How To Improve Delay Throughput In Wireless Networks With Multipath Routing And Channel Codeing

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1 Delay-Throughput Enhancement n Wreless Networs wth Mult-path Routng and Channel Codng Kevan Ronas, Student Member, IEEE, Amr-Hamed Mohsenan-Rad, Member, IEEE, Vncent W.S. Wong, Senor Member, IEEE, Sathsh Gopalarshnan, Member, IEEE, and Robert Schober, Fellow, IEEE Abstract Mult-path routng and adaptve channel codng are two well-nown approaches that have been separately appled to wreless networs n order to mprove the effectve throughput. However, t s usually expected that achevng a hgh throughput would be at a notceable cost of ncreasng the average end-toend delay and causes major degradaton n the overall networ performance. In ths paper, we show that a combnaton of mult-path routng and adaptve channel codng can mprove throughput and reduce delay, and that t s possble to trade off delay for throughput and vce versa. Ths s n contrast to the general expectaton that hgher throughput can only be acheved wth notceable degradatons n the end-to-end networ delay. In ths regard, we jontly formulate the end-to-end data rate allocaton and adaptve channel codng at the physcal layer wthn the general framewor of networ utlty maxmzaton NUM. Dependng on the choce of the objectve functon, we formulate two NUM problems: one amng to maxmze the aggregate networ utlty; another one amng to maxmze the mnmum utlty among the end-to-end flows n order to acheve farness, whch s of nterest n certan vehcular networ applcatons. Smulaton results confrm that we can decrease the average delay sgnfcantly at the cost of a small decrease n throughput. Ths s acheved by maxmzng the aggregate utlty n the networ when farness s not the domnant concern. Furthermore, we also show that even when resource allocaton s performed n order to provde farness, we can stll decrease the maxmum end-to-end delay of the networ at the cost of a slght decrease n the mnmum throughput. Keywords: Ln relablty, mult-path routng, adaptve channel codng, delay-throughput trade-off, utlty maxmzaton, farness, non-convex optmzaton, sgnomal programmng. I. INTRODUCTION Whle most of the new multmeda applcatons have strct qualty-of-servce QoS requrements [], the exstng besteffort traffc delvery model cannot provde any servce guarantee wth respect to the mnmum throughput and maxmum delay of the end-to-end flows. Therefore, t s mportant to Manuscrpt was receved on May 4th 200, revsed on Oct. 25th 200, and accepted on Nov. 26th 200. Ths wor was supported by the Natural Scences and Engneerng Research Councl NSERC of Canada. The revew of ths paper was coordnated by Prof. Peter Langendoerfer. Copyrght c 200 IEEE. Personal use of ths materal s permtted. However, permsson to use ths materal for any other purposes must be obtaned from the IEEE by sendng a request to [email protected]. K. Ronas, V.W.S. Wong, S. Gopalarshnan, and R. Schober are wth the Department of Electrcal and Computer Engneerng, Unversty of Brtsh Columba, Vancouver, BC, V6T Z4, Canada, emal: {evanr, vncentw, sathsh, rschober}@ece.ubc.ca. A. H. Mohsenan-Rad s wth the Department of Electrcal and Computer Engneerng, Texas Tech Unversty, Lubboc, TX, 79409, emal: [email protected]. desgn wreless networs wth hgh performance n regard of delay and throughput. Followng the wor by Kelly et al. [2], networ utlty maxmzaton NUM has been wdely used as a framewor to systematcally devse resource allocaton strateges that can enhance the networ performance subject to varous capacty and QoS constrants [3] [6]. It s nown that mult-path routng mproves the networ performance by not only dstrbutng the traffc over dfferent lns, but also by provdng alternatve paths for those sessons whch are exposed to hgh bt error rates due to envronmental condtons [7], [8]. The mprovements lead to reducng networ congeston, ncreasng throughput, and also hgher energy effcency [9]. On the other hand, adaptve channel codng cf. [6], [0] s used n the wreless networng context to mprove the relablty of the transmssons,.e., ncreasng the number of error-free delvered pacets. Through adaptve channel codng, we provde hgher resstance to errors n data pacets by addng redundant bts. Ths n turn decreases the aggregate nformaton sendng rate on each ln and correspondngly ntroduces a trade-off between throughput and relablty. Recently, we nvestgated the trade-off between relablty and throughput n achevng the hghest possble effectve throughput, whch s the end-to-end throughput that the recever s able to receve []. We focused on mult-path routng wreless systems, where adaptve channel codng s also performed at the physcal layer. However, we dd not address the ssue of delay n our earler wor. In ths paper, we explctly ncorporate delay n the utlty of each sesson and propose a jont data rate and codng rate allocaton algorthm that leads to maxmzng the networ aggregate utlty across all sessons. Our wor complements the exstng results n the lterature as follows. The recent wor by O Nell et al. [2] used NUM wth adaptve modulaton to determne the optmal sendng rates and transmt powers that maxmze system performance. The trade-off between data rate, energy consumpton, and delay s studed. However, O Nell et al. dd not ncorporate delay nto the utlty functon n ther problem formulaton [2] and the proposed desgn nether mnmzes the delay nor provdes a bound on end-to-end delay. On the other hand, Saad et al. [3] used the M/G/ queueng model to estmate the delay as the summaton of transmsson delay and queueng delay. The same authors examned upper bounds on delay [4] but dd not focus on

2 delay reducton. In wor by Kalltss et al. [5], resources are allocated to maxmze the throughput of the networ and mnmze the delay. Delay s modeled usng networ calculus and s ncorporated drectly nto the utlty functon. Another research drecton focuses on resource allocaton to enhance the networ performance by only mnmzng the delay e.g., L et al. [6] and Kalyanasundaram et al. [7]. However, the mpact of adaptve channel codng has not been consdered n ths context. On the other hand, channel codng s consdered n [6]; but no analyss s performed related to delay. Fnally, our problem s closely related to the recent wor by L et al. [8], whch only addresses sngle-path routng wthn the context of wred networs or wreless networs wth fxed capacty lns. The contrbutons of ths paper can be summarzed as follows: We model a wreless networ wth several uncast data sessons, multple routng paths for each sesson, and adaptve channel codng at the physcal layer. To model the end-to-end delay, we use the average watng tme n an M/D/ queueng system [9]. We then formulate the NUM problem of jontly fndng optmal sendng rates and code rates n the networ to acheve the maxmum networ utlty as a functon of throughput and delay. We formulate two desgn optmzaton problems wth and wthout farness provsonng. In the former one, we am to maxmze the mnmum utlty n the networ. In the latter case, we maxmze the overall utlty of the networ. Far resource allocaton s of partcular nterest n vehcular networs n whch movng vehcles frequently swtch among statonary access ponts. To overcome the non-convexty due to channel codng, mult-path routng, delay and relablty consderaton, we ntroduce new varables, constrants, and approxmatons n the orgnal problem and reformulate t as a seres of tractable geometrc programmng problems [20]. We develop an teratve algorthm to solve the formulated problem. To the best of our nowledge, there has been no pror wor on jontly mprovng throughput and delay n a wreless mult-path routng networ wth channel codng appled at the physcal layer. Smulaton results for random topologes show that, when farness s not a concern, we can decrease the average delay by 60% at the cost of only a margnal < 0.% degradaton n throughput. We also show that f farness s addressed, we can decrease the maxmum delay across the networ by more than 35% wth less than 2% decrease n mnmum throughput. Paper Organzaton: The system model and problem formulaton are descrbed n Secton II. The delay-aware optmal data rate and codng rate allocaton approach s ntroduced n Secton III. The numercal results are shown n Secton IV. The paper s concluded n Secton V. II. SYSTEM MODEL A wreless networ s modeled as a drected graph GV, E, where V represents the set of nodes and E represents the set of wreless lns, as t s shown n Fg.. For each uncast sesson Fg.. A sample topology wth fve uncast mult-path data sessons. Data sessons are 2 5,7 8,9 20,2 23, and These sessons have 6,, 2, 2, and 4 avalable paths, respectvely. I, where I = {,2,...,I}, the source and destnaton nodes are denoted by s and t, respectvely. We defne K, wth K = K, as the set of all avalable routng paths from s to t. Moreover, for each sesson I, each =,...,K, and each ln e E, we defne {, f ln e th routng path for sesson, = 0, otherwse. For each sesson I, let α denote the data rate at source s on ts th routng path, =,...,K. Channel codng can mprove the relablty over lossy wreless channels by addng redundant bts to data pacets. For each ln e E, we defne R e as the ln codng rate,.e., the rato of the number of data bts at the nput of the encoder to the number of data plus redundant bts at the output. Notce that f channel codng s not performed on ln e, then R e =. Gven the data rates at the sources α = α, I, =,...,K and the ln codng rates R = R e, e E, the aggregate traffc load on K R e I a α each ln e E s u e =. The smaller the codng rate R e, the more redundant data s added to the transmtted pacets on ln e E leadng to more relable transmssons,.e., transmssons wth lower error probablty. However, ths wll be at the cost of exposng the ln to hgher traffc. Let R 0 = R 0e, e E, where R 0e s the cut-off rate on wreless ln e E, that s an upper bound for the rate R e achevable wth certan codes e.g., convolutonal codes [2]. In general, the cut-off rate R 0e depends on the receved sgnal-to-nose-rato SNR and the modulaton scheme beng used. Gven codng rate R e R 0e, the error probablty on ln e can be modeled as [2] P e = 2 TR0e Re, 2 where T s the codng bloc length. Based on the ln falure model n 2, the probablty that a pacet s successfully transmtted along the th routng path, =,...,K for sesson I s gven by e E, = P e = e E a P e. From the above equaton, for each sesson I, the aggregate effectve throughput at destnaton t becomes K α e E a P e. 3 To obtan the average end-to-end delay, we model each

3 ln as a sngle M/D/ queue based on the Klenroc ndependence approxmaton [9]. Here, we assume that the arrval rates n the source nodes follow a Posson dstrbuton. Snce the transmsson tmes over all lns are determnstc, the number of arrvals for each queue n any tme nterval can be assumed to follow a Posson dstrbuton wth rate λ e = I α /L, 4 where L s the pacet length. From Lttle s Theorem [9], the average watng tme for each queue e correspondng to ln e E s gven by δe Q L = I 2c e R e c e R e I K = a α K = a α, 5 where c e denotes the nomnal data rate of ln e E. By addng the watng tme and the transmsson tme δe T = L c er e together, we have δ e = δe Q +δe T for each ln e E. Then, the average end-to-end delay for each path =,...,K of sesson I can be wrtten as δ = L K 2+ I = a α 2 c e R e e E c e R e K. I = a α 6 To model the mutual nterference among the wreless lns n the networ, we use the concept of contenton graph. In the contenton graph G C V C,E C correspondng to networ GV,E, the set of vertcesv C represents the set of all wreless lns E n the networ graph G. An edge connects any two vertces n set V C f the correspondng wreless lns n the networ graph mutually nterfere wth each other. That s, f the recever node of one ln s wthn the nterference range of the sender node of the other ln. Gven the contenton graph, each complete subgraph s called a clque. A maxmal clque s a clque whch s not a subgraph of any other clque [22]. We denote the set of all maxmal clques n G C by Q. In each nstant, only one ln among all members of a maxmal clque Q Q can be actve. The rato ue c e denotes the porton of tme that ln e E s actve when t s beng used wth data rate u e. It s requred that u e e Q c e ν for each clque Q Q where ν 0,] s called the clque capacty. Note that ν = s a necessary constrant on the clque capacty. It may not always be possble to fnd feasble schedules that acheve a clque capacty of ν =. Shannon showed that ν = 2 3 s a suffcent condton on the clque capacty n order to obtan a feasble schedule for the lns n the clque [23]. We formulate the problem of jontly allocatng codng rates and sendng data rates such that the utlty of the networ be maxmzed. The utlty of each sesson I s defned as U α,r = w α e E K a P e w 7 where δ s as n 6. Here, the utlty of sesson s a weghted trade-off between the sesson s aggregate effectve throughput and ts average delay. It s a trade-off because t can δ, be ncreased by ether ncreasng the throughput or decreasng the delay. We can tune the mportance of delay by changng ts weght, w. By ncreasng w, we move on the trade-off curve towards decreasng delay at the cost of decreasng the throughput. We defne the utlty of the networ as ether the summaton of all utltes of data sessons I, or just the one wth the mnmum value. Maxmzng the Aggregate Utlty of the Networ: Ths problem s formulated as maxmze α 0, 0 R R 0 subject to w I w I e Q I α e E δ a P e α R e c e ν, Q Q, δ δmax, I, =,...,K, 8 where δ max s the maxmum delay that can be tolerated for each path of sesson I. The set of constrants declare that the porton of tme that all lns n a maxmal clque are actve must be less than the clque capacty. The expressons for P e and δ are as n 2 and 6, respectvely. 2 Maxmzng the Mnmum Utlty of the Networ: Ths problem s formulated as K maxmze mn w α 0, 0 R R 0 I subject to e Q I α e E K K a P e w δ α R e c e ν, Q Q, δ δmax, I, =,...,K. 9 Unle 8, here the desgn addresses the noton of maxmn farness among sessons. III. DELAY-AWARE OPTIMAL DATA RATE AND CODING RATE ALLOCATION The optmzaton problem n 8 s non-convex and nonseparable due to the product forms n the objectve functon wth respect to the effectve throughput, the fractonal forms n the frst set of constrants and n the delay constrants n 6, the exponental forms n the objectve functon wth respect to error probabltes, the non-separablty of relablty and throughput due to mult-path routng, and the couplng across varables because of delay constrants and channel codng. Most of the above propertes are due to the fact that we consder mult-path routng and wreless nterference. For example, f we assume there s no nterference, whch s true for wred networs, the clque capacty constrants would reduce to lnear ln capacty constrants for any ln e E: R e c e I α, I α R ec e 0. 0 We can also show that the non-convexty due to the product forms n the objectve functon can be resolved f there s

4 only a sngle routng path for each sesson [6]. However, all sources of complexty reman n place when mult-path routng s used and wreless transmssons are subject to nterference. In the followng, we use varous technques to overcome the complexty of the problem formulaton and convert problem 8 nto a convex problem. Consder the exponental form of P e n 2. For notatonal smplcty, we can rewrte 2 as P e = X e expz R e for each ln e E, where X e = 2 TR0e and Z = T ln2. We can use Taylor seres expanson and rewrte the above equaton as Z R P e = X e n e n=0 n!. Clearly, for some bounded nteger Z R e n n=0 Ne N e, we can approxmate P e as X e n! for each ln e E. We nvestgate the value of N e necessary for obtanng a good approxmaton through smulaton. If the error probabltes P e are small, we can rewrte the recevng rates n each sesson as α e E K a P e α e E P e. Due to the polynomal forms n the objectve functon and the constrants, we can solve problem 8 by usng geometrc programmng technques. In ths respect, usng the approxmated value for P e, we replace n the objectve functon of problem 8 and ntroduce varable t such that t s a lowerbound for the objectve functon. That s, N e α a X e ZR e n +w n! I δ t+ w Ie En=0 w α. I 2 Then, we follow the sgnomal programmng technques [20] to approxmate the polynomal n the rght-hand sde of 2, whch s only a functon of α, as a monomal,.e., a polynomal wth only one term and postve multpler. Ths approxmaton can be done around some ntal pont ˆα. For a parameter f s >, whch s close to, we have Iα ˆα I K α I ˆα K ˆα / I = ˆα, α [ˆα/f s,f sˆα], 3 where[ˆα/f s,f sˆα] s a small neghborhood around ntal pont ˆα. For notatonal convenence, we defne ˆΛ, whch only de- pends on the ntal pont ˆα, as ˆΛ K = I ˆα. Then, nequalty 2 can be approxmated around the ntal pont ˆα as ˆΛ w t+ w N e α a X e Z R e n n! I e E n=0 +w K α δ ˆα ˆΛ 4 ˆα. I I The above constrant s a posynomal,.e., a polynomal wth only postve terms. Posynomals are the buldng blocs n geometrc programmng [20]. By mnmzng t, we maxmze the objectve functon n 8. To tacle the fractonal forms n the delay constrants, we can wrte 6 n an nequalty form δ L K 2 c e R e 2+ I = a α e E c e R e K, α I = I, =,...,K. 5 It can be shown that 5 s always satsfed wth equalty for the optmal soluton. Ths can be proved by contradcton. Assume that 5 s not satsfed wth equalty n the optmal soluton for some and. Note that δ s not lower bounded n any other set of constrants. Therefore, we can decrease δ such that the correspondng constrant s satsfed wth equalty. Ths leads to further ncreasng the value of the objectve functon by choosng a soluton dfferent than the optmal soluton whch s a contradcton. That s, t s an actve nequalty constrant. For each ln e E, we ntroduce new varables Y e such that Y e c e + I K = α R e, e E. 6 c e We can show that 5 s satsfed f 6 holds and we have δ L 2 + Y K e I = a α 2 c e R e c e R 2, e E e I, =,...,K. 7 Smlarly, we can show that 6 and 7 are always satsfed wth equalty for the optmal soluton. By ntroducng t as n 4 and addng constrants 6, and 7 to the constrants of problem 8, t s equvalent to the problem 8 n whch the objectve s to mnmze t whch s equal to maxmzng t where t s declared to be a lower bound for the networ utlty functon n the frst set of constrants. The second set of constrants declare the capacty constrants and the thrd and fourth set are actve constrants 7 and 6, respectvely. The last set of constrants guarantees all end-to-end delays to be bounded: mnmze t>0,ˆα/f s α f s ˆα, 0 R R 0,δ 0,Y 0 subject to ν ˆΛ w N e t+ w I e E n=0 +w K α δ ˆα I e Q I I t α a X e ZR e n n! ˆα ˆΛ, α R e c e, Q Q,

5 L 2 e E Y e c e 2R e +R 2 e Y e K R K α I = δ, I, =,...,K, + e c α, e E, e I = δ δmax, I, =,...,K. 8 Problem 8 s a standard geometrc programmng problem that can be converted nto a convex optmzaton problem [20] and can be solved around an ntal pont. It has been shown that teratvely solvng 8 converges to the optmal soluton of problem 8 [20]. In each teraton, 8 s ntalzed wth the optmal soluton of the problem correspondng to the last teraton. As dscussed, we may move on the throughput-delay trade-off curve by tunng the delay mportance weght w. w must be chosen such that the objectve functon n problem 8 remans postve. Smlarly, we can convert problem 9 nto a convex optmzaton problem. Compared to solvng problem 8, there are two dfferences. Frst, varable t s ntroduced such that t w N e X e n=0 Z R e n w δ n!, α e E I. 9 As n the earler case, we use sgnomal technques to convert 9 nto a constrant n the standard form of geometrc programmng problems. By applyng a smlar technque n 3 ths tme to K α, we can rewrte 9 as N e ˆΛ α w t+ w a X e Z R e n +w n! K α ˆα e En=0 ˆα ˆΛ, I, 20 where ˆΛ = K ˆα. Second, nequaltes 6 and 7 may not be actve anymore and so nequalty 5 may not be satsfed wth equalty. In ths case, we are n fact dealng wth the upper bounds of the average end-to-end delay n the objectve functon. In ths way, the performance of the networ s better than what we would expect from the obtaned soluton n terms of average delay snce the upper bounds on the average delay are used n the objectve functon. The rest of the formulaton s the same as the one n 8. Agan, w must be chosen such that the objectve functon n problem 9 remans postve. IV. NUMERICAL RESULTS In ths secton, we numercally solve problem 8 to determne the optmal sendng and codng rates such that the utlty of the networ.e., the trade-off between the aggregate effectve throughput and the average delay s maxmzed. We show that maxmzng the aggregate networ utlty leads to hgher benefts n the throughput-delay trade-off.e., we obtan lower delays at the cost of lower decrease n throughput, δ Normalzed Average Delay of the Networ w = 0 w = Delay Importance Weght w Fg. 2. The average delay decreases as ts mportance weght n the objectve functon ncreases. Delay values are normalzed over the correspondng values for whch w = 0. We observe a decrease of almost 58% when w = 0.5. compared to the case of maxmzng the mnmum utlty n the networ. In the former case, no farness s acheved and some sessons may be starved. Therefore, we also solve problem 9 to determne the sendng rates and codng rates such that the mnmum utlty of the networ s maxmzed. We show that at the cost of loosng some gan n the throughput-delay trade-off we can provde farness among all sessons. In our set of smulatons, we use T = 0, L = 8000 bts, c e = Mbps, N e = 5, f s =., R 0e =, and ν = 2 3 [23]. The proper values for parameters N e and f s are obtaned from smulatons. We solve problem 8 for dfferent values of w n a feasble range across 50 dfferent random topologes. Each random topology s a 5 5 grd topology for whch 20 nodes are placed n random locatons. Fve pars of nodes are randomly selected as the source and destnaton pars. We observe that by consderng the delay n the objectve functon, even wth a small weght, we can decrease the average delay by 37% compared to the case wth no delay consderaton Fg. 2. We also note that by further ncreasng the mportance weght of delay n the objectve functon the average delay decreases by 58%. The more a ln s utlzed, the hgher wll be the queung delays for that ln. Therefore, decreasng the average delay leads to the use of the ntermedate lns at a lower rate that n turn leads to a slght decrease 0.% n aggregate throughput. Ths confrms the delay-throughput trade-off. We can also see that by decreasng the throughput by a small amount, the delay decreases dramatcally at the startng pont. Ths s because delay s an exponental functon of the utlzaton rate. Maxmzng the total throughput usually requres sacrfcng farness among sessons. That s, some sessons may starve whle some other sessons use the networ wth a hgher throughput. For nstance after solvng problem 8 for a sample topology, we observe that sessons and 3 use the networ at a rate of 2 Mbps whle sessons 2 and 5 starve and sesson 4 sends data at a rate of 4.5 Mbps. To provde farness among sessons, we solve problem 9 to maxmze the mnmum utlty across sessons for dfferent feasble choces of parameter w and for 50 randomly selected topologes. Maxmzng the

6 Normalzed Maxmum Delay n the Networ w = 0 w = Delay Importance Weght w Farness Index ψ Maxmn Farness Aggregate Utlty Maxmzaton Delay Importance Weght w Fg. 3. The normalzed maxmum delay among the users n the networ decreases as the correspondng mportance weght n the objectve functon ncreases. Delay values are normalzed over the values correspondng to w = 0. We observe almost 37% decrease n the maxmum delay n the networ when w reaches 0.5. Normalzed Mnmum Throughput n the Networ w = 0.27 w = 0.5 w = Normalzed Maxmum Delay n the Networ w = 0 Fg. 4. The trade-off between the maxmum delay and the mnmum throughput n the networ. We may move on the curve by tunng w, the delay mportance weght. Delay and throughput are normalzed over ther correspondng values at w = 0. mnmum utlty of the networ, we expect that there wll be no sesson wth starvaton. We can see that the normalzed maxmum end-to-end delay n the networ among all routng paths decreases by almost 5% on average when we consder the delay only by a very small weght Fg. 3. We can further decrease the delay by 37% when w ncreases. Agan, there exsts a trade-off between the maxmum end-to-end delay of the networ and the aggregate throughput of the sesson wth the mnmum aggregate throughput n Fg. 4. By tracng the graph startng from the upper rght corner w = 0 to the lower-left corner w = 0.5, we gan a 37% mprovement n the maxmum delay at a cost of a slght decrease at only % n the mnmum throughput when we are n proper ponts of the curve. We use Jan s farness ndex to quanttatvely measure the farness of the throughput attaned among dfferent uncast sessons. Let Ψ denote Jan s farness ndex. We have Ψ = Fg. 5. Farness ndex s shown for both problem 8 aggregate utlty maxmzaton and problem 9 maxmn farness. Maxmum Delay n the Networ ms Delay Importance Weght w Wthout delay guarantee Maxmum delay of 20 ms Maxmum delay of 0 ms Fg. 6. Average maxmum delay s shown when there s no guarantee on the maxmum delay, there s a guarantee of 0 ms, and 20 ms. Snce the guarantee s mposed on the upper bound of the delay, the delay may not reach the guaranteed value. I x2 I I x2 where x denotes the total effectve throughput of flow I from 3. We can see n Fg. 5 that farness s mproved when the resource allocaton s based on the soluton of problem 9. By now, we consdered the normalzed values of delay over ther value when w = 0 delay s not consdered. It s nterestng to see how the average maxmum delays n the networ change under dfferent delay guarantees. We solve problem 9 wthout consderng the last set of constrants delay guarantee constrants, and also when δ max s 0 ms and 20 ms for all I Fg. 6. We can see that the delay s guaranteed to be less than δ max. As mentoned earler, the decrease n delay s ganed at the cost of decreasng the utlty of the lns whch n turn leads to a decrease n the overall throughput. Ths throughput degradaton can be compensated for by usng channel codng. To determne the effect of channel codng, we consder the throughput-delay trade-off n a networ n whch channel codng s not performed and we study how ths can affect the networ performance. We assume a pacet error rate of 30%

7 at each ln and solve problem 9 wthout channel codng to show how t affects the performance. By ncreasng the weght of delay, we can only decrease the maxmum delay by around 3% at the cost of 22% decrease n mnmum throughput n Table I. w vares n ts feasble range. Ths shows how performance degrades when channel codng s not used and reveals the mportance of channel codng. TABLE I THE TRADE-OFF BETWEEN THE MAXIMUM DELAY AND THE MINIMUM THROUGHPUT IN THE NETWORK WHEN CHANNEL CODING IS NOT BEING USED. w Normalzed Maxmum Normalzed Mnmum Delay Throughput V. CONCLUSION In ths paper, we consdered the trade-off between decreasng the end-to-end delay and ncreasng the aggregate throughput n wreless networs wth channel codng and showed that a notceable enhancement across both desgn goals s feasble f a combnaton of mult-path routng and adaptve channel codng are employed. We jontly formulated the end-to-end data rate allocaton and adaptve channel codng wthn the general framewor of networ utlty maxmzaton NUM under two varatons. The frst problem s formulated for maxmzaton of the aggregate networ utlty,.e., the overall system performance. The second problem s formulated for maxmzaton of the mnmum utlty among the end-toend flows to acheve farness. Due to non-convextes such as n product terms and fractonal terms n the objectve functon and the constrants, the formulated optmzaton problems are non-convex and non-separable, and dffcult to solve. Nevertheless, we ntroduced an algorthm that can solve the two NUM problems wth low computatonal complexty. Through our smulaton studes, we note that, n many cases, sgnfcant mprovement n end-to-end delay can be obtaned wth margnal decrease n aggregate throughput, suggestng that satsfyng strngent delay requrements can be acheved f mult-path routng and adaptve channel codng are employed. The far resource allocaton aspect of our proposed desgn s of nterest n vehcular networs where multple vehcles share an access pont n order to obtan connectvty to the Internet. The centralzed soluton that we have proposed n ths paper can partcularly be used n the case when the statonary access pont provdes connectvty for all vehcles that t serves. It can also serve as a benchmar for dstrbuted algorthms whch are to be developed n future. Nevertheless, a dstrbuted algorthm can support much broader ranges of applcaton types. For future wor, we plan to study the possblty of fndng the data and channel code rates n a dstrbuted manner usng Lyapunov stablty theory, smlar to the bacpressure algorthms [24]. REFERENCES [] D. Ren, Y. T. H. L, and S. H. G. Chan, Fast-mesh: A low-delay hgh-bandwdth mesh for peer-to-peer lve streamng, IEEE Trans. on Multmeda, vol., no. 8, pp , Dec [2] F. P. Kelly, A. Maulloo, and D. 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8 Kevan Ronas S 05 was born n Isfahan, Iran n 98. He receved the B.Sc. degree n electrcal and computer engneerng from Isfahan Unversty of Technology, Isfahan, Iran n He receved the M.Sc. degree from the Unversty of Tehran, Tehran, Iran n Currently, he s a Ph.D. canddate at the Unversty of Brtsh Columba, Vancouver, Canada. Hs research nterests nclude modelng and desgn of relable wreless communcaton networs, networ codng, and stochastc networ optmzaton. Amr-Hamed Mohsenan-Rad S 04, M 09 receved masters degree n Electrcal Engneerng from Sharf Unversty of Technology n 2004 and Ph.D. degree n Electrcal and Computer Engneerng from The Unversty of Brtsh Columba UBC n Currently, he s an Assstant Professor n the Department of Electrcal and Computer Engneerng at Texas Tech Unversty. Dr. Mohsenan-Rad s the recpent of the UBC Graduate Fellowshp, Pacfc Century Graduate Scholarshp, and the Natural Scences and Engneerng Research Councl of Canada NSERC Post-doctoral Fellowshp. He s an Assocate Edtor of the Elsever Internatonal Journal of Electroncs and Communcaton and serves as a Techncal Program Commttee member n varous conferences, ncludng IEEE Globecom, ICC, VTC, and CCNC. Hs research nterests nclude the desgn, optmzaton, and game-theoretc analyss of computer and communcaton networs and smart power grds. Robert Schober S 98, M 0, SM 08, F 0 was born n Neuendettelsau, Germany, n 97. He receved the Dplom Unv. and the Ph.D. degrees n electrcal engneerng from the Unversty of Erlangen-Nuermberg n 997 and 2000, respectvely. From May 200to Aprl 2002 he was a Postdoctoral Fellow at the Unversty of Toronto, Canada, sponsored by the German Academc Exchange Servce DAAD. Snce May 2002 he has been wth the Unversty of Brtsh Columba UBC, Vancouver, Canada, where he s now a Full Professor and Canada Research Char Ter II n Wreless Communcatons. Hs research nterests fall nto the broad areas of Communcaton Theory, Wreless Communcatons, and Statstcal Sgnal Processng. Dr. Schober receved the 2002 Henz MaerLebntz Award of the German Scence Foundaton DFG, the 2004 Innovatons Award of the Vodafone Foundaton for Research n Moble Communcatons, the 2006 UBC Kllam Research Prze, the 2007 Wlhelm Fredrch Bessel Research Award of the Alexander von Humboldt Foundaton, and the 2008 Charles McDowell Award for Excellence n Research from UBC. In addton, he receved best paper awards from the German Informaton Technology Socety ITG, the European Assocaton for Sgnal, Speech and Image Processng EURASIP, IEEE ICUWB 2006, the Internatonal Zurch Semnar on Broadband Communcatons, and European Wreless Dr. Schober s also the Area Edtor for Modulaton and Sgnal Desgn for the IEEE Transactons on Communcatons. Vncent W.S. Wong SM 07 receved the B.Sc. degree from the Unversty of Mantoba, Wnnpeg, MB, Canada, n 994, the M.A.Sc. degree from the Unversty of Waterloo, Waterloo, ON, Canada, n 996, and the Ph.D. degree from the Unversty of Brtsh Columba UBC, Vancouver, BC, Canada, n From 2000 to 200, he wored as a systems engneer at PMC-Serra Inc. He joned the Department of Electrcal and Computer Engneerng at UBC n 2002 and s currently an Assocate Professor. Hs research areas nclude protocol desgn, optmzaton, and resource management of communcaton networs, wth applcatons to the Internet, wreless networs, smart grd, RFID systems, and ntellgent transportaton systems. Dr. Wong s an Assocate Edtor of the IEEE Transactons on Vehcular Technology and an Edtor of KICS/IEEE Journal of Communcatons and Networs. He s the Symposum Co-char of IEEE Globecom 0, Wreless Communcatons Symposum. He serves as TPC member n varous conferences, ncludng IEEE Infocom and ICC. Sathsh Gopalarshnan s an Assstant Professor of Electrcal and Computer Engneerng at the Unversty of Brtsh Columba. Hs research nterests center around resource allocaton problems n several contexts ncludng real-tme, embedded systems and wreless networs. Pror to jonng UBC n 2007, he obtaned a Ph.D. n Computer Scence and an M.S. n Appled Mathematcs from the Unversty of Illnos at Urbana-Champagn. He has receved awards for hs wor from the IEEE Industral Electroncs Socety Best Paper n the IEEE Transactons on Industral Informatcs n 2008 and at the IEEE Real-Tme Systems Symposum n 2004.