Network Coding-Aware Queue Management for Unicast Flows over Coded Wireless Networks

Transcription

1 Network Coding-Aware Queue Management for Unicast Flows over Coded Wireless Networks Hulya Seferoglu, Atina Markopoulou EECS Dept, University of California, Irvine {seferog, Abstract We are interested in unicast flows over wireless networks wit intersession network coding (suc as COPE [1]). TCP flows over coded wireless networks do not fully exploit network coding opportunities due to teir bursty beavior and to te fact tat TCP is agnostic to te underlying network coding. In tis paper, we take te following steps. First, we formulate congestion control for unicast flows over coded wireless networks as a network utility maximization problem and we present a distributed solution. Second, by mimicking te structure of te optimal solution, we propose a network-coding aware queue management sceme (NCAQM) at intermediate nodes. We make no canges to TCP or MAC protocols. We demonstrate, via simulation, tat TCP over NCAQM performs significantly better tan TCP over COPE. Index Terms Network coding, wireless networks, congestion control, transport protocols, queue management. I. INTRODUCTION Wireless environments lend temselves naturally to network coding, tanks to te inerent broadcast and overearing capabilities. We are particularly interested in wireless mes networks wit opportunistic network coding, wic ave been extensively studied in teory and practice [1], [2]. We consider unicast flows (particularly TCP, wic is te dominant traffic type today) transmitted on top of suc networks. In tis setting, it as been demonstrated tat network coding can significantly increase trougput [1]. However, it as also been observed [1] tat TCP does not exploit te full potential of te underlying network coding, mainly due to its bursty beavior. Rate mismatc between flows can significantly reduce te coding opportunities, as tere may not be enoug packets from different flows at an intermediate node to code togeter. One possible solution is to artificially delay packets at intermediate nodes [3], until more packets arrive and can be coded togeter. However, te trougput increases wit small delay (due to more coding opportunities) but decreases wit large delay (wic reduces te TCP rate); te optimal delay depends on te network topology and te background traffic and also may cange over time. We consider te same problem, but propose a different solution. Because te mismatc between flow rates is due to te bursty nature of TCP, te problem can be eliminated by making modifications to congestion control mecanisms (at te end-points) and/or to queue management scemes (at intermediate nodes) to make tem network coding-aware. Tis work was supported by NSF CAREER grant and by AFOSR MURI award FA First, we formulate te congestion control problem over wireless networks wit intersession network coding witin te network utility maximization (NUM) framework [4], [5]. We consider tat a constructive network coding sceme is deployed in a wireless mes network according to some predetermined rules, e.g., COPE in [1] for one-op network coding. Te optimal solution of te NUM problem decomposes into several parts, eac of wic as an intuitive interpretation, namely rate control, queue management, and sceduling. Second, motivated by te analysis, we explore modifications to congestion control mecanisms, so as to mimic te optimal solution of te NUM problem and fully exploit te potential of network coding. It turns out tat te optimal solution dictates minimal and intuitive implementation canges. We propose a network coding-aware queue management sceme at intermediate nodes (NCAQM), wic stores coded packets and drops packets based on bot congestion and network coding information. We note tat te queues, wic are already used for network coding, are a natural place to implement suc canges. In contrast, we do not modify TCP or MAC (802.11) protocols, wic enables te practical deployment of our proposal. Finally, we evaluate our proposal via simulation in GloMoSim and we sow tat TCP over te proposed sceme (NCAQM) outperforms significantly TCP over COPE (e.g., it doubles te trougput improvement in some scenarios). Te rest of te paper is organized as follows. Section II discusses related work. Section III presents te system model. Section IV presents te optimization problem and solution. Section V presents te network coding-aware protocol design. Section VI presents simulation results and Section VII concludes te paper. II. OUR WORK IN PERSPECTIVE Our work relies on COPE [1] to do te underlying network coding and provide te available coded and uncoded flows to iger layers. We ten seek to optimize te treatment of tese flows at te end-points and/or at intermediate nodes so as to maximize network coding opportunities. COPE [1] as also noticed te problem wit TCP performance due to rate mismatc, wic motivated tis study. As discussed in te introduction, [3] addressed tis problem by delaying packets to code wit oters. We propose a different solution via queue management and congestion control. In terms of analysis, our NUM formulation is witin te classic framework [5]. Several optimization problems ave

2 already been studied for networks wit network coding. In [7], minimum cost multicast over network coded wireline and wireless networks was studied. Tis work was extended for rate control in [8] for wireline networks. Te rate region of multicast flows wen network coding is used is studied in [9], [10]. Resource allocation problems ave also been considered for intersession and intrasession network coding for unicast flows. Rate control, routing, and sceduling for generationbased intrasession network coding over wireless networks is considered in [11]. Optimal sceduling and optimal routing for COPE are considered in [12] and [13], respectively. NUM is used in [14] for end-to-end pairwise intersession network coding. Energy efficient opportunistic intersession network coding over wireless is proposed in [15]. Compared to prior work, we focus on te congestion control problem for multiple unicast flows over wireless wit a given intersession network coding sceme. Te most similar formulation is probably [8] for intra-session network coding; we consider intersession network coding for multiple unicast flows. In terms of implementation, to te best of our knowledge, our work is te first to take te step from teory (optimization) to practice (protocol design), specifically for te problem of congestion control over intersession network coding. We propose implementation canges, wic ave a number of desired features: tey are justified and motivated by analysis, tey perform well (double te trougput in simulations), and tey are minimal (only queue management is affected, wile TCP and MAC remain intact). Te extended version of tis paper can be found in [20]. III. SYSTEM MODEL Sources/Flows. Let S be te set of flows between some source-destination pairs. Eac flow s S is associated wit a rate x s and a utility function U s (x s ), wic we assume to be a strictly concave function of x s. Wireless Network. A yperarc (i, J ) is a collection of links from node i N to a non-empty set of next-op nodes J N. A ypergrap H = (N, A) represents a wireless mes network, were N is te set of nodes and A is te set of yperarcs. For simplicity, = (i, J ) denotes a yperarc, (i) denotes node i and (J ) denotes node J, i.e., (i) = i and (J ) = J. We use tese representations intercangeably. We consider te protocol model of interference [16], according to wic, eac node can eiter transmit or receive at te same time and all transmissions in te range of te receiver are considered as interfering. Given a ypergrap H, we can construct te conflict grap C = (A, I), wose vertices are te yperarcs of H and edges indicate interference between yperarcs. A clique C q A consists of several yperarcs, at most one of wic can transmit simultaneously witout interference. Network Coding: We assume tat intermediate nodes use COPE [1] for one-op opportunistic network coding. Eac node i listens all transmissions in its neigborood, stores te overeard packets in its virtual buffer, and periodically advertises te content of its virtual buffer to its neigbors. Fig. 1. X topology. a transmits a flow wit rate x a to e and b transmits a flow wit rate x b to d over c. a and b transmit teir packets p 1 and p 2, in two time slots, and c receives tem. Furtermore, d overears p 1 and e overears p 2, because a d and b e are in te same transmission range and tey can overear eac oter. In te next time slot, c broadcasts te network coded packet, p 1 p 2 over yperarc (c, {d, e}). Since d and e ave overeard p 1 and p 2, tey can decode teir packets p 2 and p 1, respectively. Ten, wen a node i wants to transmit a packet, it cecks or estimates te contents of te virtual buffer of its neigbors. If tere is a network coding opportunity, te node combines te relevant packets using simple coding operations (XOR) and broadcasts te combination to J. Note tat it is possible to construct more tan one network code over a yperarc (i, J ). Let K i,j be te set of network codes over a yperarc (i, J ). Let S k S be te set of flows, wose packets are coded togeter using code k K i,j and broadcast over (i, J ). In tis paper, we primarily assume one-op network coding based on COPE [1]. However, our formulations are general enoug to also apply to butterfly structures [6], and in general to multi-op constructive coding scemes for multiple unicasts, as long as te underlying coding sceme is considered known. We present te multi-op extensions in [20]. Routing: Eac flow s S follows a single pat P s N from te source to te destination. Tis pat is pre-determined by a routing protocol, e.g., OLSR or AODV, and given as input to our problem. However, note tat several different yperarcs may connect two consecutive nodes along te pat. We define = 1 if s is transmitted troug yperarc (i, J ) using network code k K i,j ; and i,j =0, oterwise. i,j Example 1: Te example sown in Fig. 1 illustrates te problem we consider. Since c can transmit p 1 p 2 in one time slot, instead of p 1, p 2 in two time-slots, network coding as te potential to improve trougput. However, if tere is mismatc between te rates x a, x b of te two flows, c may not ave packets from te two flows to code togeter at all times, and tus does not exploit te full potential of network coding. We confirmed tis intuition troug simulations in tis example topology. Wen te buffer size was set to 10 packets at eac node and te bandwidt was 1Mbps for eac link, we observed tat 50% of te time, tere were no packets from te two flows at te same time at c to code togeter. For smaller queue sizes and larger transmission rates, tere were even fewer coding opportunities. Tis means tat tere is potential for improvement by updating te protocols so as to mitigate te rate mismatc between TCP flows. Tis is te observation tat motivates tis paper.

3 IV. OPTIMAL CONGESTION CONTROL A. Problem Formulation Our objective is to maximize te total utility function by optimizing te flow rates x s at sources s S, teir traffic splitting parameter α s,k (following te terminology of [8]) into network codes k K over yperarc at intermediate nodes, and te percentage of time τ eac yperarc is used: U s (x s ) max x,α,τ s.t. max{ k k K (J ) A αs,k x s} R τ, A α s,k k K k = 1, s S, i P s C q τ τ, C q A (1) Te first constraint is te capacity constraint. αs,k x s indicates te part of flow rate x s allocated to te k-t network code over yperarc. Te rate of te k-t network code is te maximum rate among flows s S k coded togeter in code k: max k { αs,k x s} [7]. Different network codes k K over sare te available capacity R τ, were R is te transmission capacity of ; since is a set of links, R is te minimum: R = min j (J ) {R i,j ξ i,j } were R i,j is te capacity of link (i, j), and ξ i,j is te probability of successful transmission over link (i, j). Te second constraint is te flow conservation constraint: at every node i on te pat P s of source s, te sum of α s,k over all network codes and yperarcs sould be equal to 1. Indeed, wen a flow enters a particular node i, it can be transmitted to its next op j as part of different network coded and uncoded flows. Te tird constraint is due to interference. As mentioned, τ is te percentage of time is used. Its sum over all yperarcs in a clique sould be less tan an over-provisioning factor, γ 1, because all ypearcs in a clique interfere and sould time-sare te medium. B. Solution By relaxing te capacity constraint in Eq. (1), we ave L(x, α, τ, q) = U s (x s ) A q ( max{ k k K αs,k x s} R τ ), (2) were q is te Lagrange multiplier, wic can be interpreted as te queue size at yperarc, as discussed later. To decompose te Lagrangian, we rewrite max k { αs,k x s} as max m s,k k αs,k x s s.t. k = 1, were is a new variable, wic we call te dominance indicator. It indicates weter te source s as te maximum rate among all flows coded togeter in te k-t network code, or not. In te next section, we will see tat only te dominant flow in a network code needs to back-off during congestion. Te Lagrange function in Eq. (2) is not strictly concave in and tis causes oscillation in its solution. We use te proximal metod [18] to eliminate oscillations; max ( m αs,k x s c(ms,k µs,k )2 ) k s.t. = 1, (3) k were c is a constant and µ s,k is an artificial variable of te proximal metod [18]. Its value is set to periodically. Let ( ) be te solution to tis problem. By rewriting te summation k K k as k K k, te Lagrange function in Eq. (2) can be expressed as: L(x, α, τ, q) = A q R τ + (U s (x s ) x s A k K k q αs,k (ms,k ). ) Now, we can decompose te Lagrangian into te following intuitive problems: rate control, traffic splitting, sceduling, and parameter update (queue management). Rate Control. First, we solve te Lagrangian w.r.t x s : x s = (U s) 1 A q k K k αs,k (ms,k ), (4) were (U s) 1 U s. If we define w s = k K k q(i) s = (J ) A q w s, te rate x s can be expressed as is te inverse function of te derivative of αs,k (ms,k ) and x s = (U s) 1 ( i P s qi s ), noting tat i = (i). In te special case were proportional fairness is desired, U s (x s ) = log(x s ), s S, leading to x s = ( ) 1, i P s qi s i.e., x s is inversely proportional to te total network coded queue sizes over te pat of flows s, wic we will be explained later. Traffic Splitting. Second, we solve te Lagrangian for α s,k : At eac node i along te pat (i.e., i P s ), te traffic splitting problem can be expressed as min α s.t. (J) A (J) A q k K k (ms,k ) α s,k k K k α s,k = 1, i P s (5) Similar to Eq. (3), we also use te proximal metod [18] to solve te optimization problem in Eq. (5). Sceduling. Tird, we solve te Lagrangian for τ. Tis problem is solved for every yperarc and every clique for te conflict graps in te ypergrap. max τ q R τ A s.t. C q τ τ, C q A. (6) Parameter (Queue Size) Update. We find te Lagrange multipliers (queue sizes) q, using gradient descent; q (t + 1) = {q (t) + c t [ k K k αs,k (ms,k ) x s R τ ]} +. Equivalently; q (t + 1) = {q (t) + c t [ αs,k x s} R τ ]} + max{ k k K (7)

4 were t is te iteration number, c t is a small constant, and te + operator makes te Lagrange multipliers positive. q can be interpreted as te queue size at yperarc A. Indeed, in Eq. (7), q is updated wit te difference between te incoming k K max k { αs,k x s} and outgoing R τ traffic at. Terefore, we call q te yperarc-queue, or - queue for brevity. We confirmed te convergence of q s via numerical calculations as in [20]. V. NETWORK CODING-AWARE IMPLEMENTATION In te previous section, we saw tat te NUM problem decomposed into Eqs. (4)-(7), eac of wic as an intuitive interpretation. In tis section, we mimic te properties of te optimal solution and we propose modifications to te corresponding protocols to make tem network coding-aware. It turns out tat canges limited to queue management at intermediate nodes are sufficient, wile TCP and sceduling can remain intact witout loss in performance. Tis makes our proposal well suited for practical deployment. A. Queue Management at Intermediate Nodes (NCAQM) 1) Summary of Proposed Sceme: We refer to our Network Coding-Aware Queue Management sceme as NCAQM. NCAQM builds on and extends COPE [1]. Its goal is to interact wit TCP congestion control in a way tat matces te rates of TCP flows coded togeter and tus increases network coding opportunities. It acieves its goal troug te following canges at intermediate nodes. NCAQM stores coded packets in te output queue Q i. NCAQM maintains state per yperarc queue q and per network code transmitted over eac yperarc k K ; tis is feasible in te setting of wireless mes wit limited number of flows. During congestion at a node, a packet is dropped from te flow tat as te largest number of packets, were tis number is computed only over -queues were tis flow is dominant. Essentially, NCAQM is longestflow first policy, tus balancing te flow lengts, but te lengt of eac flow is calculated so as to take into account a key feature of inter-session network coding. We note tat intermediate nodes perform already network coding operations and are a natural place to implement tese additional canges. 2) Detailed Description of Proposed Sceme: Maintaining Queues: A wireless node i maintains a single pysical output queue, Q i, wic stores all packets (coded and uncoded depending on te opportunities) passing troug it. On te oter and, motivated by te fact tat Lagrange multiplier (-queue), we maintain -queue virtually for eac yperarc, wic keeps track of packets tat are network coded and broadcast over. Te size of an -queue is Q and ow it is determined in practice will be explained later. Network Coding (Alg. 1): Motivated by te fact tat te incoming traffic in Eq. (7) is te sum of te network coded flows over, we code packets wen tey are inserted to output queues. If a network coding opportunity does not exist wen te packet arrives at node i, we just store it in Q i in a FIFO way. Periodically, Alg. 1 runs to ceck all packets in te queue for network coding. Let Q i = {p 1, p 2,..., p l } were p 1 is te Algoritm 1 Network coding in output queue Q i at node i 1: for m = 1...L do 2: if p m Q i ten 3: for n = (m + 1)...L do 4: if p m p n is eligible ten 5: p m p m p n 6: end if 7: end for 8: end if 9: Update Q i 10: end for Algoritm 2 Packet dropping at node i during congestion 1: Initialization: Φ s i = 0, s S, S i = 2: if l > L ten 3: for s S do 4: Calculate Φ s i = (J ) A Q ˇw s 5: end for 6: S i = arg max {Φ s i } 7: Coose a flow s S i randomly 8: if p n Q i, n = 1..l, from flow s ten 9: Drop p n 10: else 11: Drop p l 12: end if 13: end if first and p l is te last packet in te queue; l L, were L is te buffer size, i.e., te maximum number of packets tat can be stored in Q i. First, p 1 is picked for network coding. Since Q i stores network coded packets, p 1 may be already a coded. Independently of weter p 1 is network coded or not, it can be furter coded wit oter packets in te queue beginning from p 2, if te following two conditions are satisfied; (i) te packets constructing p 1 and p 2 sould be from different flows, and (ii) p 1 p 2 sould be decodable at te next op of all packets tat construct te network code. If tese conditions are satisfied, we say tat te network code is an eligible network code, and p 1 is replaced by p 1 p 2. Ten p 1 p 3 is cecked for network coding, etc. After all packets are cecked for network coding, te output queue Q i is updated: (i) te final packet p 1 is stored in te first slot of te output queue, and (ii) te memory allocated to oter packets are freed. Ten, te same algoritm is run for packet p 2, etc. Wen a transmission opportunity arises, te first packet from te output queue is cecked for network coding again and broadcast over te yperarc. Let te number of packets from flow s in node i be Q s i. Qs i captures te difference between te incoming and outgoing traffic for flow s at node i. Since an -queue captures te difference between te incoming and outgoing traffic over a yperarc, we calculate its size using te following euristic: Q = k K max k { ˇαs,k Qs i }, were ˇαs,k is te approximate traffic splitting, explained next. Troug numerical calculations, we made te following observation: eac α s,k converges to te percentage of time tat packets from flow s are transmitted wit te k-t network code over at node i. At eac packet transmission, we calculate te probability tat a network code k over yperarc can be used for flow s, over a time window. Te average over tis window

5 (a) Alice-and-Bob Topology (b) Cross Topology (c) Grid Topology Fig. 2. Topologies and traffic scenarios used in simulations. gives an estimate of te traffic splitting parameter, ˇα s,k. Packet Dropping (Alg. 2): Wen a node is congested, it decides wic packet to drop. In order to eliminate te potential of rate mismatc between flows coded togeter, we propose tat te node compares te number of all (coded and uncoded) packets of eac flow, in queues were te flow is dominant ( = 1). Tis is motivated by te optimal rate control in Eq. (4). Specifically, for eac flow s, we calculate Φ s i = (J ) A Q ˇw s, were ˇws = k K k and ˇαs,k ˇms,k. Upon congestion, te Φs i s are compared and a packet from te flow wit te largest Φ s i is dropped, preferably te last uncoded packet. If all packets from te selected flow are coded, a newcoming packet(s) is dropped instead. To estimate te dominance indicator ˇ needed in Alg. 2, we compute euristically an estimate ˇ as follows. If ˇαs,k Qs i < H s,k ˇα s,k Qs i s.t. s S k {s}, ten ˇ = 0. Oterwise, ˇ = ( Sk max ) 1 were Sk max = {s s S k ˇαs,k Qs i =,k max{hs ˇα s,k Qs i s S k }}. B. Rate Control at te Sources Te optimal rate x s is inversely proportional to te sum of te queue sizes qi s across all nodes i on te pat P s of flow s according to Eq. (4) for logaritmic utility (i.e., x s = ( i P s qi s) 1. qi s ). However, it is impractical to feed back to te source te full information i P s qi s. Instead, wen a queue is congested, a packet is dropped or marked [4]. Te source uses tis binary information as a signal to reduce its rate, mimicking te inverse relationsip. Te exact adaptation of te flow rate depends on te TCP version used. In te simulations, we used TCP-SACK witout any modification. Te only cange we propose is te packet dropping sceme at te queue. TCP still reacts to drops but tese drops are caused according to network coding requirements (Alg. 2). C. Sceduling Te sceduling part in Eq. (6) as two parts: intra- and inter-sceduling tat determine wic packet to transmit from a node and wic node sould transmit, respectively. Bot ave difficulties in practice. Intra-sceduling causes packet reordering at TCP receivers. Inter-sceduling requires centralized knowledge and it is NP ard and ard to approximate [5]. Given tese difficulties and our goal to make minimal canges, we limit our modifications to te queue management. VI. PERFORMANCE EVALUATION In tis section, we evaluate te trougput of TCP over our proposed sceme (NCAQM) in various topologies and traffic scenarios. We compare it to TCP over te following baseline scemes: no network coding (nonc), wic uses FIFO witout network coding; COPE [1], wic stores native packets in a FIFO and decides wic packets to code togeter at eac transmission opportunity; and te optimal control. A. Simulation Setup We used te GloMoSim simulator [19], wic is well suited for wireless. We implemented from scratc te modules for one-op network coding over wireless mes networks (COPE) as well as for our proposed sceme (NCAQM). 1) Topologies: We simulated four illustrative topologies sown in Fig. 1 and Fig. 2. In X, Alice-and-Bob (a and b transmit to eac oter via te relay c), and cross (a, b and d, e communicate troug te relay c) topologies, c is placed in te center of a circle wit 90m radius over 200m 200m terrain and all oter nodes are placed around te circle. In te grid topology nodes are distributed over a 300m 300m terrain, divided into 9 cells of equal size. 15 nodes are divided into sets consisting of 1 or 2 nodes and eac set is assigned to a different cell. If bot sender and receiver are in te same cell or in neigboring cells, tere is a direct transmission; oterwise, a node in a neigboring cell acts as a relay. If tere are more tan one neigboring cells, one is cosen at random. 2) MAC: In te MAC layer, we simulated IEEE wit RTS/CTS enabled and wit te modifications proposed in [1] for network coding. 3) Wireless Cannel: We used te two-ray pat loss model and Rayleig fading (wit good link quality) in GloMoSim. 4) TCP Traffic: We consider FTP/TCP traffic on top of te wireless network. In te Alice-and-Bob, X, and cross topologies, TCP flows start at random times witin te first 5sec and live until te end of te simulation. In te grid topology, TCP flows arrive according to a Poisson distribution wit average 6 flows per 30sec. Te sender and te receiver of a TCP flow are cosen randomly. B. Simulation Results In tis section, we present simulation results for te four topologies. We compare: (i) TCP over NCAQM (TCP+NCAQM) to (ii) TCP over COPE (TCP+COPE) as

6 TABLE I AVERAGE THROUGHPUT IMPROVEMENT COMPARED TO NO-NC. Optimal TCP+NCAQM TCP+COPE Alice-and-Bob Topology 33% 27% 12% Cumulative Fraction Cross Topology 60% 31% 16% X Topology 33% 22% 10% Grid Topology - 19% 8% TCP+NCAQM TCP+COPE Trougput Improvement Percentage of improvement (a) CDF (b) Trougput improvement Fig. 3. (a) CDF, buffer size is 10 packets. (b) Te effect of buffer size (in # of packets). Average trougput improvement compared to nonc in several scenarios over te Alice-and-Bob topology TCP+NCAQM TCP+COPE Buffer Size (number of packets) well as to (iii) te optimal solution working togeter wit te optimal queue management in Eq. (7). We report te average trougput of eac sceme as % improvement over te trougput of te baseline TCP+noNC. Table I presents te results for te following parameters: te buffer size at eac intermediate node is 10 packets; te packet size of 1000B; te cannel capacity is 1Mbps; te simulation duration is 1min. Te results are averaged over 10 simulations. Te first observation is tat our sceme (TCP+NCAQM) doubles te trougput improvement compared to TCP+COPE in all four topologies. We note tat te buffer size was purposely cosen to be limited to make network coding opportunities scarce. TCP+NCAQM as two advantages in tis callenging scenario: (i) it stores network coded, instead of native, packets tus saving buffer and (ii) it drops packets to increase network coding opportunities. Te second observation is tat TCP+NCAQM performs close to te optimal for te Alice-and-Bob and X topologies. For te cross topology, tere is still a gap due to te very limited buffer size for 4 flows at te relay (rater tan 2 flows in Alice-and-Bob and X topologies). Fig. 3(a) sows te cumulative distributed function (CDF) for te Alice-and-Bob topology, buffer size of 10 packets and 40 simulations. Te CDF of TCP+NCAQM is sifted to significantly iger trougput levels compared to TCP+COPE. E.g., TCP+NCAQM improves trougput more tan 20% in more tan 90% of te realizations. Fig. 3(b) sows te trougput improvement vs. buffer size. Wen buffer sizes are small, te difference between TCP+NCAQM and TCP+COPE is significant. Te trougput of TCP+COPE increases wen buffer sizes increase, wic is intuitively expected. Te problem addressed in tis paper was te mismatc between rates of flows coded togeter, due to te bursty nature of TCP, wic reduces coding opportunities. However, wen buffer sizes increase, tere are more packets available in queues for coding. Fig. 3(b) demonstrates tat our sceme is particularly beneficial in ars conditions. VII. CONCLUSION In tis paper, we sowed ow to improve te TCP performance over wireless networks wit a given intersession network coding sceme. Te key intuition was to eliminate te rate mismatc between flows tat are coded togeter, troug a synergy of rate control and queue management. First, we formulated te NUM problem and derived a distributed solution. 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