Diverse: Application-Layer Service Differentiation in Peer-to-Peer Communications

Transcription

1 Divere: Application-Layer Service Differentiation in Peer-to-Peer Communication Chuan Wu, Student Member, IEEE, Baochun Li, Senior Member, IEEE Department of Electrical and Computer Engineering Univerity of Toronto {chuanwu, Abtract The peer-to-peer communication paradigm, when ued to dieminate bulk content or to tream real-time multimedia, ha enjoyed the ditinct advantage of calability when compared to the client-erver model, ince it take advantage of available upload bandwidth at participating peer to alleviate erver load. A multiple concurrent peer-to-peer eion co-exit in the Internet, it i natural to demand differentiated ervice in different eion, with repect to Quality of Service metric uch a bit rate and latencie. The problem of ervice differentiation acro eion, however, ha never been addreed in the literature at the application layer. In thi paper, we open a new direction of reearch that treat different peer-to-peer eion with different prioritie, and preent Divere, a novel applicationlayer approach to achieve ervice differentiation acro different eion. An extenive evaluation of our implementation of Divere in an emulated peer-to-peer environment ha demontrated it effectivene in achieving our deign objective. I. INTRODUCTION The paradigm of peer-to-peer (P2P) communication over the Internet [], [2], [3] ha been uccefully implemented in current-generation Internet application. Well known example application include large-volume peer-to-peer content ditribution (e.g., BitTorrent [4]), a well a on-demand or live peer-to-peer multimedia treaming [5], [6]. A one of the mot ignificant benefit of peer-to-peer communication, participating peer in a content ditribution or treaming eion eek to maximally utilize their upload bandwidth capacitie to erve other peer in the ame eion, alleviating the load on dedicated content ditribution or treaming erver. Such an advantage i epecially prominent when the number of participating peer in a peer-to-peer eion cale up, a in a typical flah crowd cenario when a particular data item or media tream interet many peer at the ame time. A the peer-to-peer communication paradigm evolve in the Internet, we expect to experience multiple content ditribution or media treaming eion, running concurrently in the peerto-peer application-layer overlay. Similar to the concept of multicat group in traditional IP multicat, each eion ha it own group of participating peer, and it own data item to be dieminated to all the participant (or media to be treamed). It i natural to expect that ome of thee eion expect a better ervice with repect to Quality of Service (QoS) metric uch a bit rate and latencie. A good example, a live peerto-peer treaming eion of premium televiion channel to paid ubcriber hould enjoy a higher priority and a better quality than another treaming eion of regular broadcat televiion channel to the general public. Furthermore, a treaming eion of live multimedia hould be handled with a higher priority than a content ditribution eion of bulk data (e.g., on-line backup). In thi work, uch a need for differentiated ervice to different peer-to-peer communication eion i referred to a ervice differentiation in applicationlayer peer-to-peer network. Although many mechanim have been propoed to upport ervice differentiation in the network layer [7], [8], [9], very few have been implemented in core and edge witche in the current Internet, which are till largely bet-effort. In thi paper, we propoe Divere, a new paradigm of peerto-peer communication with upport for different level of ervice differentiation. In Divere, we treat different eion with different prioritie, and propoe a novel application-layer approach to achieve ervice differentiation acro peer-to-peer communication eion. Toward thi objective, our original contribution are two-fold. Firt, we eek to contruct and cutomize optimal peer-to-peer topologie for each of the concurrent eion in the peer-to-peer overlay, baed on their priority level. Second, baed on thee optimal topologie, we apply priority-baed meage cheduling at each of the participating peer in the application layer, which further improve the quality experienced by high-priority eion over thoe of lower prioritie. Highlight of Divere include the deign of a practical protocol to implement ervice differentiation in peerto-peer network, which adapt to network dynamic including peer join, departure and network congetion. To our bet knowledge, thi paper i the firt that identifie the need for ervice differentiation acro peer-to-peer communication eion, and that addree the correponding challenge with pure application-layer approache. The remainder of thi paper i organized a follow. In Sec. II, we preent our ytem model and motivate the deign of Divere. A detailed decription of the main component in Divere are dicued in Sec. III. In Sec. IV, we preent practical and fully ditributed protocol that implement Divere. Evaluation reult of it implementation in an emulated peer-to-peer environment are preented in Sec. V. We dicu related work and conclude the paper in Sec. VI and Sec. VII, repectively.

2 II. DIVERSE: SYSTEM MODEL AND MOTIVATIONAL INSIGHTS In thi paper, we conider a collection of peer, with each peer participating in one or multiple peer-to-peer communication eion. In each peer-to-peer communication eion, there i one original data ource, and the ret of the peer are receiver. The connectivity graph among the ource and receiver in one eion contitute a meh overlay topology. The entire peer-to-peer overlay conit of all uch meh topologie, each in an peer-to-peer communication eion. Such a peer-to-peer overlay can be modeled a a directed graph G = (N,A), where N i the et of all the vertice (peer) and A i the et of directed arc (directed peer-to-peer link). Let S be the et of eion that concurrently exit in the peer-to-peer overlay. Let v () be the ource for eion, S, and T = {v (),v (2),v (3),...} be it et of receiver. A i the et of peer-to-peer link in eion. When peer i i the uptream peer erving peer j in eion, i.e., peer j i the downtream peer of i in, the link (i,j) i in A. We then have N = S ({v () } T ) and A = S A. Each eion i aigned to a certain priority level, denoted by C, with a larger number denoting a higher priority level. An example of uch a peer-to-peer overlay with two eion i illutrated in Fig.. Peer-to-peer eion Peer-to-peer eion 2 All concurrent peer-to-peer eion (4) (4) () () (2) (2) (2) (2) () () () () () () (3) (3) (3) () () (3) () (4) (4) during retrieval. In a peer-to-peer overlay, performance bottleneck mainly occur at the peer at the edge of the Internet, rather than at Internet backbone router. Thi i due to the fact that peer uually have very limited and heterogeneou proceing and bandwidth capacitie. Baed on thee aumption, the deign objective of an effective ervice differentiation mechanim i to provide better performance to high-priority eion and a certain degree of fairne to low-priority eion, while till adapting well to the dynamic in the network. In addition, we wih to make the bet ue of the limited upload capacitie at each of the peer in the application layer. We now motivate the deign of Divere by identifying a few influential parameter that determine the main performance metric of a peer-to-peer communication eion: end-to-end delay and throughput experienced by each peer in the eion. A careful inpection of the end-to-end delay in the peerto-peer eion lead to the following parameter: () The meage queueing delay at each intermediate peer; (2) the bandwidth hare allocated by each peer for the eion, which determine it tranmiion delay; (3) the number of overlay hop travered by data flow in the eion from the ource; and (4) the delay on each overlay link between peer (determined by the um of delay in the underlying IP-layer link). In Divere, to reduce the meage queueing delay at each peer, we apply an application-layer priority cheduling algorithm, henceforth referred to a the overlay priority cheduling algorithm. Such cheduling of meage belonging to different eion allow for differentiated queueing delay at the peer, with repect to eion at different priority level. To addre the challenge of differentiating other delay parameter and throughput acro different eion, we propoe a priority-baed optimal topology contruction and bandwidth allocation algorithm, referred to a optimal bandwidth allocation algorithm. In thi algorithm, by chooing better overlay path for high-priority eion, we take into conideration the number of overlay hop the path travere, a well a the quality of overlay link. By allocating upload bandwidth baed on the priority level, we further guarantee the bandwidth hare for high-priority eion. Divere repreent the deign of efficient algorithm that implement thee key inight. Fig.. Concurrent peer-to-peer communication eion: an example. In the deign of Divere in thi paper, we make the following realitic aumption: At different time in a communication eion, a peer may witch to different uptream peer to retrieve it available data content at the moment. Therefore, the meh topologie of the eion are changing dynamically. In uch a meh network featuring parallel downloading, there are rik the ame content may be unnecearily upplied by multiple uptream peer. In thi paper, we aume uch delivery redundancy problem i olved by applying a certain coding cheme, e.g., network coding, and there i no need to reconcile the content difference III. DIVERSE: EFFECTIVE SERVICE DIFFERENTIATION Divere repreent a complete olution toward the realization of ervice differentiation acro eion of different prioritie. It conit of two main component: overlay priority cheduling and priority-baed optimal bandwidth allocation. A. Overlay priority cheduling When data meage belonging to different eion arrive at a peer, the cheduling of the order in which they are proceed and relayed to other peer play a ignificant role in differentiating their queueing delay. Therefore, we deign two priority cheduler at each peer, for incoming and outgoing meage, repectively. An example of the two priority cheduler i hown in Fig. 2, in which Peer i i participating in 4 eion,

3 Uptream peera Uptream peer B Uptream peer C Uptream peer D II Seion Seion 2 Seion 3 Seion 4 I Incoming Scheduler Peer i Proceor Bandwidth Allocator Outgoing Scheduler II I Flow : eion to downtream peer E Flow 2: eion to downtream peer F Flow 3: eion 2 to downtream peer F Flow 4: eion 3 to downtream peer G Flow 5: eion 4 to downtream peer G Fig. 2. Overlay cheduling with two priority cheduler: an example. with eion and 2 in the high priority level II, eion 3 and 4 in the low priority level I. At the incoming cheduler of each peer, an incoming meage queue i etablihed for each of the eion the peer i participating in, and thee queue are organized baed on their priority level. Meage in different queue are proceed tarting from the highet priority level. If there are C priority level in total, the cheduler erve the meage from the queue at priority level c only if there doe not exit any meage in the queue at priority level c +, c + 2,..., C. For queue in the ame priority level, a round robin approach i applied to chedule meage from different queue to the proceor. In the example hown in Fig. 2, the incoming queue of eion and 2 are proceed before thoe of eion 3 and 4, a long a they are not empty. At the outgoing cheduler, a meage queue i et up for each of the outgoing meage flow of a eion, which i detined to a downtream peer. Thee queue are cheduled to end data meage in the order of their eion prioritie, and at the optimal rate computed by the priority-baed bandwidth allocator, which implement the optimal bandwidth allocation algorithm to be dicued in the following ection. The regulation of allocated bandwidth for the meage flow are implemented by keeping track of the time to end the next meage for each of the queue. The time to end the next meage for an outgoing queue i initialized to zero, and increaed by the time ued to end one meage, i.e., the meage ize divided by the allocated bandwidth, whenever a meage of thi queue i ent. Therefore, the outgoing cheduler goe through the outgoing queue in the order of their prioritie, and end meage from a queue a long a the current time i later than the time to end the next meage of thi queue. A an analytical example baed on Fig. 2, if data meage are all of the ame ize and the bandwidth allocated to five outgoing flow are 2, 4, 3, 2, repectively, the outgoing cheduler end (on average) 2, 4, 3, 2, meage in one round for queue to 5, repectively. With the two cheduler, data meage belonging to highpriority eion are guaranteed a lower queueing delay at the peer. However, the rik of tarving low-priority eion may arie with uch priority cheduling. To eliminate uch a rik, in our deign, we alo optimally allocate upload capacity of a peer to all the eion baed on their priority level. In Divere, the implementation of priority cheduling at peer in the application layer effectively compenate the lack of uch upport at underlying IP router. A we aume performance bottleneck of a peer-to-peer overlay lie in the peer rather than the router, we believe uch applicationlayer priority cheduling can actually achieve better ervice differentiation acro multiple peer-to-peer eion. B. Priority-baed optimal bandwidth allocation We next preent the derivation of our optimal bandwidth allocation algorithm, which contruct priority-baed optimal topologie and compute bandwidth hare along the link for all the eion in the peer-to-peer overlay. Toward thi objective, we firt et up a convex optimization model that maximize overall utilitie received by the peer in all the eion. Better path election and favorable bandwidth allocation for high-priority eion are achieved by effectively formulating eion prioritie and the quality of overlay link into utility function. We then dicu it olution algorithm baed on Lagrangian relaxation technique and ubgradient algorithm. ) Problem formulation: We ue U to repreent the utility that peer j can receive by retrieving content of eion from uptream peer i. It i a non-decreaing function of the variable, the bandwidth allocated for eion along link (i,j). We further aume U ( ) i trictly concave and twice differentiable []. Baed on our bottleneck aumption, we conider contraint of the heterogeneou upload and download capacitie of each peer i, denoted by O i and I i repectively. Let R be the maximum rate of eion. We aume that a receiver only participate in eion whoe total rate can be accommodated by it download capacity, i.e., :i T R I i. In thi cae, we include the eion rate contraint at each receiver in the convex program, but omit the download capacity contraint, which will otherwie be redundant. The convex program i formulated a follow: P: ubject to max S U (i,j) A ( ) ()

4 j:(i,j) A O i, i N, i:(i,j) A R, j T, S, (2) S, (i,j) A, S. An optimal olution to convex program P, {, (i,j) A, S}, provide an optimal bandwidth allocation trategy, and determine the optimal delivery path for all the eion in the network. In order to elect better path and guarantee the rate for high-priority eion, we determine the utility function U, (i,j) A, S, a follow: it value i larger if eion i in a higher priority level, and if the quality of link (i,j) i better. The quality of link (i,j) can be determined by the delay or lo rate on the link, or the tability of uptream peer i. We will mainly ue delay to evaluate the link quality in our protocol. With C being the priority of eion and Q denoting the quality of link (i, j), we formulate the utility function a U = C log( + Q ). By maximizing utility function in thi form, the convex optimization guarantee delivery rate of higher priority eion rather than thoe of lower priority eion, and aign larger bandwidth for the former on the link with better quality. In addition, fairne of bandwidth allocation to all eion i alo guaranteed with thi trictly-concave logarithmic function []. We alo note that the input eion topologie to the optimization problem are dynamically determined by the content availability at the peer. Therefore, the uptream peer of a receiver in the input topologie are thoe which already have the content it attempt to retrieve. Thi implicitly take overlay hop count into conideration in the optimization, and thu the receiver are guaranteed to be in cloe proximity to the ource in term of overlay hop count in the reulting optimal topologie. 2) Subgradient olution: In order to derive a fully decentralized algorithm to olve convex program P, we utilize the ubgradient algorithm baed on Lagrangian relaxation technique, which i an efficient olution technique for convex program and can naturally achieve ditributed implementation [2], [3]. We tart by analyzing the decompoition of convex program P into multiple ubproblem which can be independently olved by each peer with it local information. For thi purpoe, we utilize Lagrangian relaxation technique and relax the contraint in (2) to derive Lagrangian dual of the primal problem P. To apply Lagrangian relaxation, we conider the equivalent tandard minimization form of the objective function in (): min S U (i,j) A ( ). (3) Aociating Lagrangian multiplier µ j, j T, S, with the contraint in (2), we modify the objective function in (3): ( ) + µ j ( R ) S S j T U (i,j) A i:(i,j) A = i N S (U j:(i,j) A ( ) µ j Then we obtain the Lagrangian dual a follow: where L(µ) = min ( P i N S µ j R ) S j T = (max P i N S ) µ j R. S j T max L(µ) (4) µ (U j:(i,j) A (U j:(i,j) A ( ) µ j ) ( ) µ j )) µ j R, (5) S j T and the polytope P i defined by the following contraint: S j:(i,j) A O i, i N,, S, (i,j) A. Here, the Lagrangian multiplier µ j can be undertood a the price provided by receiver j to it uptream peer for eion. Such an interpretation will become clear a we come to the adjutment of µ j with the ubgradient algorithm. We oberve that the Lagrangian ubproblem in (5) can be decompoed into multiple ub convex optimization problem, each to be independently olvable by a peer i, i N: ubject to max S (U j:(i,j) A ( ) µ j ) (6) S j:(i,j) A O i, (7), S, j : (i,j) A. (8) Baed on thi nice decompoable tructure of the Lagrangian ubproblem in (5), we are able to olve the Lagrangian dual in (4) with ubgradient algorithm in a ditributed fahion. In what follow, we dicu the ubgradient algorithm, which olve the Lagrangian dual and alo derive the optimal olution to the primal problem P. We tart with a et of initial non-negative Lagrangian multiplier µ j [], j T, S. During each iteration k of the ubgradient algorithm, k =, 2,..., given the current Lagrangian multiplier value µ j [k], we olve the N ubproblem in (6) by an approach imilar to water filling (pp. 245, [4]), which goe a follow: The water-filling approach. Let f(x) be the objective function in (6), i.e., f(x) = S (U j:(i,j) A Then the marginal utility for df(x) d ( ) µ j ). i = U ( ) µ j.

5 Beginning with one thi =, j : (i,j) A, S, we find with the larget poitive marginal utility and increae. A U ( ) i trictly concave, U ( ) decreae with the increae of. We increae thi until it marginal utility i no longer the larget. Then we find a new with the currently larget marginal utility and increae it. Thi proce repeat until the um of all, j : (i,j) A, S, reache O i or all the marginal utilitie become zero. Thi water-filling approach can be intuitively undertood a follow: we alway allocate the upload capacity of peer i, i.e., O i, to uch a bandwidth variable, that the objective function f(x) achieve the larget gain. We further prove the correctne of the approach in the following theorem: Theorem. The above water-filling approach obtain an optimal olution for the convex optimization problem in (6). We potpone detailed proof of theorem to Appendix I. With the optimal [k] computed by the water-filling method, we then update the Lagrangian multiplier by µ j [k + ] = max(,µ j [k] + θ[k]( [k] R )), i:(i,j) A j T, S, (9) where θ i a equence of tep ize that guarantee the convergence of the ubgradient algorithm, if it atifie the following condition (pp. 26, [2]): θ[k] >, lim k θ[k] =, and θ[k] =. () k= In our algorithm, we chooe the tep length equence θ[k] = a/(b + ck), k,a >,b,c >, which atifie the above condition. Eq. (9) how the adjutment of price at each receiver j for all the eion it participate in, baed on the allocated upload bandwidth from it uptream peer. If the total acquired bandwidth for eion exceed the eion rate, contraint (2) i violated, and thu price µ j i raied; if the total bandwidth fail to reach the eion rate, the price i reduced. The ubgradient algorithm to olve Lagrangian dual in (4) i ummarized in Table I. TABLE I OPTIMAL BANDWIDTH ALLOCATION ALGORITHM. Chooe initial Lagrangian multiplier value µ j [], at each receiver j in eion, S. 2. Repeat the following iteration until convergence: at time k =, 2,... ) Solve the convex program in (6) with the water-filling approach at each peer i in N, and derive x ij [k], j : (i, j) A, S; 2) Update Lagrangian multiplier µ j [k + ] = max(, µ j [k] + θ[k]( P i:(i,j) A x [k] R )), where θ[k] = a/(b + ck), at each receiver j in eion, S. Thi ubgradient algorithm not only converge to the optimal Lagrangian multiplier value for the Lagrangian dual, but alo derive the optimal olution to the primal problem P, which i formally tated in the following theorem. Theorem 2. With the ubgradient algorithm decribed in Table I, tarting from any nonnegative multiplier vector µ, where µ = (µ j, j T, S), the equence of vector {µ[k]} converge to it optimum µ, and the equence of vector {x[k]}, where x = (, (i,j) A, S), converge to the unique optimal olution x of the primal problem P. We again potpone the proof to Appendix II. 3) An illutrative example: We now give a imple illutrative example to demontrate the convergence of the algorithm to priority-baed optimal topologie. Fig. 3 how a peer-topeer overlay network with two eion from two ource to four common receiver, with eion rate R = R 2 = 5 Kbp, and prioritie C = 2 and C 2 =. O i for the ix peer, v (), v() 2, v(), v (2), v (3) and v (4), are,,.5,.9,.3 and.5 (in Mbp), repectively. Number labeled on the link of Fig. 3 (A) indicate link delay. With the ubgradient algorithm, the price vector µ converge within 5 iteration, a hown in Fig. 3 (B). The reulting optimal topologie for both eion are depicted in Fig. 3 (C) and (D) repectively, with the allocated bandwidth labeled on the link (in Mbp). Evidently, high-priority eion ue better link with allocate rate for all the peer up to the maximum eion rate, while eion 2 pick up the remaining available bandwidth, and it maximum rate i not achieved by all the participant. IV. DIVERSE: PRACTICAL DISTRIBUTED PROTOCOLS In thi ection, we deign practical protocol to implement Divere optimal bandwidth allocation algorithm and overlay priority cheduling, a well a to handle variou dynamic in realitic peer-to-peer network. A. Optimal bandwidth allocation protocol The ubgradient algorithm in Table I i directly implementable with a fully decentralized protocol. In the protocol, at each peer i, a a downtream peer, it maintain it price µ i for all the eion it participate in; a an uptream peer, it i reponible for allocating upload bandwidth to it downtream peer, by olving the ub optimization problem in (6). Let S i be the et of eion peer i i in. In each iteration, peer i end it price µ i, S i to it uptream peer in the correponding eion. Meanwhile, after it receive the current price µ j from all it downtream peer for all the eion in S i, it allocate it upload capacity with the water-filling approach. Then it communicate the computed optimal bandwidth,, j : (i,j) A, S i, to the correponding downtream peer. A it uptream peer are allocating their own upload capacitie a well, peer i receive it allocated hare, x (ui), u : (u,i) A, S i, at the ame time. When it ha collected all the allocated bandwidth for eion, it adjut it price for the eion, µ i, baed on Eq. (9), and again communicate the updated price to the uptream peer. We implement two type of meage in the protocol: Price Update (PU) meage, carrying updated price from a downtream peer; Bandwidth Update (BU) meage, containing

6 .6 () () V () V (2) 2 4 V (3) V (4) 3 mu Iteration number ().5 V () V (2) V (3) V (4) ().5.5 V () V (2).4.3 V (3) V (4) (A) (B) (C) (D) Fig. 3. Uptream peer A Uptream peer B Fig. 4. Priority-baed optimal bandwidth allocation: an example with two eion. BU PU PU BU Peer i PU BU PU BU Downtream peer E Downtream peer F Meaging model for the optimal bandwidth allocation protocol. allocated bandwidth from an uptream peer. An illutrative example for the meaging in each iteration of the ubgradient algorithm i given in Fig. 4, and detail of the ditributed optimal bandwidth allocation protocol are ummarized in Table II. B. Overlay priority cheduling protocol The peudocode for the priority cheduling protocol to be implemented at the incoming and outgoing cheduler of a peer i given in Table III. C. Handling network dynamic A peer-to-peer communication network i inherently dynamic: peer may join and leave at will, delay may fluctuate and congetion may occur along an overlay link, etc. Such dynamic poe a ignificant challenge to our protocol implementation, epecially for the priority-baed optimal bandwidth allocation protocol. In Divere, we conider appropriate handling of network dynamic a one of our main deign objective. In our implementation, time i divided into lot, which are the time interval for updating local meaurement and topology information, and for executing the optimal bandwidth allocation protocol with updated information. In every time lot, each peer actively collect or update local information for it optimal upload bandwidth allocation, e.g., pinging neighbor peer to meaure the overlay link delay. With the updated information, at the beginning of a time lot, a peer initiate the protocol execution by ending out it new price if it ha detected any change in the previou time lot, e.g., join/departure of a neighbor peer, delay variation on the adjacent overlay link, etc. A peer who ha not experienced any change in it local topology will alo participate in the protocol execution, when it receive any price update or allocated bandwidth update from it neighbor peer. In thi way, local change will propagate throughout the network, and all the affected peer cooperate in a new round of optimal bandwidth allocation. Note that in thi cenario, the optimization protocol alway run from the previou optimal value, thu expediting it convergence to the new optimum. Only light modification to the protocol in Table II are required for it to run in uch a dynamic environment. Intead of initializing µ j to zero, we tart the optimization protocol with µ j being the optimal price obtained in the previou time lot. In addition to executing the optimal bandwidth allocation protocol once every time lot, each peer alo promptly adapt to local dynamic inide each time lot, in order to provide conitent performance guarantee for high-priority eion. We divide our dicuion into three cae. ) Peer join: In a time lot, when a peer join eion, it i boottrapped with U initial uptream peer. Then it requet bandwidth R U from each of thee uptream peer. Upon receiving uch a requet from a new peer, an uptream peer firt aign it pare upload bandwidth to it. If that i not ufficient, it further hare the bandwidth allocated to eion whoe prioritie are lower than, in proportion to their priority value. 2) Peer departure: When a peer detect the departure or failure of an uptream peer from eion, it trie to obtain more upload bandwidth from it remaining uptream peer to compenate it rate lo. When an uptream peer receive uch a requet for more bandwidth, it handling i imilar to the peer joining cae. The uptream peer firt aign it pare upload bandwidth to the requeting peer, and then proportionally deprive bandwidth allocated to lower priority eion. 3) Network congetion: In our ytem model, we aume capacity bottleneck occur at the peer, rather than at router underlying overlay link. Therefore, while available overlay link bandwidth may fluctuate due to cro traffic variation at the router, it till doe not contitute the bottleneck in mot cae, and thu doe not affect optimal upload bandwidth allocation. Neverthele, in Divere, we do conider handling of evere congetion that may occur along the overlay link in ome time lot. In thi cae, delay on a congeted overlay link become much larger than previouly detected delay on the ame link.

7 TABLE II OPTIMAL BANDWIDTH ALLOCATION PROTOCOL EXECUTED AT PEER i Notation: S i: the et of eion peer i participate in. 5 Update in DB i, S i, j : (i, j) A M i: the et of price peer i offer for all eion in S i. 6 for each downtream peer j, (i, j) A, S i P i: the et of received price from downtream peer. 7 Send j a BU meage containing, S i UB i: the et of received allocated bandwidth from uptream 8 end for peer. 9 P i φ DB i: the et of allocated bandwidth to downtream peer. end if Initialization: Upon receiving a BU meage: P i φ Retrieve allocated bandwidth x (ui) from the meage 2 UB i φ 2 UB i UB i {x (ui) } 3 DB i φ 3 for each eion, S i 4 M i {µ i µ i =, S i} 4 if UB i contain all the allocated bandwidth for eion 5 Send PU meage containing initial µ i to all the uptream, i.e., x (ui), u : (u, i) A peer, u, (u, i) A, S i 5 µ i max(, µ i + θ( P u:(u,i) A x (ui) R )) 6 Update µ i in M i Upon receiving a PU meage: 7 for each uptream peer u in eion, (u, i) A Retrieve price µ j from the meage 8 Send u a PU meage containing µ i 2 P i P i {µ j } 9 UB i UB i {x (ui) } 3 if P i contain all the price µ j, S i, j : (i, j) A end for 4 Compute x, S i, j : (i, j) A, by olving (6) end if with the water-filling method 2 end for TABLE III PRIORITY SCHEDULING PROTOCOLS AT PEER i Notation: S i: the et of eion peer i i participating in 5 m firt meage in inqueue[c][q] P i: the highet priority level among eion in S i 6 dequeue and proce m inqueue[c]: the et of incoming data meage queue at priority 7 end if level c, in which each queue contain the incoming meage for 8 end for one eion in S i 9 end while outqueue[c]: the et of outgoing data meage queue at priority end for level c, in which each queue contain the outgoing meage of a eion in S i to one downtream peer Outgoing cheduler: I[c]: the number of peer i incoming queue at priority level c for c = P i to O[c]: the number of peer i outgoing queue at priority level c 2 for q = to O[c] timefornextmg[q]: time to end the next meage for queue q 3 while current time timefornextmg[q] : allocated bandwidth to downtream peer j in eion 4 m firt meage in the queue outqueue[c][q], which belong to eion and i detined to downtream peer j Incoming cheduler: 5 dequeue m and end m to j for c = P i to 6 timefornextmg[q] timefornextmg[q] + m.ize 2 while the queue in inqueue[c] are not empty 7 end while 3 for q = to I[c] 8 end for 4 if the incoming queue inqueue[c][q] i not empty 9 end for Then, in the optimal bandwidth allocation protocol executed at the next time lot, le upload bandwidth will be allocated along thi link, a we conider link delay in the utility function of the optimization. Beide, inide the time lot, uch congetion i actively detected and adapted a well, in the follow way: Each peer periodically etimate it achieved receiving rate in each eion from each uptream peer. When it receiving rate i le than the allocated upload bandwidth, which i the ending rate at the uptream peer, we know congetion ha occurred along the link. The downtream peer then feed back thi rate dicrepancy to the ender. At the uptream peer, it decreae it allocated bandwidth along the congeted link correpondingly. When multiple eion are haring a ame link, it tart to reduce bandwidth from thoe eion at the lowet priority level. Meanwhile, an affected downtream peer will actively eek more upload bandwidth from it other uptream peer, o a to compenate it rate lo. With uch adaptation to network dynamic inide and acro time lot, Divere maximally enure the ervice quality for high-priority eion and i able to achieve excellent ervice differentiation reult at all time. V. EXPERIMENTAL EVALUATION With the C++ programming language, we have implemented Divere protocol in an emulated peer-to-peer overlay environ-

8 Number of iteration Fig Number of peer in the network (A) Running time () Convergence peed in tatic network Number of peer in the network ment. Our implementation include the priority-baed meage cheduling and queue adminitration in the application layer, and the ditributed optimal bandwidth allocation protocol at each peer. Our implementation alo provide meaurement of QoS metric and upport for network parameter emulation, uch a peer upload/download capacitie. It run in the UNIX operating ytem (Linux, Mac OS and other BSD variant), and ue tandard Berkeley ocket to etablih TCP connection between peer. Actual data meage in each peer-topeer eion are tranmitted from the ource, cheduled at intermediate peer, and received at the receiving peer. With Divere implementation, we have conducted extenive experimental evaluation on a high-performance cluter coniting of 5 Dell 425SC and Sun v2z dual-cpu erver, each equipped with dual Intel Pentium 4 Xeon 3.6GHz and dual AMD Opteron 25 proceor. In order to emulate our protocol in realitic network etting, we generate random network topologie baed on power-law degree ditribution with the Boton topology generator, BRITE [5]. In each topology, a peer ha ix neighbor on average. Download and upload capacitie for the peer are uniformly choen from the range of Mbp and.6.9 Mbp, repectively. Overlay link delay are uniformly elected between m and m. Except for the experiment in Sec. V-D.2, we run two eion in each network: Seion, a high-priority treaming eion with priority C = 2; Seion 2, a low-priority data downloading eion, with priority C 2 =. In each network, there i one ource for each eion, and the remaining peer participate in both eion. A. Performance of optimal bandwidth allocation in tatic network We firt invetigate the convergence peed and meaging overhead of Divere optimal bandwidth allocation protocol in tatic network of different number of peer. In each of the tatic network, the protocol run from the beginning, where all the price µ are initialized to zero. Maximum eion rate of the treaming and downloading eion are et to 5 Kbp and Mbp repectively in thi experiment. In Fig. 5, we oberve that the number of iteration executed for algorithm convergence remain almot the ame for network of peer number from 5 up to 5. Alo, the total running time to converge doe not change much, which reveal that the running time for each iteration i imilar regardle of the network ize. Such reult meet our expectation, a our (B) Ave. no. of mg per peer per iteration Number of peer in the network Fig. 6. (A) Ave. meaging bandwidth per peer (KB/) Communication overhead in tatic network Number of peer in the network optimal bandwidth allocation algorithm i fully decentralized, and thu exhibit it outtanding calability a the network ize increae. The communication overhead for ending PU and BU meage in the protocol i illutrated in Fig. 6. Fig. 6 (A) how that each peer end out 6 7 meage on average in each iteration in all the network, a the average edge denity i ix link per peer, and communication mainly occur among neighboring peer. Fig. 6 (B) how the average meaging bandwidth ued at each peer for the protocol execution. A a PU or BU meage i imply compoed of an application-layer meage header of 24 byte and a payload of a few double value, the meaging overhead i a low a 7 8 KB/, which i trivial compared to the data rate in the eion. Alo noting that the protocol execution take only a very hort period of time, we conclude that our ditributed protocol to derive the optimal bandwidth allocation i indeed very lightweight. B. Performance of optimal bandwidth allocation in dynamic network We next examine the dynamic behavior of our protocol in practical network with peer join and departure. We invetigate two peer dynamic cenario. In each cenario, we conider two eion, treaming and downloading a tated earlier, with maximum rate of 5 Kbp and Mbp repectively. The length of each time lot i et to 3 econd. Baed on dicuion in Sec. IV-C, our optimal bandwidth allocation protocol i executed at the beginning of each time lot, baed on peer dynamic occurred in the previou time lot, and from the previou optimal value. Meanwhile, our dynamic handling protocol alo actively adapt to peer dynamic in each time lot. ) Scenario : In the firt cenario, both eion run for a total of 22.5 minute. In the firt minute, 2 peer join the eion at random time; then tarting from 2.5 minute, peer tart to leave the network. The reult of thi experiment are ummarized in Fig. 7. Fig. 7 (A) how the dynamic of peer number in the network. Fig. 7 (B) illutrate the convergence of price vector µ from it previou optimal value in each time lot during the entire proce, with the additional number of iteration for the convergence hown in Fig. 7 (C). We can ee that in each time lot, convergence to a new optimal price vector from the previou one take much fewer iteration and much horter time, compared to running from the very beginning in (B)

9 Number of peer mu Number of additional iteration Average throughput (Mbp) Time (econd) (A) Time (econd) 3 2 (B) Time (econd).5 (C) High-priority treaming eion Low-priority downloading eion Time (econd) Fig. 7. Convergence during a peer join phae and a departure phae: a 2-peer dynamic network with two eion. the cae of tatic network of the ame ize. A peer join and departure are practical cenario in realitic peer-to-peer network, thi ugget that our optimal bandwidth allocation algorithm can actually delivery good performance in practice. The average throughput at each peer in each of the two eion i illutrated in Fig. 7 (D). We note that throughput for the high-priority treaming eion alway remain at the required treaming rate of 5 Kbp. For the data downloading eion, at the beginning when there are few peer and more pare upload capacitie in the network, it i able to achieve high downloading throughput. However, with more peer joining and competing for bandwidth, it downloading throughput decreae. It will increae again when more bandwidth capacitie are provided in the network due to further peer joining. Similarly, in the peer departure phae, the downloading eion loe bandwidth when there are le upload bandwidth in the network, and pick up the pare bandwidth when more bandwidth capacitie are left. 2) Scenario 2: In the econd cenario, during a -minute period, 2 peer join and leave the eion following an ON/Off model, with On/Off period both following an exponential ditribution with an average of T econd. We monitor the achieved throughput at each peer in both eion during thi proce and illutrate the average throughput in Fig. 8. The reult demontrate that our protocol maximally guarantee teady throughput for the eion even under high peer (D) Average throughput (Mbp) High priority treaming eion Low priority downloading eion Time (minute) Fig. 9. Average throughput in cae of congetion: a -peer network with two eion. churn rate, baed on the combination of optimal bandwidth allocation and active dynamic handling. For example, in the cae that each peer join/leave every 2 econd, on average there are join/departure every econd in uch a 2-peer network. We can ee the throughput achieved at exiting peer in the high-priority treaming eion i till quite conitent, while that for the downloading eion repreent more fluctuation, due to our priority-baed dynamic handling. C. Adaptation to network congetion In our evaluation, we have alo invetigated the impact of varying available overlay link capacitie on the optimal upload bandwidth allocation. We experimented with realitic link bandwidth, choen from the ditribution of meaured available bandwidth between PlanetLab node [6]. However, we find the bandwidth are generally much larger than the eion rate, o their light variation do not affect our reult much. Therefore, we omit the experiment reult for thi cae. Given the over proviioning ituation in the core of the current Internet, we believe uch finding from available bandwidth ditribution among PlanetLab node can repreent the general cenario. Still, we examine the adaptation of Divere in the cae that evere network congetion occur omewhere at an underlying router. For thi purpoe, we deign the following experiment: We introduce congetion to a teady-tage peer-to-peer network of peer, where the average throughput achieved at peer in the two eion are around 5 Kbp and 3 Kbp repectively. In a period of 7 minute, congetion occur twice in the underlying IP network, at 5 25 and minute repectively, and affect % and 2% overlay link, repectively. From Fig. 9, we oberve that the throughput for the highpriority eion i almot never affected during the firt congetion period and i lightly affected during the econd. Thi i achieved at the cot of the low-priority eion, whoe throughput i reduced whenever congetion occur. The obervation from Sec. V-B and V-C clearly demontrate the effectivene of our priority-baed optimal bandwidth allocation and dynamic handling protocol, which conitently guarantee the delivery rate for high-priority eion

10 .6 Highpriority treaming eion Lowpriority downloading eion.6 Highpriority treaming eion Lowpriority downloading eion.6 Highpriority treaming eion Lowpriority downloading eion Average throughput (Mbp) Average throughput (Mbp) Average throughput (Mbp) Time (econd) Time (econd) Time (econd) (A) T = S (B) T = 5S (C) T = S Fig. 8. Average throughput with different on/off interval length: a 2-peer dynamic network with two eion. in cae of all kind of network dynamic, and alo maximize the utilization of network bandwidth. D. Effectivene of application-layer ervice differentiation We next deign two experiment to further evaluate the efficiency of Divere in improving ervice differentiation. ) Comparion among four cheme: The firt experiment aim at invetigating the effect of both overlay priority cheduling and optimal bandwidth allocation protocol. Toward thi objective, we compare end-to-end delay in two peer-to-peer eion with four different cheme: NSNA: No overlay priority cheduling and no optimal bandwidth allocation. Meage of the two eion are proceed in a round robin fahion and they fairly hare the upload bandwidth of their common uptream peer. WSNA: Overlay priority cheduling i applied, but not the optimal bandwidth allocation protocol. NSWA: Priority-baed optimal bandwidth allocation protocol i applied, but not overlay priority cheduling. Divere: Both overlay priority cheduling and optimal bandwidth allocation are applied. In thi experiment, peer equentially join the two eion in 3 minute. The maximum rate for both eion are 5 Kbp, and the ize of data meage i 5K byte. We monitor the average end-to-end delay per peer in both eion, which i computed a the bit tranmiion delay (BTD), i.e., meage delay divided by the meage ize. Fig. how the average end-to-end delay conitently increae due to the expanion of network diameter with peer join. With NSNA, the two eion are not differentiated and thu their curve overlap each other. By applying overlay priority cheduling in WSNA, the delay in the highpriority eion i lightly reduced and that for the lowpriority eion increae. With the cheme where optimal bandwidth allocation i applied, i.e., NSWA and Divere, there i a ditinct drop of end-to-end delay in the high-priority eion and a correponding notable delay increae in the low-priority eion. Thi i becaue our optimal bandwidth allocation protocol alway chooe the bet low-delay path and guarantee the maximum rate for the high-priority eion. A comparion between WSNA and NSWA further reveal that the end-to-end delay in peer-to-peer eion are more dominated by tranmiion rate and overlay hop count, than Average end to end delay (m) Seion with NSNA Seion 2 with NSNA Seion with WSNA Seion 2 with WSNA Seion with NSWA Seion 2 with NSWA Seion with Divere Seion 2 with Divere Time (minute) Fig.. Comparion among four ervice differentiation cheme: a -peer joining cae with two eion. by queueing delay at the peer. Therefore, in Divere, the optimal bandwidth allocation protocol play a ignificant role in achieving ervice differentiation acro eion. Neverthele, the combination of overlay priority cheduling and optimal bandwidth allocation i able to achieve the bet reult. 2) Comparion acro different number of eion: In the econd experiment, we compare the effect of ervice differentiation achieved by Divere in cae that there are more than two concurrent eion in the peer-to-peer network. We deploy multiple eion in a peer-to-peer network with 5 peer. Each eion i at a different priority level, whoe priority decreae with the increae of eion indice. The maximum rate of all the eion are 5 Kbp. At the teady tage of the eion, we meaure the average throughput achieved and the average end-to-end delay experienced by each peer in each eion. Again, the end-to-end delay i computed a the end-to-end BTD. Fig. (A) how that even with more eion competing for peer bandwidth, the eion with the highet priority can alway achieve a throughput near it maximum eion rate, while the allocated bandwidth for lower-priority eion are reduced to accommodate the additional eion. Correpondingly in Fig. (B), with the increae of eion number, delay in low-priority eion increae rapidly, while that for the highet-priority eion remain unchanged. Thee reult reveal that Divere can effectively provide differentiated performance for multiple eion baed on their priority level.

11 Average throughput (Mbp) Seion Seion 2 Seion 3 Seion 4 Seion 5 Seion 6 Average end-to-end delay (m) Number of eion Number of eion (A) (B) Seion Seion 2 Seion 3 Seion 4 Seion 5 Seion 6 Fig.. Comparion acro different number of eion: a 5-peer network. VI. RELATED WORK There exit little literature that touche upon the topic of application-layer ervice differentiation in peer-to-peer network. Their main focu ha been on the aignment of prioritie to different peer and the proviion of differentiated ervice quality to them thereafter [7], [8], [9]. A thee prioritie are uually decided by their contribution of ervice and reource, uch ervice differentiation erve a a natural incentive to encourage the peer to cooperate. Ma et al. [7] propoe uch a peer-to-peer ervice differentiation cheme, which ditribute the bandwidth among competing peer by deigning a competition game for them. Similarly, Gupta et al. [8] provide differentiated ervice quality level to peer during the content earching and downloading proce, baed on their reputation core, which are determined by the atifaction of other peer with their contributed ervice. There are fundamental difference between our work and exiting literature. Other than prioritizing peer, we aign different priority level to different peer-to-peer communication eion, and proviion differentiated Quality of Service for each eion. Further, we guarantee better ervice qualitie for high-priority eion acro the entire peer-to-peer network, and aim at achieving global utility maximization. Exiting work uually only conider a one-hop cenario, where multiple peer are directly retrieving from the ource [7]. To the bet of our knowledge, we are not aware of any exiting work that dicue ervice differentiation acro multiple peer-to-peer eion with application-layer approache. One piece of lightly imilar work i by Key et al. [2], which regulate the rate of background data tranfer eion, uch a downloading operating ytem update, by adjuting their receiver window. In thi way, tranfer of uch lowpriority flow only dynamically utilize any available bandwidth, without affecting active eion of high-priority flow. Though thi paper conider a client-erver model, it reult i remotely imilar to that achieved by Divere, when only two priority level are conidered in the peer-to-peer overlay. However, it propoed mechanim till require changing the TCP receiver window. In contrat, rate regulation in Divere i computed with the optimal bandwidth allocation algorithm and implemented at the outgoing cheduler of each peer, baed on the calculation of the time to end the next meage. Divere doe not involve any change to the network protocol tack, yet till able to adapt to network dynamic. In the general area of enhancing ervice QoS with application-layer approache, Service Overlay Network [2] purchae bandwidth from network domain to build ervice network which guarantee quality for QoS-enitive ervice. Thi propoal relie on bandwidth proviioning from the underlying domain to meet performance requirement of thee ervice. A another repreentative piece in thi area, OverQoS [22] aim at improving the perceived QoS of a eion by prioritizing packet within the eion itelf, other than improving performance for high-priority eion at the cot of low-priority eion. In thi way, it reduce the lo rate of important packet at the expene of le important one. Overlay bandwidth allocation ha been utilized to achieve differentiation of ervice quality toward different peer [7], [9], or to improve the overall performance in peer-to-peer eion [23], [24], [25]. In the former cae, Clevenot et al. [9] formulate the bandwidth allocation problem in a multi-cla peer-to-peer network into ytem of differential equation. They mainly addre the problem in tatic etting with a centralized olution, without conidering any peer dynamic. In our work, we achieve optimal bandwidth allocation by maximizing the overall utilitie in a convex program. Compared to previou work that ue optimization model to improve performance uch a maximizing throughput or minimizing cot in overlay multicat [23], [24], [25], our optimization model i tailored to the pecial requirement of ervice differentiation acro multiple peer-to-peer eion in heterogeneou peer-to-peer network. We have alo derived a fully ditributed protocol to achieve optimality, a well a to adapt to network dynamic. Thee realitic concern have not been addreed in previou optimization-baed approache, mot of which are largely theoretical in nature. Finally, in Divere, we have introduced overlay cheduling algorithm to achieve better ervice differentiation. Baed on our knowledge, thi i the firt paper that invetigate benefit of applying priority cheduling at the application layer in a peer-to-peer network. Combining overlay cheduling with optimal bandwidth allocation, we take advantage of every tool at our dipoal within the application layer, in order to provide differentiated ervice qualitie for multiple concurrent peer-topeer eion with different performance requirement. VII. CONCLUSION We conclude thi paper with the belief that applicationlayer ervice differentiation i an effective mechanim to compenate the lack of uch upport in the current IP Internet infratructure. Divere pioneer thi direction of reearch, which addree the challenge of providing differentiated ervice qualitie for peer-to-peer communication eion over the bet effort Internet. In Divere, it optimal bandwidth allocation algorithm efficiently contruct optimal eion topologie that maximize priority-baed utilitie. In addition, priority cheduling i applied at the peer in the application layer, which further improve the ervice quality experienced by high-priority eion. With example, analyi and experimental reult uing a realitic implementation, we have demontrated a complete Divere mechanim, that effectively diverifie ervice quality of different eion. Divere i fully ditributed, optimal and adaptive to dynamic at the ame

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Li, Efficient and Ditributed Computation of Maximum Multicat Rate, in Proc. of IEEE INFOCOM 25, March 25. APPENDIX I PROOF OF THEOREM Proof: Let, j : (i,j) A, S, be the optimal olution to (6). Introducing Lagrangian multiplier λ for the contraint in (7) and ν for contraint in (8), we obtain the KKT condition for the convex problem in (6) a follow (pp. 244, [4]): O i, = S j:(i,j) A x,λ,ν, λ ( O i ) =, () S j:(i,j) A ν =, j : (i,j) A, S, (2) (U ( ) µ j ) + λ ν =, j : (i,j) A, S. (3) For >, we have ν = from (2), and U ( ) µ j = λ from (3). Since U i increaing, trictly concave and twice differentiable, the invere function of U, i.e., U, exit. Then we have { if λ U () µ j, U (λ + µ j ) if λ < U () µ j. (4) Therefore, in order to achieve a ame marginal utility value λ for all the poitive, we alway decreae the larget marginal utility U ( ) µ j by increaing the correponding. In thi way, we are reducing the marginal utilitie toward the ame value of λ. If λ >, we will finally have S j:(i,j) A O i = baed on (); if λ =, all the marginal utilitie for poitive will be reduced to zero. Therefore, thi water-filling proce continue until O i i ued up, i.e., S j:(i,j) A = O i, or all the marginal utilitie, U ( ) µ j, j : (i,j) A, S, are zero. APPENDIX II PROOF OF THEOREM 2 Proof: We firt prove that the equence of vector {µ[k]} converge to it optimum µ. We know µ i bounded, a it i lower bounded by and alo upper bounded baed on the interior point aumption (pp. 226 [4]). Further, becaue the bandwidth variable are bounded, the dual ubgradient i:(i,j) A R, j T, S, are bounded too. Therefore, baed on Theorem 3 in [2] (pp. 26), by the ubgradient algorithm with tep length pecified by (), the Lagrangian multiplier vector {µ[k]} converge to µ. Then under the aumption that U i increaing, trictly concave and twice differentiable, U exit and i continuou and one-to-one. Baed on Eq. (4) in Appendix I, given µ[k], there i a unique maximizer x[k] for the Lagrangian ubproblem in (5). Therefore, we have x = g(µ), where g i

13 a continuou function decided by (4). Let x be the unique maximizer of the Lagrangian ubproblem in (5) for µ, i.e., x = g(µ ). Baed on the KKT condition for convex program P in (), we know an optimal olution to P i alo a maximizer to it Lagrangian ubproblem in (5) with µ (pp. 244, [4]). Therefore, x i the unique optimal olution to P. Further, ince g i a continuou function, we conclude that the equence x[k] converge to the primal optimum x. protocol deign. Chuan Wu. Chuan Wu received her B.Engr. and M.Engr. degree from Department of Computer Science and Technology, Tinghua Univerity, China, in 2 and 22, repectively. She i currently a Ph.D. candidate at the Department of Electrical and Computer Engineering, Univerity of Toronto, Canada. Her reearch interet include ditributed algorithm and protocol deign to improve Quality of Service of overlay multicat application. She i particularly intereted in deriving inight from optimization and game theory to guide practical Baochun Li. Baochun Li received hi B.Engr. degree in 995 from Department of Computer Science and Technology, Tinghua Univerity, China, and hi M.S. and Ph.D. degree in 997 and 2 from the Department of Computer Science, Univerity of Illinoi at Urbana-Champaign. Since 2, he ha been with the Department of Electrical and Computer Engineering at the Univerity of Toronto, where he i currently an Aociate Profeor. He hold the Nortel Network Junior Chair in Network Architecture and Service ince October 23, and the Bell Univerity Laboratorie Chair in Computer Engineering ince July 25. In 2, he wa the recipient of the IEEE Communication Society Leonard G. Abraham Award in the Field of Communication Sytem. Hi reearch interet include application-level Quality of Service proviioning, wirele and overlay network. He i a enior member of IEEE, and a member of ACM. Hi addre i bli@eecg.toronto.edu.