The maximum number of allowed los segmens is condiional on he cwnd size, i.e. he number of received segmens has o be a leas 3 o allow TD indicaions. Any sae of he se S SS S CA experiencing from o TO los segmens, will move o (cwnd')s FR wih ' cwnd cwnd and ransiion rae p L. Since each segmen sen in he cwnd represens an independen even and can be equally affeced by he consan oal loss probabiliy p oal, i is assumed ha he segmen loss paern follows a binomial disribuion. Hence, p L is defined as: TO cwnd losses ( cwnd losses) L ( ) losses oal ( oal ) losses p cwnd C p p (6) In he FR phase i is only possible o recover TO losses occurred in CA. If more losses ake place, a sae from ss SS S CA will move o S TO wih ransiion rae (-p NL -p L ). Unlike Reno, he NewReno version avoids muliple halving of he cwnd every ime a loss is deeced. The recepion of TD ACKs caused by he firs loss occurring in SS or CA, riggers he Fas Reransmi algorihm and is inheren rae halving whils he recepion of parial ACKs caused by he subsequen losses do no rigger any furher sending rae reducions. Once in he FR mode, he reransmission imer is rese afer he firs parial ACK is received, as saed in [7]. Therefore, i will ulimaely imeou afer TO s in which TO segmens are reransmied given ha i is only possible one reransmission per. TCP reransmis he los segmen as soon as i receives he TD ACKs and i has o wai one once in FR, in order o deec a subsequen loss. If a cumulaive ACK is received afer he s, no furher losses occured in CA and he process can move back o CA. Oherwise, if a parial ACK is received, more han one loss has occurred and he los segmen is reransmied immediaely. Thus, he sysem will move from ss FR back o a corresponding ss CA wih a rae of [p NL (cwnd)+p L (cwnd)], where p L can be calculaed hrough Equaion 6 considering he maximum number of losses equal o TO insead of TO. If he number of losses during he FR is higher han TO, ss FR will ener a corresponding sae (Th) S TO pnl pl wih a ransiion rae TO. By considering he maximum number of segmens which can be los in CA and recovered in FR, TO, and ha which can be los and recovered in FR, TO, we are characerising he NewReno algorihm which is he mos significan difference from he Reno analyical model of [4]. Any sae ss SS S CA S FR going o he TO phase will halve is cwnd. This value will be he hreshold of ss TO. I will also be he hreshold value in he SS phase when he chain moves back o (cwnd,th) S SS in order o coninue he daa ransfer. The ransiion rae from he TO saes o he SS mode is, as expeced,. TO If he applicaion sops sending daa o TCP, he chain will ener s (OFF) wih a rae regardless of is curren sae. However, here are no ransiions among ss TO and s (OFF) because once he reransmission imer expires, i sill needs o reransmi he whole cwnd which conains he los segmen(s). TCP. The expeced of TCP segmens is necessary o calculae, herefore i is calculaed as: E D E D ACK (7) [ ] TCP wired HARQ TCP where D wired is he delay in he wired secion of he nework, E HARQ [D] is he delay in he LL buffer, defined in Equaion, and ACK TCP is he TCP ACK ransmission ime over he wireless link. Thus, E TCP [] grealy depends on he LL buffer delay which subsequenly impacs on TCP performance. 4.. TCP Performance Parameers TCP hroughpu. In order o calculae he TCP hroughpu, he seady-sae probabiliies of he CTMC, TCP s, are calculaed by he algorihm developed in [8]. The average MSS generaion rae per second, whils he applicaion is acive, is calculaed as in [4]: cwnd TCP () s TCP () s ON ssto ssto ON OFF (8) where ON and OFF are he average ime duraions in s ON and s OFF, respecively, given by ON and OFF. The receiving TCP bi rae is compued by: Throughpu ( p ) MSS (9) TCP TCP energy efficiency. SDUs are dropped by he LL buffer or discarded by he HARQ because eiher he oal Copyrigh 00 SciRes.

8 6 N. L. EWALD-AROSTEGUI ET AL. Figure 5. Nework opology se up in ns- validaion. Table. TCP-HARQ sysem simulaion seings. Seing TCP file sizes SDU size= MSS Maximum cwnd FEC code raes R c PDU size arge Wireless bandwidh BS LL buffer size D wired Value 5, 0 & 0MB 500B 4MSS 7,,, & bis.5, & 3dB Mbps Cx, =00ms 50ms buffer is full or several of heir PDUs sill presen unrecoverable errors afer he allowed number of reransmissions. Since segmens are recovered hrough FRs or TOs, hese TCP reransmissions have a direc impac on he wireless link efficiency. The lower he TCP reransmissions, he higher he link efficiency which depends on he HARQ error correcion capabiliy. TCP energy efficiency, E TCP [M], is defined o measure his effec: E M E M p (0) TCP HARQ oal Figure 6. TCP NewReno hroughpu for arge =.5dB. Figure 7. TCP NewReno hroughpu for arge = db. 5. TCP-HARQ Model Performance Validaion In his secion, he accuracy of he analyical predicions of he cross-layer TCP-HARQ model is validaed hrough ns- simulaions. 5.. Validaion Scenario The validaion scenario is shown in Figure 5 where he TCP connecion under analysis is ha from hos 0 o he MS. A wo-sae error module models he wireless link, his radio channel is used solely by he segmens of he TCP flow under consideraion. In order o model he error module, p G and p B are numerically compued according o Secion 3. The simulaion seings are displayed in Table. The TCP ransfers occured under differen raffic condiions which include no-raffic and a mixure of Reno Figure 8. TCP NewReno hroughpu for arge = 3dB. and NewReno as well as UDP flows which were sared a random imes o simulae he Poisson naure of Inerne raffic. Up o 0 flows were ineracing a once in he nework, 5 were TCP and 5 were UDP flows in order o represen he greaer percenage of TCP raffic in he Inerne. All bu he MS were sending and receiving differen ypes of raffic. The core rouer buffers of he wired nework are well provisioned, so no congesion occurs on hem. Copyrigh 00 SciRes.

9 N. L. EWALD-AROSTEGUI ET AL. 7 Figure 9. TCP NewReno energy efficiency E TCP [M] for arge =.5dB. Figure 0. TCP NewReno energy efficiency E TCP [M] for arge = db. Figure. TCP hroughpu for differen muliples of ypical buffer size Cx. The TO duraion is se o in he analyical model, 5 as generally suggesed in he lieraure [7]&[3], whils ON and OFF are se equal o s. The following fixed-poin approximaion is used o iniialise he TCP-HARQ model and o measure is performance: ) The maximum cwnd, TO duraion, E TCP [] and p oal are fed ino he TCP model in order o calculae TCP iniial arrival rae o he LL and is corresponding hroughpu (Equaions 8 and 9). E TCP [] and p oal are iniiallly considered D wired and 0.0, respecively. ) The prediced TCP iniial arrival rae is inpu ino he HARQ model where he corresponding p oal and E HARQ [D] are calculaed per each se of (R c,m ) (Equaions and ). 3) These HARQ performance values are fed back o he NewReno model where he E TCP [] and TCP bi rae are again compued (Equaions 7 and 8). 4) This process is repeaed unil p oal, E TCP [] and TCP hroughpu values converge ino consan values per each (R c,m ) se. Simulaneously, TCP hroughpu, p oal and E TCP [] are moniored in he ns- simulaions for he (R c,m ) ses under differen arge. These values are compared o hose calculaed analyically o assess he accuracy of he model. 5.. TCP-HARQ Performance Figure. TCP NewReno energy efficiency E TCP [M] for arge = 3dB. Typical required SNR values considered in link budge design of UMTS, for high-rae daa and urban environmens, are assumed [9]. The.4GHz wireless link is experiencing slow fading herefore correlaed errors occur in he ransmied PDUs. As he channel fading correlaion properies depend direcly on he normalised Doppler bandwidh f D [30], f D was considered equal o 0.. The impac of HARQ parameers on TCP performance under arge =.5, and 3dB represening high, moderae and low error raes, respecively, is shown in Figures 6. The impac of he buffer size on he TCP-HARQ sysem is shown in Figure TCP Throughpu High error raes. Under arge =.5dB, he code raes of 3 and are beneficial o TCP hroughpu as shown is Figure 6. The res of he code raes exhibi lower bi raes Copyrigh 00 SciRes.

10 8 N. L. EWALD-AROSTEGUI ET AL. and similar loss probabiliies o he NewReno flow wih no-coding. The main facor which negaively affecs he performance of he flows wih R c = and 3 is ha p G and p B (he mean PDU error probabiliies in he Good and Bad sae) are very high. Therefore, more reransmissions are necessary o successfully ransmi a MSS, which ranslaes ino higher buffer occupancy, which increases he wired loss probabiliy, p K. On he oher hand, wih low redundancy (R c = and 7 ), he wireless 3 8 loss probabiliy, p W, is he main facor which causes TCP o recover he los segmens mosly hrough TOs. As a resul of his and of he high service imes, he cwnd does no reach is maximum value during he connecion causing lower hroughpu. All code raes show he same rend: heir hroughpu is improved wih an increasing number of reransmissions. However, his gain is no unbounded, i depends on R c, on he required number of ransmissions o successfully send a PDU E PDU [M ], on he buffer size and, of course, on he available bandwidh. For arge =.5dB, he maximum number of ransmissions suppored by he HARQ analyical model of a flow wihou coding or wih R c = 7 is M =. Furher reransmissions caused 8 E[SDU] C (Equaion 3) o exhibi complex values because of he high service imes in he buffer, i.e. he raffic inensiies reach high values due o he high buffer occupancy imes. The flow wih R c = also presened 3 complex values bu hey appeared for lower persisance levels, M =7, and due o he high raffic inensiies caused by he high code rae. In he cases of complex values in he analyical model, heir simulaion counerpars exhibied lower hroughpus given ha he high p oal caused TCP o recover he los MSSs hrough mosly TOs. The TCP connecion whose PDUs are encoded wih R c = shows he maximum achievable hroughpu, 9 MSS/s, for he nd ransmission; higher reransmissions do no increase is MSS rae. This occurs because he required number of ransmissions o successfully send a PDU, E PDU [M ], becomes quasi-consan for M, as do he service imes. Then, p K also shows quasi-consan values, which causes a similar number of dropped segmens for M. In his specific connecion, for low persisance levels, TOs are due o mainly p W whils FRs rarely occur. In conras, corrupive losses are increasingly recovered by FRs and hose congesive by TOs as M increases, i.e. as a resul of he high number of reransmissions needed o successfully send a segmen, he raffic inensiy grows causing p K o also grow. Then, he buffer discards arriving segmens of he same cwnd in such a manner ha hey can only be recovered by TOs. The imporance of considering a finie buffer size can be undersood hrough his close inerrelaion beween p K and p W, which will dicae TCP-HARQ sysem performance. Since he maximum achievable hroughpu of R c = 3 is 4 MSS/s for M =7, he opimal parameers which provide he highes NewReno hroughpu for arge =.5dB are R c =, M =. Moderae error raes. The impac of moderae error raes on NewReno performance can be clearly seen in Figure 7. In conras o he previous case, he maximum hroughpu is achieved wih a significan lower number of reransmissions, M =8 and no-coding. More reransmissions do no ranslae ino higher hroughpus because, as explained previously, E PDU [M ] is almos invariable for M 8. Even when he highes receiving MSS rae is significanly higher han ha under arge =.5, i represens roughly 40% of he available bandwidh. In his case, a higher number of MSS is recovered by FRs because of he lower p W. However, he TOs caused by p K appear for lower persisance levels han in he case of arge =.5dB. Beer channel qualiy causes lower required reransmissions per PDU, E PDU [M ], which subsequenly causes lower. This lower makes TCP behave more aggressively: is cwnd increases rapidly causing higher inpu raffic raes in he buffer and a higher p K. Since TCP has o implemen muliple FRs and TOs o recover losses, is sending MSS rae is coninuously reduced. This reducion causes low p K which ogeher wih low p W, allow again, he rapid cwnd growh which leads o early hroughpu oscillaions and, ulimaely, a reducion in he average hroughpu. In Figure 7, he flow wih R c = exhibis a higher 3 hroughpu up o M =7, however is rae growh is bandwidh bounded for M =8. In his specific case, he redundan bis are having a negaive impac on he hroughpu. The performance gain of adaping HARQ parameers according o he SNR insead of using fixed-seings is obvious. If insead of selecing he opimal parameers for arge =db, (R c =,M =8), fixed-seings were used, e.g. M =4 (Long Rery Limi in WLANs), R c = will provide he bes possible performance. However, his will exhibi a lower hroughpu (MSS/s) han ha given by HARQ wih adapive parameers (3 MSS/s). Low error raes. For arge =3dB, i is clear from figure 8 ha he maximum NewReno hroughpu has increased, compared o he previous wo cases, using fewer reransmissions. The highes receiving MSS rae shows a growh of 30% and 40% compared o hose of arge=.5 and db, respecively. As expeced, he flow, which performs bes, is ha Copyrigh 00 SciRes.

11 N. L. EWALD-AROSTEGUI ET AL. 9 wih no-coding. I reaches is bes hroughpu for M =6. The hroughpu shows negligible gain above his value due o he almos invariable E PDU [M ]. The average hroughpu represens 50.5% of he available radio link bandwidh. The performance is mainly affeced by congesion, ha is, he buffer size and, in he case of he res of he flows, he high degree of redundancy. The MSSs discarded by he LL buffer are recovered mosly hrough TOs whils fewer FRs due o p W ake place because of he opimal SNR of he wireless link. From hese resuls, we can say ha TCP connecions over wireless links exhibiing high error raes need he implemenaion of boh error conrol schemes, i.e. boh high FEC coding and ARQ. For moderae and low error raes, he sole use of ARQ improves NewReno performance. In addiion, he adapive selecion of he code rae and he number of reransmissions will provide higher TCP improvemen han ha of HARQs wih fixed-seings TCP Energy Efficiency The NewReno energy efficiencies, E TCP [M ], are shown in Figures 9 where i is observed ha he efficiency increases wih he number of reransmissions. This occurs because increasing he ARQ reransmissions hide more losses from TCP, which decreases he number of TCP reransmissions. However, above a cerain number of reransmissions, E TCP [M ] becomes almos invariable as p oal shows negligible change due o he quasi-consan E PDU [M ] and he finie buffer size. As expeced, he higher arge, he beer E TCP [M ]. Ineresingly, he NewReno flow wih R c = 3 exhibis a differen rend in Figure 9. I iniially has a beer E TCP [M ] which decreases wih he number of reransmissions. Since is p W is lower due o he effec of he coding, he average number of reransmissions per PDU is lower han ha of he res of he flows. This riggers a beer use of he link specrum. However, increasing M raises p K and is resuling p oal due o he negaive impac of R c which causes a greaer number of losses o be recovered by TCP. The flow which achieves he highes radio channel efficiency in Figure 9 is ha wih no-coding and M = which are no he opimal HARQ parameers seleced previously. In conras, for moderae and low error raes, he HARQ parameers providing he highes hroughpu also provide he bes use of he wireless link bandwidh as shown in Figures 0 and. Again, he advanages of adapive HARQ seings are demonsraed for his cross-layer scheme Impac of Buffer Size The impac of buffer size on he performance of TCP- HARQ sysem is shown in Figure. Differen muliples of he buffer size were esed wih he opimal HARQ parameers previously seleced for each arge, i.e. arge=.5db: (R c =,M =), arge =db: (R c =,M =8) and arge =3dB: (R c =,M =6). In he case of arge =.5dB, i is only possible o increase he buffer size (Cx) by 45%, oherwise he model presens complex values. I can be seen ha he analyical model predics similar TCP hroughpu for buffer sizes in he order of 0.35Cx. Neverheless, he hroughpu of he ns- simulaions shows lower values wih his buffer capaciy. The MSS rae of he simulaions reaches he opimal value of (R c =,M =) for buffer sizes of 0.70Cx. Therefore, even when he buffer capaciy is no reduced as dramaically as prediced, i can be safely reduced by 30% wihou derimen o TCP hroughpu. For arge =db, he analyical hroughpu is equal o he opimal given by (Rc=,M=8) for buffer capaciies in he order of 0.50Cx. The simulaions exhibi his behaviour for buffer sizes of 0.60Cx. The difference beween he mahemaical and he simulaed hroughpu is lower in his case. Incremening he buffer capaciy does no conribue o an improvemen in he hroughpu given he higher buffer occupancy imes of hese larger buffers. For arge =3dB, he prediced TCP hroughpu is equal o he opimal of (R c =,M =6) for buffer sizes of 0.45Cx. Simulaions exhibi he opimal hroughpu wih buffer capaciies of 0.60Cx. Increasing he ypical buffer size in hese condiions resuls in MSS rae reducion which differs from he previous case, arge =db, where no hroughpu change was exhibied. This occurs because, under arge =3dB, p K significanly increases wih respec o p W. Therefore, more TOs occur which compromise he hroughpu. I has been demonsraed ha, in his TCP-HARQ analyical scheme, higher buffer sizes do no provide lower wired loss probabiliies because of he high raffic inensiies. However, LL buffer sizes can be safely reduced in he order of 30-40% of he radiional buffer sizes according o he curren SNR of he radio channel. Beer ransmission condiions lead o higher capaciy reducions. A decrease in he buffer capaciy no only saves buffer memory bu also causes lower delays (which is of paricular imporance if mulimedia applicaions are o be sen hrough he buffer). Furhermore, hese resuls agree wih hose of [3] where i is saed ha rouer buffers can be reduced. Even hough [3] refers o buffers in core neworks, he resuls here have shown ha, in he case of his HARQ-TCP sysem, i can also apply for egress links. However, i is necessary o analyse ypical raffic paerns of he paricular link. 6. Conclusions The accuracy and correcness of he analyical model of he TCP-HARQ sysem predicions is demonsraed even Copyrigh 00 SciRes.

12 30 N. L. EWALD-AROSTEGUI ET AL. wih he number of assumpions made in he developmen of HARQ and TCP characerisaions. In paricular, he assumpions of he wo differen loss models assumed in he link and ranspor layers: HARQ is modelled under he assumpion of correlaed losses due o a slow fading channel whils losses deeced by TCP are modelled as Bernoulli losses. Thus, he use of HARQ randomises he correlaed losses of he radio channel and makes hem appear independen a he TCP level. I was also shown ha he opimal code rae and persisence level depend on he wireless channel error rae. The use of a runcaed HARQ improves TCP NewReno hroughpu over a radio link experiencing high channel error raes, whils he use of lile or no redundancy and runcaed ARQ provides hroughpu enhancemen for TCP flows over links experiencing moderae or low error rae. For hese ypes of link i is also possible o achieve he bes usage of he wireless bandwidh if opimal HARQ seings are used. In addiion, a HARQ sysem, which dynamically selecs opimal parameers, will provide higher hroughpu improvemen han ha of a HARQ wih fixed-seings. Higher improvemen is shown in oher works (e.g. [5] or [7]) since hey do no consider a finie buffer size, somehing which does impac performance. As he SNR of he wireless channel increases, he congesive losses increasingly dicae he oal loss probabiliy of he sysem. Even for connecions wih opimal radio channel qualiy, he rapid growh of he cwnd causes high wired loss probabiliies in he buffer. As a resul, a higher percenage of los segmens is recovered by TCP reransmissions wih a subsequen reducion in he average hroughpu. Furher, i was shown ha LL buffer sizes can be reduced by 30-40% wih respec o he ypical size, according o he curren SNR, wihou derimen o TCP NewReno hroughpu. Since i is assumed ha he LL has informaion abou he ransmission qualiy of he radio channel, cross-layer communicaion has o ake place beween he physical and link layers. As i is also considered ha he op-down TCP explici noificaion conains informaion abou he delay in he wired secion of he nework, furher cross-layer communicaion involving he rouers in he TCP connecion pah also occurs. In addiion, if mechanisms such as IP QoS rouing are implemened on he wired links, he TCP performance predicions compued by he LL eniy will be more precise, i.e. if he TCP connecion over he wired link is required o no exceed cerain delay bounds, D wired will be more accurae. Thus, he imporance of cross-layer communicaion schemes in he improvemen of nework performance can be undersood. The model presened ses an analyical framework and fuure work can consider he impac of adapive modulaion schemes and IP QoS rouing on he TCP NewReno-HARQ sysem, as well as he adequacy of he model for differen nework opologies and several mobile nodes. 7. Acknowledgemens N. L. Ewald-Arosegui was funded by he Naional Council on Science and Technology of Mexico under gran References [] K. 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