Achieving High Throughput and Low Delay by Accurately Regulating Link Queue Length over Mobile Data Network

Transcription

1 24 IEEE h Inernaonal Conerence on Wreless and Moble Compung, eworkng and Communcaons (WMob) Achevng Hgh Throughpu and Low Delay by Accuraely Regulang Lnk ueue Lengh over Moble Daa ework e Lu Sae ey Laboraory o Compuer Archecure Insue o Compung Technology Chnese Academy o Scences Emal: luke@c.ac.cn Jack Y. B. Lee Deparmen o Inormaon Engneerng The Chnese Unversy o Hong ong, Hong ong Emal: yblee@e.cuhk.edu.hk Absrac nowledge o he queue lengh o he boleneck lnk has many poenal applcaons such as congeson conrol, rac engneerng, rac polcng, conen adapaon, os monorng and provsonng, ec. A recen work proposed a new Sum-o-Delay wh Tmesamp (SoD-TS) algorhm whch can accuraely esmae queue lengh n moble neworks wh boh bandwdh varaons and uplnk delay varaons by explong he exsng TCP Tmesamp opon. By makng use o SoD-TS we developed a novel ranspor proocol queue-lengh-aware TCP (TCP-LA), ha ackles he problem o buerbloa o provde beer os or applcaons requrng low end-o-end delay and/or hgh bandwdh ulzaon. Trace-drven smulaon shows ha compared o TCP CUBIC TCP LA can reduce he RTT by a acor o 2.7 whle sll achevng over 97% bandwdh ulzaon. Moreover, TCP-LA urher reduces RTT by 5% compared o delay-based TCP such as FAST TCP and TCP Vegas. Index Terms: queue lengh, TCP, bandwdh ulzaon. I. ITRODUCTIO TCP [-5] have snce evolved over he years and been adoped as he ranspor proocol or numerous Inerne applcaons. Gven he lack o os conrol n he curren Inerne s essenal o desgn TCP o adap o varaons n nework condons. Wh he emergence o moble daa neworks such as 3G/4G [6], he challenge o changng nework condons s even more crcal or applcaon desgners, conen provders as well as moble operaors. Among he TCP varans, TCP CUBIC [5], he domnaed TCP varan n use n Inerne servers, can acheve he good bandwdh ulzaon bu resuls n he problem o buerbloa [7] over moble daa neworks, as keeps ncreasng CWnd unl lnk buer overlow, hus buldng up a large backlog n he lnk buer. I s a ac ha queue lengh o boleneck lnk can have sgncan mpac o TCP s perormance. Thus one can accuraely esmae he queue lengh and regulae o a arge queue lengh, hen can manan low end-o-end delay whle sll achevng hgh bandwdh ulzaon. Prevous works such as Vegas mehod [2] and Sum-o-delays mehod (SoD) [8] only ncorporae he lnk bandwdh varaons n esmang he queue lengh bu do no consder delay varaons n he uplnk,.e., rom he moble devce o he Inerne, and smply assumed o be consan. Inerne server Inerne T w L U q c T m Moble daa neworks(e.g., 3G.LTE) Moble recever Fg. The sysem model or analyzng he TCP-LA algorhm. In mos Inerne applcaons he drecon o daa ranser s ypcally rom he Inerne o he moble devce. Thus racs n he uplnk are usually much less and prmarly consss o applcaon requess (e.g., HTTP reques) and AC packes generaed by he TCP recever. Hence uplnk bandwdh s rarely he boleneck. However, he recen measuremens [8, 9] conduced n producon 3G/LTE moble neworks revealed ha he uplnk delay can and do exhb some varaons, even s no congesed. We conjecure ha he varaons are due o acors such as lnk-layer reransmssons [6], rado resource schedulng, and queueng a he uplnk. aurally hs wll aec he esmaon accuraces o Vegas and SoD mehods. Our prevous work proposed a praccal soluon Sum-o-Delay wh Tmesamp (SoD-TS) [], o hs problem by explong TCP s Tmesamp Opon [] whch s wdely mplemened by moble devces. We urher showed ha SoD-TS can be appled o TCP CUBIC by explong he esmaed queue lengh as sgnals or TCP CUBIC s congeson wndow ncrease/decrease. In hs work we ake queue-lengh-based congeson conrol urher by developng a novel ranspor proocol queue-lengh-aware TCP (TCP-LA), o ackle he problem o buerbloa over moble daa neworks whle mananng hgh nework ulzaon. TCP-LA s desgned o regulae he queue lengh a he boleneck lnk o a arge queue lengh o manan low end-o-end delay whle sll achevng hgh bandwdh ulzaon. Boh sysem model and race-drven smulaons show ha compared o TCP CUBIC TCP-LA can reduce he round-rp me (RTT) by a acor o over 2.7 whle sll achevng over 97% bandwdh ulzaon. Addonally, compared o delay-based TCP such as FAST TCP and TCP Vegas, TCP-LA reduces RTT by 5% as /4/$3. 24 IEEE 562

2 24 IEEE h Inernaonal Conerence on Wreless and Moble Compung, eworkng and Communcaons (WMob) requres a smaller arge queue lengh o acheve near % bandwdh ulzaon, hus always resuls n he lowes RTT. TCP-LA s parcularly desrable or applcaons requrng low end-o-end delay and hgh bandwdh ulzaon, such as lve vdeo sreamng. The res o he paper s organzed as ollows: Secon II revews some relaed works on queue lengh esmaon mehod. Secon III presens he proposed TCP-LA; Secon IV presens a sysem model o TCP-LA and proves s several neresng properes. Secon V evaluaes TCP-LA va race-drven smulaons. Secon VII summarzes he sudy and oulnes some uure work. II. UEUE LEGTH ESTIATIO METHOD In hs secon we brely revs several queue lengh esmaon mehods. A. Vegas Mehod Frs, some TCP varans do employ relaed echnques o eher mplcly or explcly esmae he queue lengh a he boleneck lnk or congeson conrol purpose. One well known example s TCP Vegas [2] whch employ an algorhm o esmae he queue lengh rom he congeson wndow sze and he derences beween curren and mnmum RTTs. Smlar algorhms have also been adoped n TCP Veno [4] and FAST TCP [3]. Speccally, he TCP sender connuously measures he RTT, denoed by r, and records he congeson wndow sze, denoed by cwnd, a he me AC packe s receved. I hen keeps rack o he mnmum r mn by, rmn mn r () and hen compue he esmaed queue lengh, denoed by n, rom he derence beween he expeced hroughpu,.e., cwnd r mn, and he acual measured hroughpu,.e., cwnd r, n he las round-rp me [2], ' cwnd( r rmn ) n (2) r Vegas mehod uses he congeson wndow sze o he curren RTT o esmae he queue lengh n he prevous RTT, whle FAST TCP addressed hs shorcomng by keepng rack o he pas congeson wndows o he prevous RTTs, and usng he one a he me o he orgnal daa ransmsson nsan o compue (2) or beer accuracy. Chan e.al [8] also showed ha he FAST mehod has he esmaon error o 4.8%, whle Vegas mehod has he esmaon error o a leas 5.8%. These esmaon errors are due o her nably o rack shor-me-scale bandwdh varaons common n moble daa neworks. Addonally, Vegas and FAST do no compensae or uplnk delay varaons and smply lump ogeher wh queueng delay varaons. Ths may lead o alse posves n congeson esmaon, resulng n lower bandwdh ulzaon. B. Sum-o-Delay Mehod To ackle he naccurae queue lengh esmaon due o bandwdh varaons Chan e.al nvened a new sum-o-delay (SoD) mehod whch compensaes or he mpac o nework bandwdh varaons n perormng queue lengh esmaons by drecly measurng he bandwdh rom AC packe mngs and keepng rack o he seres o pas bandwdh measuremens. The ollowng s a smpled descrpon o he SoD algorhm based on he sudy by Chan and Lee [8]. Fg. depcs he sysem model where a sngle sender ransms packes va he rado nerace o a recever. Le T w be he orwardng delay rom he Inerne server o he rado nerace; T m be he orwardng delay rom he rado nerace o he moble recever. The recever acknowledges receved packe by sendng back an AC packe o he sender whch akes u seconds or AC o reurn o he sender. In he orgnal SoD algorhm he uplnk delay s consan,.e., u =U or all. one o he boleneck lnk s parameers are known a pror. The goal s o esmae he queue lengh, denoed by q. The prncple o SoD s o make use o he seres o AC packe mngs o oban an esmae o he packe ransmsson me, he laer o whch ncorporaes he mpac o nework delay and bandwdh varaons. By dervng wo nequales,.e., (7) and (), whch bound he queueng delay, one could hen oban an esmae o he queue lengh n (2). Speccally, le be he ransmsson me or packe whch can be esmaed rom he measured AC packe ner-arrval mes or packes and (), denoed by r and r - respecvely: r r (3) provded ha he lnk does no become dle durng hs me. Suppose packe arrves a he boleneck lnk o nd ha here are n packes already queueng, plus packe ( n ) currenly beng ransmed. Then he queueng delay o packe, denoed by q, s equal o he oal me o ransm all he n queueng packes,.e., he sum o ransmsson delays o packe ( ) o ( n ), plus he resdual me o ransm packe ( n ), denoed by : q 2... n (4) where he resdual ransmsson me s bounded by n (5) Subsung (5) no (4) gves he correspondng bounds or q : 2... n q 2... n n (6) whch becomes he rs nequaly or q : k q k k n k n (7) ueue lengh esmaon s hen equvalen o ndng n. The only remanng unknown erm s q whch canno be measured drecly by he sender. However one can oban a lower bound or q. Consder he RTT or packe : r q U Tw Tm (8) and he mnmum RTT measured so ar: rmn mn{ q } U Tw Tm (9) Subrac (9) rom (8) elmnaes he unknown erms excep q : r rmn q mn{ q } () q q, Rearrangng we hen have he second nequaly or q : 563

3 24 IEEE h Inernaonal Conerence on Wreless and Moble Compung, eworkng and Communcaons (WMob) q r r () mn wh all hree erms n he R.H.S. known o he sender. Fnally, we noe ha q mus sasy boh nequales n (7) and (), and hence we can esmae n rom: n mn x k r rmn, x,,... (2) k x The smalles n ha sases (2) hen becomes he esmaed queue lengh n. Ther resuls showed ha SoD can acheve sgncanly hgher esmaon accuracy even n moble neworks wh rapdly changng bandwdh. everheless, one assumpon n he prevous analyss s ha he uplnk delay s consan,.e., u =U,. Le λ, λ max λ, denoe he uplnk delay varaon experenced by he h AC packe receved by he sender. As delay varaons are relave we dene such ha he AC packe experencng he mnmum uplnk delay known as he reerence AC, has a delay varaon o zero. Comparng o he AC packe recepon me whou he delay varaon, denoed by r, he acual recepon me, denoed by r, now becomes r =r +λ (3) and he acual RTT measured, denoed by r, s gven by r =r +λ. (4) To ncorporae uplnk delay varaons we replace, r, and k n (2) wh, r, and k respecvely o oban ' ' ' n mn x k r rmn, x,,... (5) k x By rearrangng he erms (5) becomes n mn x k r rmn x2, x,,... (6) k x Comparng o (2) we can clearly see he mpac o uplnk delay varaon,.e., x 2, whch resul n over-esmaon o he queue lengh and s esmaon error s shown o be bounded by, max / mn packes. C. Sum-o-Delay wh Tmesamp Mehod To compensae he uplnk delay varaons we proposed a Sum-o-Delay wh Tmesamp (SoD-TS) mehod [], o urher mprove SoD s esmaon accuracy n neworks wh large uplnk delay varaons by explorng he TCP mesamp opon [] or hs propose. Speccally, assumng he recever generaes an AC mmedaely upon recevng a daa packe. Then he TCP sender can compue he daa packe ransmsson me drecly rom he correspondng AC packe s ransmsson mesamp TSval. Le r denoe he TSval o he h AC. Then n (6) can be compued rom =r r -. (7) ex we updae (5) by replacng he wh n (7), and subsung (4) no (5) o oban n mn x k r rmn, x,,... (8) k x Thus he only remanng unknown s. We observe ha aer he SoD algorhm converges, r mn would be known and we would also know whch packe,.e., he reerence packe, resuled n he mnmum RTT. Le he reerence packe be packe number re, and le r re and r be he arrval me and AC generaon me o he reerence packe respecvely. Le r denoe he acual AC recepon me and r denoe he AC generaon me. The uplnk delay varaon experenced by he h AC can be compued rom ( r ' rre ) ( r rre ) (9) We also showed ha he delay-varaon compensaed SoD-TS algorhm has a queue lengh esmaon error bounded by - packe,.e., underesmae by a mos one packe. Resuls rom race-drven smulaons also showed ha (a) ypcal uplnk delay varaons such as ms can degrade he esmaon accuraces o SoD by as much as %; and (b) he SoD-TS can eecvely elmnae he esmaon errors due o uplnk delay varaons, e.g.,.95%.esmaon error. III. UEUE-LEGTH-AWARE COGESTIO COTROL Armed wh he accurae knowledge o queue lengh rom SoD-TS we propose a novel ranspor proocol ueue-lengh-aware TCP (TCP-LA) ha connuously esmaes he queue lengh usng SoD-TS algorhm, hen deermnes he CWnd accordngly o accuraely regulae he queue lengh oscllang around a arge queue lengh, whch s able o manan low end-o-end delay whle sll achevng hgh bandwdh ulzaon. TCP-LA s organzed n wo key sages: () sar-up phase and () adapve phase. Speccally, le W denoe he nal CWnd, TCP-LA use a burs o W packes o provde an nal esmae o he BDP o he nework. Thereaer, TCP-LA adjuss he ransmsson rae o regulae he queue lengh oscllang a arge queue lengh usng SoD-TS algorhm. A. Sarup Phase I s a ac ha he modern moble neworks mplemen large rado lnk buers (e.g., 277.5B or 3G/HSPA). Moreover, he rado lnk buers are allocaed on a per user bass [2, 3] and hus are no shared even when mulple users are acve nsde he same moble cell. Compared o he large lnk buer sze, exsng TCP mplemenaons are oen oo conservave n resrcng he number o packes nlgh va he congeson wndow, hereby lmng he achevable hroughpu. Insead, TCP-LA sars a new connecon wh a burs o W packes. The exac value o W can be derved by explong knowledge o he properes o he moble nework. Ideally, s desrable or TCP-LA o ll he nework o more han he maxmum BDP. Speccally, le C max denoe he maxmum bandwdh o he rado nework (e.g., 7.2 Mbps or 3G/HSPA), and D max denoe he maxmum propagaon delay o he moble daa nework ncludng he maxmum uplnk delay varaons (e.g., 287ms or 3G/HSPA), hus TCP-LA wll se W =C max D max (e.g., 8 packes), s relavely small compared o he sze o he rado lnk buer (e.g., 852 packes), hus wll no lkely cause buer overlow. In conras, re 564

4 24 IEEE h Inernaonal Conerence on Wreless and Moble Compung, eworkng and Communcaons (WMob) convenonal TCP adops a small nal congeson wndow sze n TCP (e.g., 2 o 4 packes). Aer recevng he rs AC packe rom he moble recever TCP-LA leaves he sarup phase and swches no he adapve phase. B. Adapve Phase As soon as recevng he s AC packe rom he moble recever TCP-LA eners he adapve phase over whch he subsequen ransmsson wll hen adap o he queue lengh esmaed va SoD-TS connuously. Smlar o TCP Vegas and FAST TCP, TCP-LA updaes CWnd accordng o esmaed queue lengh once per RTT. Speccally, le T denoe he arge queue lengh and n j denoe he esmaed queue lengh a he begnnng o he j h RTT. Upon recevng he rs AC o he j h RTT, n j T, TCP-LA ncreases CWnd by T n j, hus wll ransm T- n j more packes besdes one ransmed packe due o AC clockng, oherwse, TCP-LA decreases CWnd by n j T, hus wll sop ransmng unl recevng n j T ACs ncludng he curren receved AC. In summary, TCP-LA updaes CWnd accordng o he ollowng rule: le W j denoe he CWnd durng he j h RTT. Upon recevng he rs AC o he j h RTT we have W W n (2) j j T j C. Loss Recovery Unlke convenonal TCP varans, he CWnd o TCP-LA s no aeced by packe loss evens. oneheless, los packes sll need o be reransmed and A-TCP sll regulaes he queue lengh around T usng (2) by explong TCP SAC [4]. As A-TCP lms he amoun o packes n he boleneck lnk buer, mplcly avods he congeson loss snce he arge queue lengh s much less han he lnk buer sze. Addonally, A-TCP guaranees he ecen bandwdh ulzaon durng loss recovery, whle convenonal TCP varans, e.g., TCP CUBIC, TCP Reno, cu down her CWnd blndly whou consderng he bandwdh ulzaon. IV. MODELLIG AD AALYSIS In hs secon we develop a sysem model or TCP-LA ha can be easly exend o model delay-based TCP such as FAST TCP; esablsh s sucen condon o ull bandwdh ulzaon and derve he properes o TCP-LA. A. Background and Assumpons Fg. depcs he sysem model ha he Inerne server s ransmng packes o he moble recever. Our ocus s on he ecen ulzaon o he rado nework and hus we assume he Inerne server and he backhaul lnkng o he moble nework are no he boleneck. Speccally, One TCP connecon s esablshed when he moble recever aemps o esablsh a connecon o he Inerne server. Upon recep o daa reques he Inerne server sars o ransm he packes and we assume ha he Inerne server always has daa wang o be ransmed o he recever. Symbol T w Table. Summary o symbols and noaons. Descrpon Downlnk delay rom Inerne server o he rado nerace. Downlnk delay rom he rado nerace o he moble T m recever. Uplnk delay rom he moble recever o he Inerne server. U U, U s a random varable whle U s he delay or he rs AC. Round rp propagaon delay,.e, D Tm U Tw. D s a D, D random varable whle D s he delay or he rs AC. The uplnk delay varaon a he me, λ() λ λ() max, where λ max s he maxmum uplnk varaons The congeson wndow a he h RTT, W W s he nal congeson wndow The esmaed queue lengh esmaed a he h RTT n n The acual queue lengh a he h RTT σ The queue lengh esmaon error n erms o packe The me aer he h RTT The ransmsson me or he rs daa packe. The amoun o daa acknowledged by delayed ACs a me, () () λ max C max C mn Mnmum lnk capacy, C mn. C max Maxmum lnk capacy, C max C mn. () Lnk buer lengh a me (n uns o bye) The number o packes receved by he rado lnk buer rom n me o me The number o packes sen ou by he lnk buer rom me o ou me The number o packes receved by he TCP recever as A n repored by ACs receved by he Inerne server rom me o me A ou The number o packes sen ou by he Inerne server rom me o me The Inerne server s conneced o he rado nerace va hgh-speed (e.g., Gbps) xed nework lnks. Le U be he uplnk delay rom he moble recever o he server. Thus he round rp propagaon delay D s gven by D=T m +U+T w. We gnore delay varaons n he downlnk as has he same eec as bandwdh varaon,.e., aecng he ransmsson me and hus s accouned or by he bandwdh esmaon process. For he uplnk we allow he delay o vary bu s bounded wh he maxmum delay. Le λ() denoe he oal uplnk delay varaon a me and λ() λ max, where λ max s he maxmum delay. Hence we have U [ Umn, Umax ] and D [ Dmn, Dmax ], where U max =U mn +λ max and D max =D mn +λmax. For he rado nerace we assume he rado lnk bandwdh over an arbrary nerval, s bounded rom above by C max and rom below by C mn, where C max >C mn. Oher han hese bounds he rado bandwdh can vary n arbrary manner rom one nerval o he nex. Table summarzes he noaons and symbols used n he sysem model. B. Sysem Model To derve he queue lengh a he rado nerace we consder he amoun o daa arrvng a and deparng rom he queue a any gven me. To smply he analyss we employ he packe-based model or packe low n he ollowng dervaons. Frs, he queue lengh s smply equal o he derence beween ncomng and ougong packes: () (2) n ou 565

5 24 IEEE h Inernaonal Conerence on Wreless and Moble Compung, eworkng and Communcaons (WMob) Where n are he number o packes arrved a an queue n he nerval (, ] and ou are he number o packes capable o be ransmed by he boleneck lnk n he nerval (, ]. oe ha () he bandwdh s ully ulzed and he value o () s queue lengh a me. ow consder he packe low rom he Inerne server o he queue. We noe ha he number o packes receved by he queue, e.g., n, s equal o he number o packes sen by he Inerne server T w seconds earler (c.., Fg. ): S Tw (22) n ou Tw S Tw where ou s he number o packes ransmed by he Tw Inerne server n he nerval ( T w, T w ]. As depced n Fg., le U be he uplnk delay experenced by he rs AC. Then he rs AC wll arrve a he server a me D +, where D =T m +U +T w. Durng he perod beore he rs AC arrves,.e., (, D + ], he ncomng daa rae o he queue s smply equal o he server s ransmsson rae n he perod (T w, D + T w ], hus D S D Tw W (23) n ou Tw n We dvde no wo sub-nervals (, D + ] and (D +, ] as ollows: D () n n D ou (24) Smlar o (23) we can oban he second erm n (24) rom ong ha Thus S Tw n D ou D Tw (25) D T ( T U T ) T w m w w Tm U S Tw n D ou T m U (26) (27) ex we consder he las erm n (24) by sub-dvdng no wo nervals (, D mn ] and (D mn, ] where D mn s he mnmum RTT: Dmn ou ou ou D (28) mn Subsung back no (24) we have D Dmn () n n D ou ou D (29) mn The rs erm on he R.H.S. o (28) s he amoun o daa sen by he rado nerace durng (, D mn ]. The ACs or hese daa are guaraneed o reurn back o he server whn he nerval [T m +U +, T w +λ max ] as delay varaon s bounded by λ max. Consder he ACs generaed rom packes ransmed by he rado lnk rom (, D mn ]. Le be he amoun o daa acknowledged by delayed ACs,.e., ACs arrvng durng [ T w, T w +λ max ] he server. We can hen rewre he rs erm n (28) as ollows: Dmn S Tw ou n (3) Tm U Where s bounded by maxcmax (3) Subsung (27) and (29) no (3) we hen have D S Tw S Tw () n ou n ou T D m U Tm U mn (32) By rearrangng he erms we have D S Tw S Tw () n ou D mn ou Tm U n Tm U (33) ex we consder he me nerval [ Tm U, Tw ] or he las wo erms n (33). Le M denoe he oal ACs receved a he nerne server durng [T m +U +, T w ], hus S Tw n M. Upon recevng every AC, TCP-LA has Tm U hree condons: ) TCP-LA ransms one daa packe due o TCP AC-clockng. 2) TCP-LA ransms T n more daa packes besdes one packe due o condon he receved AC s he rs AC o he h RTT and n T ; 3) TCP-LA s possble no o ransm any daa packe, snce TCP-LA sops ransmng unl recevng n T ACs n T when recevng he rs AC o he h RTT; Le m denoe he number o receved ACs ha TCP-LA goes o condon, hus M m s he number o receved ACs ha TCP-LA goes o condon 3. Le denoe he number o RTT durng [T m +U +, T w ]. Accordng o condon 2 and 3 TCP-LA wll ransm max( T n, ) packes upon recevng he rs AC o every RTT. Thereore we have, S Tw S Tw max n, mm ou Tm U n T Tm U (34) where m s he number o packes ransmed due o condon. Le k={x x } denoe he se o RTTs durng he nerval [T m +U +, T w ], le k denoe he subse o k ha condon 3 occurs, hus we have, T n M m (35) k We can om he max uncon n he rs erm o R.H.S. o (34) by addng he L.H.S. o (35) o (34), hus we have, S Tw S Tw n, n mm ou Tm U n T T Tm U k (36) Cancel he las wo erms o (36) accordng o (35) and Subsue (36) no (33) we have, () W ou D mn T n (37) Le n denoe he acual queue lengh, hus n =n +σ, where σ s he esmaon error resuled rom he queue lengh esmaon mehod a he begnnng o he h RTT. Hence (37) becomes, () W ou D mn T n (38) Rearrange he erms we have, 566

6 24 IEEE h Inernaonal Conerence on Wreless and Moble Compung, eworkng and Communcaons (WMob) ou D mn T () W n (39) Le σ max dene he maxmum esmaon error resuled rom he queue lengh esmaon mehod and hus σ σ max or all. Subsue σ wh σ max we have he mnmum o (), mn(()) as ollows, () mn W n ou Dmn T max (4) Accordng o he above sysem model we can derve several neresng properes n he ollowng secons. C. Guaraneeng Full Bandwdh Ulzaon The sucen condon o ull bandwdh ulzaon s mn(()) or all, hus we have he ollowng heorem: THEOREM : One possble sucen condon o sasy mn(()) or all s W CmaxDmax (4) and T max n / (42) Proo: Obvously, subsue (4) and (42) no (4) we have () mn CmaxDmax ou D (43) mn As ou D + D mn mncmax maxcmax, we have () or all. oe ha he mnmum requred arge queue lengh s acheved when he equaly n (42) s sased. D. Targe ueue Lengh As shown n (42), TCP-LA needs o ncorporae σ max o se T o have he ull bandwdh ulzaon. In [] we proved ha SoD-TS s esmaon error s only bounded by [, ] packe, hus σ max, sod-s =. Smlarly, we also showed ha σ max, sod s bounded by, max / mn packes and σ max, as max / mn snce σ max, as mgh conan he esmaon error due o bandwdh varaons besdes he one due o uplnk delay varaons. I s obvous ha σ max, as >σ max, sod >σ max, sod-s, hus we have he ollowng heorem: THEOREM 2: Le T, qla, T, sod and T, as denoe he mnmum requred arge queue lengh o TCP-LA, TCP-SoD and FAST TCP o ully ulze he bandwdh under all nework condons, hus we have T, qla < T, sod < T, as. Proo: As he hree TCP varans updaes CWnd every RTT, we have derved rom (39) a r and =n +, where n + s he accurae esmaon o a he sender aer a eedback delay. Subsue wh n + n (39) we have + n = W ou D mn T (44) Smlarly, Subsue - wh n we have - = n W ou D mn T (45) Le (44) subrac (45) we have n ou Dmn ou Dmn T (46) Snce n + =, we have n + he proocol ully ulzes he bandwdh, hus we have T + ou + D mn ou D mn (47) Snce TCP-LA, TCP-SoD and FAST TCP experences he same nework condons, he las our erms o R.H.S. o (47) are he same or all he proocols. Hence T s only aeced by he esmaon error σ k and ncreasng wh σ k. As σ max, as >σ max, sod >σ max, sod-s, we have T, qla < T, sod < T, as. oe ha TCP-SoD s anoher verson o TCP-LA ha uses SoD mehod o esmae he queue lengh nsead o SoD-TS. Addonally, o model FAST TCP usng he same sysem model we assume FAST TCP adops a large nal CWnd accordng o (4) hus FAST TCP skps TCP slow sar phase and eners TCP congeson avodance phase drecly over whch FAST algorhm s appled. E. ueueng Delay I s a ac ha under he same bandwdh varaons he esmaon error σ ncreases wh he ncrease n uplnk delay varaon λ. Subsue T, qla, T, sod and T, as no (39) and le () qla, () as and () sod denoe he queue lengh o TCP-LA, TCP-SoD and FAST TCP a me, we ound ha () sod and () as decreases wh he ncrease n uplnk delay varaons, whle () qla s no aeced by he uplnk delay varaons, hence we have he ollowng heorem, THEOREM 3: under he same bandwdh varaons () qla, () as and () sod sasy he ollowng relaon: () qla () sod () as, and he equaly s acheved when operang under he maxmum uplnk delay varaons. Proo: Accordng o Theorem 2, he mnmum T or a proocol o sasy he ull bandwdh ulzaon or all s le T = max +max ou + D mn ou D mn (48) Subsue T n (46) wh (48) we have n ou Dmn ou Dmn max ou D mn ou D mn max When σ =σ max, we have n ou Dmn ou Dmn max ou D mn ou D mn Whch mples ha he queueng lengh s he same or every proocol he esmaon error reaches he maxma, e.g., σ =σ max. Snce he σ s ncreasng wh he uplnk delay varaon, we have () as =() sod =() qla when operang under he maxmum uplnk delay varaons. In he oher cases, e.g., σ <σ max we have () as >() sod >() qla as σ max, as >σ max, sod >σ max, sod-s. 567

7 24 IEEE h Inernaonal Conerence on Wreless and Moble Compung, eworkng and Communcaons (WMob) recevng hroughpu (Mbps) 6 5 cp-qla = cp-sod =7 as cp =8.3 cp-qla =2 cp vegas =8.29 cp-sod =6 as cp =6 cp vegas =4 cp vegas = RTT (s) cp-sod =3 as cp =3 cp-qla =5.26 as cp =4 cp-sod =5 cp vegas =5 as cp = Fg. 2 Throughpu and RTT perormance o ve congeson conrol algorhms versus deren arge queue lengh. recevng hroughpu (Mbps) LA-3 hroughpu FAST-8 hroughpu Vegas-8 hroughpu Cubc hroughpu SoD-7 hroughpu LA-3 RTT FAST-8 RTT Vegas-8 RTT Cubc RTT SoD-7 RTT uplnk delay varaons (ms) Fg. 3 Throughpu and RTT perormance o ve congeson conrol algorhms versus deren levels o uplnk delay varaons (zero random loss). recevng hroughpu (Mbps) SoD-7 RTT Fas-8 hroughpu LA-3 RTT Cubc RTT LA-3 hroughpu SoD-7 hroughpu Fas-8 RTT.5.2 Vegas-8 RTT Cubc hroughpu Vegas-8 hroughpu uplnk delay varaon (ms) Fg. 4 Throughpu and RTT perormance o ve congeson conrol algorhms versus deren levels o uplnk delay varaons (.5% random loss). Theorem 3 shows ha TCP-LA always resuls n he lowes queueng delay under varous nework condons, whle sll ully ulze he bandwdh, whch s benecal or some applcaons requrng boh hgh hroughpu and low end-o-end delay such as vdeo conerence RTT (s) RTT (s) V. PERFORMAE EVALUATIOS In hs secon we evaluae he perormance o he proposed TCP-LA, and compare o oher TCP varans usng race-drven smulaons usng S2 [5] n he conex o modern 3G/HSPA nework. We mplemened he TCP-LA algorhm descrbed n Secon III n he S2 smulaor. We se up he nework opology n Fg. wh a lnk buer sze o 852 packes and a base propagaon delay o 6ms measured rom a producon o 3G/HSPA nework. To capure he acual bandwdh varaons n producon 3G/HSPA neworks, we measured he raw bandwdh o producon moble neworks usng UDP by sendng UDP daagrams rom a wred server o a 3G-conneced recever a a rae hgher han he moble lnk capacy. The receved daa rae race a he recever sde hus capures he acual bandwdh avalable over he rado lnk. These bandwdh races are hen ed no he smulaor o replcae he bandwdh varaons n he smulaed rado downlnk. For he uplnk we nroduce random delay varaons whch are unorm-dsrbued wh sandard devaon rangng rom o ms, approxmang he uplndk delay varaons observed n producon neworks. Each se o smulaon lased seconds and he resuls are averaged over runs wh deren bandwdh races. Frsly, we valdae he heorems derved rom he sysem model n Secon IV. Speccally, we plo he recevng hroughpu and RTT resuls o TCP varans usng deren T. To derve he mnmum requred T o every TCP varans or curren producon o 3G/HSPA nework, we eed he same bandwdh races no he smulaor or all cases. The average bandwdh o he races s 4.76Mbps. Addonally, we se he sandard devaon o uplnk delay varaons o he maxma, e.g., ms. As shown n Fg. 2, TCP-LA can acheve near % bandwdh ulzaon (e.g., 4.63/4.76=97.3%) wh T =3 packes, whle TCP-SoD and FAST TCP requres T =7 and 8 packes o acheve he smlar bandwdh ulzaon respecvely as hey have he larger queue lengh esmaon errors. Ths valdaes he Theorem 2 n Secon III, hus T, qla =3,, T, sod =7 and T, as =8. Generally, TCP-LA requres a smaller T han TCP-SoD and FAST TCP o acheve he smlar bandwdh ulzaon, e.g., TCP-LA acheves 7.2% wh T =5 packes, whle TCP-SoD and FAST TCP requre T =3 and 4 packes o acheve respecvely. On he oher hand, TCP-LA, TCP-SoD and FAST TCP resul n he smlar end-o-end delays, e.g., 3ms, usng T, qla,, T, sod and T, as respecvely, whch s shown by Theorem 3 ha hey wll resul n he same () under he maxmum uplnk delay varaons. We second compare he long-erm hroughpu and he RTT o ve TCP varans: (a) TCP-LA wh T =3 (TCP-LA-3); (b) TCP-SoD wh T =7 (TCP-SoD-7); (c) FAST TCP wh T =8 (FAST-TCP-7); (d) TCP Vegas wh T =8 (TCP-Vegas-8); and (e) TCP CUBIC. oe ha TCP varans n (a)-(d) adop he mnmum arge queue lengh derved rom Fg. 2. We vary he degree o uplnk delay varaons wh sandard devaon rangng rom o ms. As shown n Fg. 3, TCP-LA-3, TCP-SoD-7, FAST-TCP-8 568

8 24 IEEE h Inernaonal Conerence on Wreless and Moble Compung, eworkng and Communcaons (WMob) and TCP CUBIC all acheve near-% bandwdh ulzaon (e.g., over 4.63/4.76=97.2%) or all levels o uplnk delay varaons. However, TCP CUBIC resuls n he larges RTT close o.s. Ths s because TCP CUBIC keeps ncreasng he number o nlgh packes unl congeson loss s deeced, hus buldng up a large backlog n he lnk buer. Compared o TCP CUBIC, FAST-TCP-8, TCP-SoD-7 and TCP-LA-3 reduce he RTT a leas by a acor o 2.2 (.33s versus.6s) as hey all lm he queue lengh n he lnk buer. Among hese, TCP-LA-3 resuls n he smalles RTT or all levels o uplnk delay varaons as shown n Theorem 3, reducng RTT a mos by 5% compared o FAST-TCP-8 and TCP-SoD-7. TCP-Vegas-8 canno ecenly ulze he bandwdh snce ncreases/decrease CWnd by one every RTT, whch s shown o be conservave n ulzng he bandwdh and responsve slowly n conrollng he queue lengh. So ar he smulaons were perormed wh no random packe loss. We repeaed he smulaons wh a random packe loss rae o.5% and ploed he resuls n Fg. 4. We observe ha he hroughpu o TCP CUBIC and TCP Vegas degraded sgncanly n he presence o random packe losses. Ths s because hey boh decrease CWnd and sshresh upon loss evens, even non-congeson-nduced ones, hus unnecessarly reduced he ransmsson rae. By conras, FAST TCP does no decrease CWnd bu keep he CWnd consan durng he loss recovery hus FAST TCP has a beer hroughpu perormance han TCP CUBIC and TCP Vegas. Unlke hem, TCP LA and TCP SoD sll regulae he queue lengh around T usng (2) durng loss recovery (c.. Secon III.C) so ha CWnd s no aeced by he loss evens. As a resul hey manan smlar hroughpu and RTT perormances as he zero-random-loss cases despe he presence o random packe losses. Ths s sgncan as random packe losses are sll common n moble daa neworks. REFERECES [] M. Allman, V. Paxson, and W. Sevens, TCP Congeson Conrol, RFC 258, Aprl 999. [2] L. Brakmo and L. Peerson, TCP Vegas: End-o-end congeson avodance on a global nerne, IEEE JSAC, Ocober, 995. [3] D. X. We, C. Jn, S. H. Low, and S. Hegde, FAST TCP: movaon, archecure, algorhms, perormance, n IEEE/ACM TO, 26. [4] C. P. Fu and S. C. Lew, TCP Veno: TCP Enhancemen or Transmsson over Wreless Access eworks, n IEEE JSAC, 23. [5] Injong Rhee and Lsong Xu, CUBIC: A ew TCP-Frendly Hgh-Speed TCP Varans, PFLDne, 25 [6] E. Dahman, S. Parkvall, J. Skold, P. Bemng, 3G Evoluon: HSPA and LTE or Moble Broadband, 2nd ed., Academc Press, 28. [7] Haqng Jang, Yaogong Wang, yunghan Lee, and Injong Rhee, Tacklng buerbloa n 3G/4G neworks, n ACM IMC, 22. [8] Sanley C. F. Chan, e Lu,. M. Chan and Jack Y. B. Lee, On ueue Lengh and Lnk Buer Sze Esmaon n 3G/4G Moble Daa eworks, n IEEE TMC, 23. [9] Yn Xu, Wa ay Leong, Ben Leong and Al Razeen. "Dynamc Regulaon o Moble 3G/HSPA Uplnk Buer wh Recever-Sde Flow Conrol". n IEEE ICP, 22. [] e Lu and Jack Y. B. Lee, "Uplnk Delay Varaon Compensaon n ueue Lengh Esmaon over Moble Daa eworks", Acceped n ICCC, 24. [] V. Jacobson, R. Braden, and D. Borman, TCP exensons or hgh perormance, RFC 323, May 992. [2] R. Chakravory, S. a, I. Pra and J. Crowcro, Usng TCP Flow-Aggregaon o Enhance Daa Experence o Cellular Wreless Users, IEEE JSAC, Vol. 23, o. 6, June 25. [3] L. Bodrog, G. Horvah, and C. Vulkan, Analycal TCP hroughpu model or hgh-speed downlnk packe access, Soware, IET, 29. [4] S. Floyd, J. Mahdav, M. Mahs, and M. Podolsky, An exenson o he selecve acknowledgemen (SAC) opon or TCP, RFC 2883, 2.. [5] S2, ework Smulaor, hp:// VI. SUMMARY AD FUTURE WOR Ths work oers a novel queue-lengh-aware TCP (TCP-LA) ha regulaes he queue lengh a he boleneck lnk o a arge queue lengh by makng use o SoD-TS mehod. By analyss and smulaon we demonsrae ha TCP-LA resuls n he lowes end-o-end delay compared o loss-based TCP such as TCP CUBIC and delay-based TCP such as FAST TCP and TCP Vegas, whle sll acheves he near % bandwdh ulzaon. We are currenly exendng hs work n wo drecons. Frs, we are exendng he analycal model n Secon III o characerze TCP-LA and he oher delay-based TCP s overall bandwdh ecency. Second, we are mplemenng he TCP-LA algorhm no he Lnux kernel o evaluae s perormance over producons o moble daa neworks. VII. ACOWLEDGEMET Ths work was parally suppored by he Sraegc Prory Research Program o he Chnese Academy o Scences under Gran o. XDA64, by aonal aural Scence Foundaon o Chna (SFC) under Gran o , Gran o. 6338, and Gran o , and by Huawe Research Program YBCB