Celerity: A Low-Delay Multi-Party Conferencing Solution

Transcription

1 Ceerity: A Low-Deay Muti-Party Conferencing Soution Xiangwen Chen Dept. of Information Engineering The Chinese University of Hong Kong Yao Zhao Acate-Lucent Minghua Chen Dept. of Information Engineering The Chinese University of Hong Kong Yunnan Wu Facebook Inc. Baochun Li Dept. of Eectrica and Computer Engineering The University of Toronto Jin Li Microsoft Research ABSTRACT In this paper, we attempt to revisit the probem of muti-party conferencing from a practica perspective, and to rethink the design space invoved in this probem. We beieve that an emphasis on ow end-to-end deays between any two parties in the conference is a must, and the source sending rate in a session shoud adapt to bandwidth avaiabiity and congestion. We present Ceerity, a muti-party conferencing soution specificay designed to achieve our objectives. It is entirey Peer-to-Peer (P2P), and as such eiminating the cost of maintaining centray administered servers. It is designed to deiver video with ow end-to-end deays, at quaity eves commensurate with avaiabe network resources over arbitrary network topoogies where bottenecks can be anywhere in the network. This is in contrast to commony assumed P2P scenarios where bandwidth bottenecks reside ony at the edge of the network. The highight in our design is a distributed and adaptive rate contro protoco, that can discover and adapt to arbitrary topoogies and network conditions quicky, converging to efficient ink rate aocations aowed by the underying network. In accordance with adaptive ink rate contro, source video encoding rates are aso dynamicay controed to optimize video quaity. We have impemented Ceerity in a prototype system, and demonstrate its superior performance over existing soutions in a oca experimenta testbed and over the Internet. Categories and Subject Descriptors C.2.4 [COMPUTER-COMMUNICATION NETWORKS]: Distributed System Distributed appications; H.4.3 [INFORMATION The area chair coordinating the review of this manuscript and approving it for pubication was Prof. Wei Tsang Ooi. This work was partiay supported by the Genera Research Fund grants (Project No. 4118, 41129, 4111, and 41111) and an Area of Exceence Grant (Project No. AoE/E-2/8), a estabished under the University Grant Committee of the Hong Kong SAR, China, as we as two gift grants from Microsoft and Cisco. Permission to make digita or hard copies of a or part of this work for persona or cassroom use is granted without fee provided that copies are not made or distributed for profit or commercia advantage and that copies bear this notice and the fu citation on the first page. To copy otherwise, to repubish, to post on servers or to redistribute to ists, requires prior specific permission and/or a fee. MM 11, November 28 December 1, 211, Scottsdae, Arizona, USA. Copyright 211 ACM /11/11...$1.. SYSTEMS APPLICATIONS]: Communications Appications video conferencing Genera Terms: Agorithm, Design, Experimentation, Performance Keywords: Peer-to-peer, Muti-party video conferencing, Low deay, Utiity maximization, Arbitrary network topoogy 1. INTRODUCTION With the avaiabiity of front-facing cameras in high-end smartphone devices (such as the Samsung Gaaxy S and the iphone 4), notebook computers, and HDTVs, muti-party video conferencing, which invoves more than two participants in a ive conferencing session, has attracted a significant amount of interest from the industry. Skype, for exampe, has recenty aunched a monthy-paid service supporting muti-party video conferencing in its atest version (Skype 5) [1]. Skype video conferencing has aso been recenty supported in a range of new Skype-enabed teevisions, such as the Panasonic VIERA series, so that fu-screen high-definition video conferencing can be enjoyed in one s iving room. We argue that these new conferencing soutions have the potentia to provide an immersive human-to-human communication experience among remote participants. Such an argument has been corroborated by many industry eaders: Cisco predicts that video conferencing and tee-presence traffic wi increase ten-fod between [2]. Whie traffic fows in a ive muti-party conferencing session are fundamentay represented by a muti-way communication process, today s design of muti-party video conferencing systems are engineered in practice by composing communication primitives (e.g., transport protocos) over uni-directiona feed-forward inks, with primitive feedback mechanisms such as various forms of acknowedgments in TCP variants or custom UDP-based protocos. We beieve that a high-quaity protoco design must harness the fu potentia of the muti-way communication paradigm, and must guarantee the stringent requirements of ow end-to-end deays, with the highest possibe source coding rates that can be supported by dynamic network conditions over the Internet. From the industry perspective, known designs of commerciay avaiabe muti-party conferencing soutions are either argey serverbased, e.g., Microsoft Office Communicator, or are separated into mutipe point-to-point sessions (this approach is caed Simucast), e.g., Appe ichat. Server-based soutions are susceptibe to centra resource bottenecks, and as such scaabiity becomes a main concern when mutipe conferences are to be supported concurrenty. In the Simucast approach, each user spits its upink bandwidth equay among a receivers and streams to each receiver separatey. Though simpe to impement, Simucast suffers from poor quaity

2 of service. Specificay, peers with ow upoad capacity are forced to use a ow video rate that degrades the overa experience of the other peers. In the academic iterature, there are recenty severa studies on peer-to-peer (P2P) video conferencing from a utiity maximization perspective [3 8]. Among them, Li et a. [3] and Chen et a. [4] may be the most reated ones to this work (we ca their unified approach Mutuacast). They have tried to support content distribution and muti-party video conferencing in muticast sessions, by maximizing aggregate appication-specific utiity and the utiization of node upink bandwidth in P2P networks. Specific depth-1 and depth-2 tree topoogies have been constructed using tree packing, and rate contro was performed in each of the tree-based oneto-many sessions. However, they ony considered the imited scenario where bandwidth bottenecks reside at the edge of the network, whie in practice bandwidth bottenecks can easiy reside in the core of the network [9, 1]. Further, a existing industria and academic soutions, incuding Mutuacast, did not expicity consider bounded deay in designs, and can ead to unsatisfied interactive conferencing experience. 1.1 Contribution In this paper, we reconsider the design space in muti-party video conferencing soutions, and present Ceerity, a new muti-party conferencing soution specificay designed to maintain ow end-to-end deays whie maximizing source coding rates in a session. Ceerity has the foowing saient features: It operates in a pure P2P manner, and as such eiminating the cost of maintaining centray administered servers. It can deiver video at quaity eves commensurate with avaiabe network resources over arbitrary network topoogies, whie maintaining bounded end-to-end deays. It can automaticay adapt to unpredictabe network dynamics, such as cross traffic and abrupt ink faiures, aowing smooth conferencing experience. Enabing the above features for muti-party conferencing is chaenging. First, it requires a new formuation that aows systematic soution design over arbitrary network capacity constraints. In contrast, existing P2P system design works with performance guarantee commony assume bandwidth bottenecks reside at the edge of the network. Second, maximizing session rates subject to bounded deay is known to be NP-Compete and hard to sove approximatey [11]. We take a practica approach in this paper that expores a 2-hop deay-bounded overay trees with poynomia compexity. Third, detecting and reacting to network dynamics without a priori knowedge of the network conditions are non-trivia. We use both deay and oss as congestion measures and adapt the session rates with respect to both of them, aowing eary detection and fast response to unpredictabe network dynamics. The highight in our design is a distributed rate contro protoco, that can discover and adapt to arbitrary topoogies and network conditions quicky, converging to efficient ink rate aocations aowed by the underying network. In accordance with the adaptive ink rate contro, source video encoding rates are aso dynamicay controed to optimize video quaity in arbitrary and unpredictabe underay network conditions. The design of Ceerity is argey inspired by our new formuation that specificay takes into account arbitrary network capacity constraints and aows us to expore design space beyond those in existing soutions. Our formuation is overay-ink based and has a number of variabes inear in the number of overay inks. This is Notation Definition L Set of a physica inks V Set of conference participating nodes E Set of directed overay inks C Capacity of the physica ink a,e Whether overay ink e passes physica ink c m y Overay ink rates of stream m, c m = [c m,e, e E] Tota overay ink traffics, y= M m=1 c m D Deay bound R m (c m, D) Session m s rate within the deay bound D q (z) Price function of vioating ink s capacity constraint p Lagrange mutipier of ink s capacity constraint G (c, p) Lagrange function of variabes c and p Note: we use bod symbos to denote vectors, e.g., c=[c 1,..., c M ]. Tabe 1: Key notations. a significant reduction as compared to the number of variabes exponentia in the number of overay inks in an otherwise tree-based formuation. We beieve our approach is appicabe to other P2P system probems, to aow soution design beyond the common assumption in P2P scenarios that the bandwidth bottenecks reside ony at the edge of the network. We have impemented a prototype Ceerity system using C++. By extensive experiments in a oca experimenta testbed and on the Internet, we demonstrate the superior performance of Ceerity over state-of-the-art soutions Simucast and Mutuacast. Due to space imitation, a proofs and pseudo-codes are in our technica report [12]. 2. PROBLEM FORMULATION AND CELER- ITY OVERVIEW One way to design a muti-party conferencing system is to formuate its fundamenta design probem, expore powerfu theoretica techniques to sove the probem, and use the obtained insights to guide practica system designs. In this way, we can aso be cear about potentia and imitation of the designs, aowing easy system tuning and further systematic improvements. Tabe 1 ists the key notations used in this paper. 2.1 Settings Consider a network modeed as a directed graph G=(N,L), where N is the set of a physica nodes, incuding conference participating nodes and other intermediate nodes such as routers, and L is the set of a physica inks. Each ink L has a nonnegative capacity C and a nonnegative propagation deay d. Consider a muti-party conferencing system over G. We use V N to denote the set of a conference participating nodes. Every node in V is a source and at the same time a receiver for every other nodes. Thus there are totay M V sessions of (audio/video) streams. Each stream is generated at a source node, say v, and needs to be deivered to a the rest nodes in V {v}, by using overay inks between any two nodes in V. An overay ink (u, v) means u can send data to v by setting up a TCP/UDP connection, aong an underay path from u to v preassigned by routing protocos. Let E be the set of a directed overay inks. For a e E and L, we define 1, if overay ink e passes physica ink ; a,e =, otherwise. (1)

3 The physica ink capacity constraints are then expressed as a T y= a,e e E m=1 M c m,e C, L, where c m,e denotes the rate aocated to session m on overay ink e and a T y describes the tota overay traffic passing through physica ink. Remark: In our mode, the capacity botteneck can be anywhere in the network, not necessariy at the edges. This is in contrast to a common assumption made in existing P2P works that the access inks of participating nodes are the ony capacity bottenecks. 2.2 Probem Formuation In a muti-party conferencing system, each session source broadcasts its stream to a receivers over a compete overay graph on which every ink e has a rate c m,e and a deay L a,e d. For smooth conferencing experience, the tota deay of deivering a packet from the source to any receiver, traversing one or mutipe overay inks, cannot exceed a deay bound D. A fundamenta design probem is to maximize the overa conferencing experience, by propery aocating the overay ink rates to the streams subject to physica ink capacity constraints. We formuate the probem as a network utiity maximization probem: M MP : max c U m (R m (c m, D)) (2) m=1 s.t. a T y C, L. (3) The optimization variabes are c and the constraints in (3) are the physica ink capacity constraints. R m (c m, D) denotes session m s rate that we obtain by using resource c m within the deay bound D, and is a concave function of c m as we wi show in Coroary 1 in the next section. The objective is to maximize the aggregate system utiity. U m (R m ) is an increasing and stricty concave function that maps the stream rate to an appication-specific utiity. For exampe, a commony used video quaity measure Peak Signa-to-Noise Ratio (PSNR) can be modeed by using a ogarithmic function as the utiity [4] 1. With these settings and observations, U m (R m ) is concave in c and the probem MP is a concave optimization probem. Remarks: (i) The formuation of MP is an overay ink based formuation in which the number of variabes per session is E and thus at most V 2. One can write an equivaent tree-based formuation for MP but the number of variabes per session wi be exponentia in E and V. (ii) Existing soutions, such as Simucast and Mutuacast, can be thought as agorithms soving specia cases of the probem MP. For exampe, Simucast can be thought as soving the probem MP by using ony the 1-hop tree to broadcast content within a session. Mutuacast can be thought as soving a specia case of the probem MP (with the upinks of participating nodes being the ony capacity botteneck) by packing certain depth-1 and depth-2 trees within a session. 2.3 Ceerity Overview Ceerity buids upon two main modues to maximize the system utiity: (1) a deay-bounded video deivery modue to distribute video at high rate given overay ink rates (i.e., how to compute and achieve R m (c m, D)); (2) a ink rate contro modue to determine c m. 1 Using ogarithmic functions aso guarantees (weighted) proportiona fairness among sessions and thus no session wi starve at the optima soution [13]. Video deivery under known ink constraints: This probem is simiar to the cassic muticast probem, and packing spanning (or Steiner) trees at the muticast source is a popuar soution. However, the unique deay-bounded requirement in muti-party conferencing makes the probem more chaenging. We introduce a deay-bounded tree packing agorithm to tacke this probem (detaied in Section 3). Link rate contro: In principe, one can first infer the network constraints and then sove the probem MP centray. However, directy inferring the constraints potentiay requires knowing the entire network topoogy and is highy chaenging. In Ceerity, we resort to design adaptive and iterative agorithms for soving the probem MP in a distributed manner, without a priori knowedge of the network conditions (detaied in Section 4). We high-evey expain how Ceerity works in a 4-party conferencing exampe in Fig. 1. We focus on session A, in which source A distributes its stream to receivers B, C, and D, by packing deaybounded trees over a compete overay graph shown in the figure. We focus on source A and one overay ink (B,C), which represents a UDP connection over an underay path B to E to F to C. Other overay inks and other sessions are simiar. Figure 1: An iustrating exampe of 4-party (A, B, C, and D) conferencing over a dumbbe underay topoogy. E and F are two routers. Soid ines represent underay physica inks. To make the graph easy to read, we use one soid ine to represent a pair of directed physica inks. Dash ines represent overay inks. We first describe the contro pane operations. For the overay ink (B,C), the head node B works with the tai node C to periodicay adjust the session rate c A,(B,C) according to Ceerity s ink rate contro agorithm. Such adjustment utiizes contro-pane information that source A piggybacks with data packets, and oss and deay statistics experienced by packets traveing from B to C. We show such oca adjustments at every overay ink resut in gobay optima session rates. The head node B aso periodicay reports to source A the session rate c A,(B,C) and the end-to-end deay from B to C. Based on these reports from a overay inks, source A periodicay packs deay-bounded trees using Ceerity s tree-packing agorithm, cacuates necessary contro-pane information, and deivers data and the contro-pane information aong the trees. The data pane operations are simpe. Ceerity uses deay-bounded trees to distribute data in a session. Nodes on every tree forward packets from its upstream parent to its downstream chidren, foowing the next-chidren tree-routing information embedded in the packet header. Ceerity s tree-packing agorithm guarantees that (i) packets arrive at a receivers within the deay bound, and (ii) the tota rate of a session m passing through an overay ink e does not exceed the aocated rate c m,e. In the foowing two sections, we first present the designs of the two main modues in Ceerity. We then describe how they are impemented in physica peers in Section 5.

4 PACKING DELAY-BOUNDED TREES Given overay ink rate vector c m and deay for every overay ink e (i.e., L a,e d ), achieving the maximum broadcast/muticast stream rate under a deay bound D is a chaenging probem. A genera way to expore the broadcast/muticast rate under deay bounds is to pack deay-bounded Steiner trees. However, such probem is NPhard [14]. Moreover, the number of deay-bounded Steiner trees to consider is in genera exponentia in the network size. In this paper, we pack 2-hop deay-bounded trees in an overay graph of session m, denoted byd m, to achieve a good stream rate under a deay bound. Note by graph theory notations, a 2-hop tree has a depth at most 2. Packing 2-hop trees is easy to impement. It aso expores a overay inks between source and receiver and between receivers, thus trying to utiize resource efficienty. In fact, it is shown in [3, 4] that packing 2-hop muticast trees suffices to achieve the maximum muticast rate for certain P2P topoogies. We eaborate our tree-packing scheme in the foowing. We first define the overay graphd m. GraphD m is a directed acycic graph with two ayers; one exampe of such graph is iustrated in Fig. 2a. In this exampe, consider a session with a source s, three receivers 1, 2, 3. For each receiver i, we draw two nodes, r i and t i, in the graphd m ; t i modes the receiving functionaity of node i and r i modes the reaying functionaity of node i. Suppose that the prescribed ink bit rates are given by the vector c m, with the capacity for ink (i, j) being c m,(i, j). Then ind m, the ink from s to r i has capacity c m,(s,i), the ink from r i to t j (with i j) has capacity c m,(i, j), and the ink from r i to t i has infinite capacity. If the propagation deay of an edge (i, j) exceeds the deay bound, we do not incude it in the graph. If the propagation deay of a two-hop path s i j exceeds the deay bound, we omit the edge from r i to t j from the graph. As a resut, every path from s to any receiver t i in the graph has a path propagation deay within the deay bound. Over such 2-ayer sub-graphd m, we pack 2-hop trees connecting the source and every receiver using the greedy agorithm proposed in [15]. Beow we simpy describe the agorithm and more detais can be found in [15]. Assuming a edges have unit-capacity and aowing mutipe edges for each ordered node pair. The agorithm packs unit-capacity trees one by one. Each unit-capacity tree is constructed by greediy constructing a tree edge by edge starting from the source and augmenting towards a receivers. It is simiar to the greedy treepacking agorithm based on Prim s agorithm. The distinction ies in the rue of seecting the edge among a potentia edges. The edge whose remova eads to east reduction in the muticast capacity of the residua graph is chosen in the greedy agorithm. We show an exampe to iustrate how the tree packing agorithm works in detais in our technica report [12, Sec. 3]. The above greedy agorithm is very simpe to impement and its practica impementation detais are further discussed in Section 5. Utiizing the specia structure of the graphd m, we obtain performance guarantee of the agorithm as foows (a) 1 2 Figure 2: (a) Iustration of the directed acycic sub-graph over which we pack deay-bounded 2-hop trees. (b) Critica cut exampe. Source s and its two receivers t 1, t 2 are connected over a directed graph. The number associated with a ink represents its capacity. (b) Theorem 1. The tree-packing agorithm in [15] achieves the minimum of the min-cuts separating the source and receivers in D m and is expressed as R m (c m, D)=min j min{c m,(s,i), c m,(i, j) }. (4) Furthermore, the agorithm has a running time of O( V E 2 ). i Hence, our tree-packing agorithm achieves the maximum deaybounded muticast rate over the 2-ayer subgraphd m. The achieved rate R m (c m, D) is a concave function of c m as summarized beow. Coroary 1. The deay-bounded muticast rate R m (c m, D) obtained by our tree-packing agorithm is a concave function of the overay ink rates c m. 4. OVERLAY LINK RATE CONTROL 4.1 Considering Both Deay and Loss We revise origina formuation to design our ink rate contro agorithm with both queuing deay and oss rate taken into account. Adapting ink rates to both deay and oss aows eary detection and fast response to network dynamics. Consider the foowing formuation with a penaty term added into the objective function of the probem MP: MP EQ : max c U(c) = M U m (R m (c m, D)) m=1 L a T y q (z) dz, (5) s.t. a T y C, L, (6) where a T y q (z) dz is the penaty associated with vioating the capacity constraint of physica ink L, and we choose q (z) = (z C ) +, (7) z where (a) + = max{a, }. If a the constraints are satisfied, then the second term in (5) vanishes; if instead some constraints are vioated, then we charge some penaty for doing so. Remark: (i) The probem MP-EQ is equivaent to the origina probem MP. Because any feasibe soution c of these two probems must satisfy a T y C, and consequenty the penaty term in the probem MP-EQ vanishes. Therefore, any optima soution of the origina probem MP must be an optima soution of the probem MP-EQ and vice versa. (ii) It can be verified that a T y L q (z) dz is a concave function in c; hence,u(c) is a inear combination of concave functions and is concave. However, because R m (c m, D) is the minimum min-cut of the overay graphd m with ink rates being c m,u(c) is not a differentiabe function [16]. We appy Lagrange dua approach to design distributed agorithms for the probem MP-EQ. The advantage of adopting distributed rate contro agorithms in our system is that it aows robust adaption upon unpredictabe network dynamics.

5 The Lagrange function of the probem is given by: G (c, p) M U m (R m (c m, D)) m=1 L L a T y q (z) dz p ( a T y C ), (8) where p is the Lagrange mutipier associated with the capacity constraint in (6) of physica ink. p can be interpreted as the price of using ink. Since the probem MP-EQ is a concave optimization probem with inear constraints, strong duaity hods and there is no duaity gap. Any optima soution of the probem and one of its corresponding Lagrangian mutipier is a sadde point of G (c, p) and vice versa. Thus to sove the probem MP-EQ, it suffices to design agorithms to pursue sadde points ofg (c, p). 4.2 A Loss-Deay Based Prima-Subgradient- Dua Agorithm There are two issues to address in designing agorithms for pursuing sadde points of G (c, p). First, the utiity function U(c) (and consequenty G (c, p)) is not everywhere differentiabe. Second,U(c) (and consequentyg (c, p)) is not stricty concave in c, thus distributed agorithms may not converge to the desired sadde points under muti-party conferencing settings [4]. To address the first concern, we use subgradient in agorithm design. To address the second concern, we provide a convergence resut for our designed agorithm. To proceed, we first compute subgradients of U(c). The proposition beow presents a usefu observation. Proposition 1. A subgradient ofu(c) with respect to c m,e for any e E and m=1,... M is given by U m (R m) R m c m,e L a,e (a T y C ) + a T y where Rm c m,e is a subgradient of R m (c m, D) with respect to c m,e. Motivated by the pioneering work of Arrow, Hurwicz, and Uzawa [17] and the foowup works [18] [19], we propose to use the foowing prima-subgradient-dua agorithm to pursue the sadde point ofg (c, p): eǫm, m=1,...m, ǫl, Prima-Subgradient-Dua Link Rate Contro Agorithm: c (k+1) m,e p (k+1) = c (k) m,e+α L [ U m ( ) R (k) R (k) m m c m,e a,e (a T y (k) C ) + a T y(k) = p (k) + 1 [ ] a T y (k) + C C p (k) a,e p (k) whereα>represents a constant step size for a iterations, and [b] + max(, b), a ; a= b, a>. L + c (k) m,e (9) (1) We have the foowing observations for the agorithm in (9)-(1): It is known that L a,e (a T y C ) + a T z can be interpreted as the packet oss rate observed at overay ink e [2]. The intuitive expanation is as foows. The term (a T y C ) + is the excess traffic rate offered to physica ink ; thus (at y C ) + a T y modes the fraction of traffic that is dropped at. Assuming the packet oss rates are additive (which is a reasonabe assumption for ow packet oss rates), the tota packet oss rates seen by the overay ink e is given by L a,e (a T y C ) + a T y. It is aso known that p updating according to (1) can be interpreted as queuing deay at physica ink [21]. Intuitivey, if the incoming rate a T y> C, then it introduces an additiona queuing deay of at y C C at ink. If otherwise a T y C, then the queueing deay is reduced by an amount of C a T y C uness hitting zero. The tota queuing deay observed by the overay ink e is simpy the sum L a,e p. It turns out that the utiity function, the subgradients, packet oss rate and queuing deay are sufficient statistics to update c m,e independenty of the updates of other ink rates. This way, we can sove the probem MP-EQ without knowing the physica network topoogy and physica ink capacities. The agorithm in (9)-(1) is simiar to the standard prima-dua agorithm, but since U(c) is not differentiabe everywhere, we use subgradient instead of gradient in updating the overay ink rates c. If we fix the dua variabes p, then the agorithm in (9) corresponds to the standard subgradient method [22]. It maximizes a non-differentiabe function in a way simiar to gradient methods for differentiabe functions in each step, the variabes are updated in the direction of a subgradient. However, such a direction may not be an ascent direction; instead, the subgradient method reies on a different property. If the variabe takes a sufficienty sma step aong the direction of a subgradient, then the new point is coser to the set of optima soutions. Estabishing convergence of subgradient agorithms for saddepoint optimization is in genera chaenging [18]. We expore convergence properties for our prima-subgradient-dua agorithm in the foowing theorem. Theorem 2. Let (c, p ) be a sadde point ofg (c, p), andḡ (k) be the average function vaue obtained by the agorithm in (9)-(1) after k iterations: Ḡ (k) 1 k 1 G ( c (k), p (k)). k i= Suppose U m(r m (c m )) Ū, m=1,..., M, where Ū is a constant, then we have B 1 2αk 2 2 α Ḡ(k) G (c, p ) B 2 2k max L C 1, where B 1 = c () c 2 and B2 = [ p () p ] T diag (C, L) [ p () p ] are two positive distances depending on (c (), p () ), and is a positive constant depending on Ū and (c (), p () ). Remarks: (i) The resuts bound the time-average Lagrange function vaue obtained by the agorithm to the optima in terms of distances of the initia iterates (c (), p () ) to a sadde point. In particuar, the averaged function vauesḡ (k) converge to the sadde point vaueg (c, p ) within a gap of max ( ) α, max L C 1 2, at a rate of 2 1/k. (ii) The requirement of the utiity function is easy to satisfied; one exampe is U m (z)=og(z+ǫ) withǫ >. (iii) Our resuts generaize the one in [18] in the sense that the resut in [18] ony appies to the case of uniform step size, whie we aow different p to update with different step size 1 C, which is critica for p to be interpreted as queuing deay and thus practicay measurabe. Our resuts aso have ess stringent requirement on the utiity function

6 than the one in [18]. (iv) Athough the resuts may not warranty convergence in the strict sense, our experiments over LAN testbed and on the Internet in Section 6 show the agorithm quicky stabiizes around optima operating points. Obtaining stronger convergence resuts that confirm our practica observations are of great interests and is eft for future work. 4.3 Computing Subgradients of R m (c m, D) A key to impementing the Prima-Subgradient-Dua agorithm is to obtain subgradients of R m (c m, D). We first present some preiminaries on subgradients, as we as concepts for computing subgradients for R m (c m, D). Definition 1. Given a convex function f, a vectorξis said to be a subgradient of f at x dom f if f (x ) f (x)+ξ T (x x), x dom f, where dom f={x R n f (x) < } is the domain of f. For a concave function f, f is a convex function. A vectorξis said to be a subgradient of f at x if ξ is a subgradient of f. Next, we define the notion of a critica cut. For session m, et its source be s m and receiver set be V m V {s m }. A partition of the vertex set, V= Z Z with s m Z and t Z for some t V m, determines an s m -t-cut. Define δ(z) { (i, j) E i Z, j Z } be the set of overay inks originating from nodes in set Z and going into nodes in set Z. Define the capacity of cut (Z, Z) as the sum capacity of the inks inδ(z): ρ(z) c m,e. e δ(z) Definition 2. For session m, a cut (Z, Z) is an s m -V m critica cut if it separates s m and any of its receivers andρ(z)= R m (c m, D). and data muticast engine. Fig. 3 describes the reationship between these components and where they physicay reside. In the foowing, we describe the functionaity impemented by peers, some critica impementations, and operation overhead. 5.1 Peer Functionaity In our impementation, a peers perform the foowing functions: Peers in every broadcast tree forward packets from its upstream parent to its downstream chidren. Sufficient information about the chidren is embedded in the packet header, for a packet to become sef-routing from the source to a eaf nodes in a tree. Every 2 ms, each peer cacuates the oss rate and queuing deay of its incoming inks and updates the rates of these inks based on the ink rate contro agorithm. The peer then sends the updated rates to the corresponding senders to take effect. Every 3 ms, each peer sends the ink state (incuding aocated rate and Round Trip Time) of a its outgoing inks for each session to the session source. Upon receiving ink states from a the inks, the source of each session uses the received ink rates and the deay information to pack a new set of deay-bounded trees, and starts transmitting session packets aong these trees. We set the deay bound to be 2 ms when packing deay-bounded trees in our impementation. When a source packs deay-bounded trees, it aso cacuates one critica cut and the derivative of the utiity for its session based on the aocated ink rates. The source embeds the information about the critica cut and the derivative of the utiity in the header of outgoing packets. When these packets are received, a peer earns the derivative of the utiity and whether a ink beongs to the critica cut or not; it then adjusts the ink rate accordingy. We show an exampe to iustrate the concept of critica cut. In Fig. 2b, s is a source, and t 1, t 2 are its two receivers. The minimum of the min-cuts among the receivers is 2. For the cut ({s, r 1, r 2, t 1 },{t 2 }), itsδ({s, r 1, r 2, t 1 }) contains inks (r 1, t 2 ) and (r 2, t 2 ), each having capacity one. Thus the cut ({s, r 1, r 2, t 1 },{t 2 }) has a capacity of 2 and it is an s (t 1, t 2 ) critica cut. With necessary preiminaries, we turn to compute subgradients of R m (c m, D). Since R m (c m, D) is the minimum min-cut of s m and its receivers over the overay graphd m, it is known that one of its subgradients can be computed in the foowing way [16]. c 1,...,c M Find an s m -V m critica cut for session m, denote it as (Z, Z). Note there can be mutipe s m -V m critica cuts in graphd m, and it is sufficient to find any one of them. A subgradient of R m (c m, D) with respect to c m,e is given by R m (c m, D) 1, if e δ(z); = (11) c m,e, otherwise. 5. PRACTICAL IMPLEMENTATION Using the asynchronous networking paradigm supported by the asynchronous I/O ibrary (caed asio) in the Boost C++ ibrary, we have impemented a prototype of Ceerity with about 17, ines of code in C++. Ceerity consists of three main functiona components: ink rate contro modue, tree-packing and critica cut cacuation modue, Figure 3: System architecture of Ceerity. 5.2 Critica Cut Cacuation The cacuation of critica cuts, i.e., the subgradient of R m (c m, D), is by the source of each session. It is the key to our impementation of the prima-subgradient-dua agorithm. There can be mutipe critica cuts in one session, but it is sufficient to find any one of them. After the source coects the aocated session rates from a overay inks, it cacuates the min-cut from itsef to every receiver, and records the min-cut. Then the source compares the capacities of these min-cuts; the cut with the smaest capacity is a critica cut.

7 5.3 Utiity Function With respect to the utiity function in our impementation, the PSNR (peak signa-to-noise ratio) metric is the de facto standard criterion to provide objective quaity evauation in video processing. The PSNR of a video stream coded at a rate z can be approximated by a ogarithmic functionβ og(z+δ) [4], in which a higher β represents videos with a arger amount of motion. δ is a sma positive constant to ensure the function has a bounded derivative for z. Due to this observation, we use a ogarithmic utiity function in our impementation. 5.4 Opportunistic Loca Loss Recovery Providing effective oss recovery in a deay-bounded reiabe broadcast scenario, such as muti-party conferencing, is known to be chaenging [23]. It is hard for error contro coding to work efficienty, since different receivers in a session may experience different oss rates and thus choosing proper coding parameters to avoid unnecessary waste of throughput is non-trivia. If re-broadcasting the ost-packets is in use, it introduces additiona deay and may cause packets missing deadines and become useess. In our impementation, we use network coding [23] [24] to aow opportunistic oca oss recovery. For each overay ink e, if the trees of a session m do not exhaust c m,e, the overay-ink rate dedicated for the session, then we send coded packets (i.e., inear combination of received packets of corresponding session) over such ink e. As such, receiver of the overay ink e can recover the packets that are ost on ink e ocay by using the network coded packets. This way, Ceerity provides certain fexibe oca oss recovery capabiity without incurring deay due to retransmission. 5.5 Fast Bootstrapping Simiar to TCP s Sow Start strategy, we impement a method in Ceerity caed quick start to quicky ramp up the session rates during conference initiaization stage. The purpose is to bootstrap the system to cose-to-optima operating points when the conference just starts, during which period peers are joining the conference and nothing significant is going on. We achieve this by using arge β in the utiity functions and arge step sizes in ink rate adaptation during the first 3 seconds. After the initiaization stage, we resetβand the step sizes to proper vaues and aow our system converge graduay, avoiding unnecessary performance fuctuation. 5.6 Operation Overhead There are two types of overhead in Ceerity: (i) packet overhead: each appication-ayer packet has a 46-byte header, containing critica cut information, derivative of the utiity, packet sequence number, coding vector, and timestamp. (ii) ink-rate contro and inkstate report overhead: every 2 ms, each peer adjusts the rates of its incoming inks and sends them to their corresponding upstream senders. In our impementation, such rate-contro overhead is.2 kbps per ink per session. For the ink state report overhead, each peer sends the ink state of a its outgoing inks for each session to the source of the session every 3 ms. In our impementation, for each peer, such ink-state report overhead is.158 kbps per ink per session. In Section 6.2, we report an overa operationa overhead of 3.9% in our 4-party Internet experiment. 6. EXPERIMENTS We evauate our prototype Ceerity system over a LAN testbed as we as over the Internet. The LAN experiments aow us to (i) stress-test Ceerity under various network conditions; (ii) see whether Ceerity meets the design goa deivering high deaybounded throughput and automaticay adapting to dynamics in the network; (iii) demonstrate the fundamenta performance gains over existing soutions, thus justifying our theory-inspired design. The Internet experiments aow us to further access Ceerity s superior performance over existing soutions in the rea word. 6.1 LAN Testbed Experiments We evauate Ceerity over a LAN testbed iustrated in Fig. 4, where four PC nodes (A, B,C, D) communicate over a LAN dumbbe topoogy. The dumbbe topoogy represents a popuar scenario of muti-party conferencing between branch offices. It is aso a tough topoogy existing approaches, such as Simucast and Mutuacast, fai to efficienty utiize the botteneck bandwidth and optimize system performance. Figure 4: The tough dumbbe topoogy of the experimenta testbed. Two conference participating nodes A and B are in one office and another twos nodes C and D are in a different office. The two offices are connected by directed inks between gateway nodes E and F, each ink has a capacity of.48 Mbps. Link propagation deays are negigibe. In our experiments, a four nodes run Ceerity. We run a fourparty conference for 1 seconds and evauate the system performance. In order to evauate Ceerity s performance in the presence of network dynamics, we reduce cross traffic and introduce ink faiures during the experiment. In particuar, we introduce an 8kpbs cross-traffic from node E to node F between the 3th second and the 5th second, reducing the avaiabe bandwidth between E and F from 48 kbps to 4 kbps. Further, starting from the 7th second, we disconnect the physica ink between A and E; this corresponds to a practica situation where node A suddeny cannot directy communicate with nodes outside the office due to middeware or configuration errors at the gateway E. Figs. 6a-6d show the sending rate of each session (one session originates from one node to a other three nodes). For comparison, we aso show the maximum achievabe rates by Simucast and Mutuacast, as we as the optima sending rate of each session cacuated by soving the probem in (2)-(3) using a centra sover. Fig. 6e shows the utiity obtained by Ceerity and its comparison to the optima. Fig. 6f shows the average end-to-end deay and packet oss rate of session A. Deay and oss performance of other sessions are simiar to those of session A. In the foowing, we expain the resuts according to three different experiment stages Absence of Network Dynamics We first ook at the first 3 seconds when there is no cross traffic or ink faiure. In this time period, the experimenta settings are symmetric for a participating peers; thus the optima sending rate for each session is 24 kbps. As seen in Figs. 6a-6d, Ceerity demonstrates fast convergence: the sending rate of each session quicky ramps up to 95% to the optima within 5 seconds. Fig. 6e shows that Ceerity quicky

8 Figure 5: Session A s trees used by Ceerity (upon convergence), Mutuacast and Simucast in the dumbbe topoogy, in the absence of network dynamics. achieves a cose-to-optima utiity. These observations indicate any other soution can at most outperform Ceerity by a sma margin. As a comparison, we aso pot the theoretica maximum rates achievabe by Simucast and Mutuacast in Figs. 6a-6d. We observe that within 2 seconds, our system aready outperforms the maximum rates of Simucast and Mutuacast. Upon convergence, Ceerity achieves sending rates that neary doube the maximum rate achievabe by Simucast and Mutuacast. This significant gain is due to that Ceerity can utiize the botteneck resource more efficienty, as expained beow. In Fig. 5, we show the trees for session A that are used by Ceerity, Mutuacast and Simucast in the dumbbe topoogy. As seen, Simucast and Mutuacast ony expore 2-hop trees satisfying certain structure, imiting their capabiity of utiizing network capacity efficienty. In particuar, their trees consumes the botteneck ink resource twice, thus to deiver one-bit of information it consumes two-bit of botteneck ink capacity. For instance, the tree used by Simucast has two branches A Cand A D passing through the botteneck inks between E and F, consuming twice the critica resource. Consequenty, the maximum achievabe rates of Simucast and Mutuacast are a 12 kbps. In contrast, Ceerity expores a 2-hop deay-bounded trees, and upon convergence utiizes the trees that ony consume botteneck ink bandwidth once, achieving rates that are cose to the optima of 24 kbps. Fig. 6f shows the average end-to-end deay and packet oss rate of session A. As seen, the oss rate and deay are high initiay, but decrease and stabiize to sma vaues afterwards. The high oss rate and deay are due to Ceerity increasing the rates aggressivey during the initiaization stage, in order to bootstrap the conference and expore network resource imits. Ceerity quicky earns and adapts to the network topoogy, ending up with using cost-effective trees to deiver data. After the initiaization stage, Ceerity adapts and converges graduay, avoiding unnecessary performance fuctuation that deteriorates user experience. By adapting to both deay and oss, we achieve ow oss rate upon convergence as compared to the case when ony oss is taken into account [25] Cross Traffic Between the 3th second and the 5th second, we introduce an 8kpbs cross-traffic from node E to node F. Consequenty, the avaiabe botteneck bandwidth between E and F decreases from 48 kbps to 4 kbps. We cacuate the optima sending rates during this time period to be 2 kbps for sessions A and B, and remain 24 kbps for sessions C and D. Seen in Figs. 6a-6d, Ceerity quicky adapts to the botteneck bandwidth reduction. Ceerity s adaptation is expected from its design, which infers from oss and deay the avaiabe resource and adapt accordingy. From Fig. 6f, we can see a spike in session A s packet oss rate around 3th second, at which time the avaiabe botteneck bandwidth reduces. The ink rate contro modues in Ceerity senses this increased oss rate, adjusts, and reports the reduced (overay) ink rates to node A. Upon receiving the reports, the tree-packing modue in Ceerity adjusts the source sending rate accordingy, adapting the system to a new cose-to-optima operating point. At 5th second, the cross traffic is removed and the avaiabe botteneck bandwidth between E and F restores to 48kbps. Ceerity aso quicky earns this change and adapts to operate at the origina point, evident in Figs. 6a-6b Link Faiure Between the 7th second and the 1th second, we disconnect the physica ink between A and E. Consequenty, node A cannot use the 2-hop threes with node C (D) being intermediate nodes; simiary node C (D) cannot use the 2-hop threes with node A being intermediate nodes. They can, however, sti use the trees with node B as intermediate nodes. We compute the theoretica optima sending rates during this time period to be 24 kbps for a sessions. We observe from Fig. 6a that node A s sending rate first drops immediatey upon ink faiure, then quicky adapts to the new operating point of around 12 kbps, ony haf of the theoretica optima. This is because Ceerity ony expores 2-hop trees for content deivery, whie in this case 3-hop trees (e.g., A B C D) are needed to achieve the optima. It is of great interest to expore beyond this 2-hop tree-packing imitation to further improve the performance without incurring excessive overhead. In Figs. 6d, we observe session D s rate first drops and then cimbs back. This is because session D happens to use trees with node A being an intermediate node right before the ink faiure. The faiure breaks these trees, and causes session D s rate to drop dramaticay. Ceerity adapts and switches to use trees with node B as the intermediate node. Consequenty, session D s rate graduay restores to around the optima. This observation shows the exceent adaptabiity of Ceerity to abrupt network condition changes. As a comparison, we observe that Simucast s maximum achievabe rates of session A, C, and D a drop to zero upon the ink faiure. This is because there is no direct overay ink between A and C (D) after the ink faiure. Consequenty, Simucast is not abe to broadcast the source s content to a the receivers in these sessions, resuting in zero session rates. 6.2 Internet Experiments Beside the prototype Ceerity system, we aso impement two prototype systems of Simucast and Mutuacast, respectivey. Both Ceerity and Mutuacast use the same og utiity functions in their rate contro modues. We evauate the performance of these systems in a four-party conferencing scenario over the Internet. We use four PC nodes that spread two continents and tree countries to form the conferencing scenario. Two of the PC nodes are in Hong Kong, one is in Redmond, Washington, US, and the ast one is in Toronto, Canada. This setting represents a common goba muti-party conferencing scenario. We run mutipe 15-minute four-party conferences using the prototype systems, in a one-by-one and intereaving manner. We seect one representative run for each system, and summarize their performance in Fig. 7. Figs. 7a-7d show the rate performance of each session. As seen, a the session rates in Ceerity quicky ramp up to near-stabe vaues within 5 seconds, and outperforms Simucast within 1 seconds. Upon stabiization, Ceerity achieves the best throughput performance among the three systems and Simucast is the worst. For instance, a the session rates in Ceerity is 2x of those in Simucast

9 Tota tree rate achieved by Ceerity Theoretica optima rate Maximum achievabe rate by Simucast Maximum achievabe rate by Mutuacast X traffic arrives X traffic departs Link fais (a) Rate Performance of Node A Tota tree rate achieved by Ceerity Theoretica optima rate Maximum achievabe rate by Simucast Maximum achievabe rate by Mutuacast X traffic arrives X traffic departs Link fais (b) Rate Performance of Node B Tota tree rate achieved by Ceerity Theoretica optima rate Maximum achievabe rate by Simucast Maximum achievabe rate by Mutuacast X traffic arrives X traffic departs Link fais (c) Rate Performance of Node C Tota tree rate achieved by Ceerity Theoretica optima rate Maximum achievabe rate by Simucast Maximum achievabe rate by Mutuacast X traffic arrives X traffic departs Link fais (d) Rate Performance of Node D utiity utiity vaue of session A utiity vaue of session B utiity vaue of session C utiity vaue of session D tota utiity vaue optima tota utiity vaue (e) Tota utiity of a sessions end to end deay(s) end to end oss rate average deay from node A to node B average deay from node A to node C average deay from node A to node D average oss rate from node A to node B average oss rate from node A to node C average oss rate from node A to node D (f) Average end-to-end deay and oss rate from node A to other nodes Figure 6: Performance of Ceerity over a dumbbe LAN testbed. (a)-(d): Sending rates and receiving rates of individua sessions. (e): Utiity vaue achieved compared to the optimum. (f): End-to-end deay and oss rate of session A. and Mutuacast, except in session C where Mutuacast is abe to achieve a higher rate than Ceerity. We further observe Ceerity s superior performance in Fig. 7e, which shows the aggregate session rates, and in Fig. 7f, which shows the tota achieved utiities. In both statistics, Ceerity outperforms the other two systems by a significant margin. Specificay, the aggregate session rate achieved by Ceerity is 2.5x of that achieved by Simucast, and is 1.8x of that achieved by Mutuacast. These resuts show that our theory-inspired soution Ceerity can aocate the avaiabe network resource to best optimize the system performance. Mutuacast aims at simiar objective but ony works the best in scenarios where bandwidth bottenecks reside ony at the edge of the network [4]. Figs. 7g-7i show the average end-to-end oss rate and deay from source to receivers for session A, session C and session D. The resuts for session B is very simiar to session A and is not incuded here. As seen, the average end-to-end deays of a sessions are within 2 ms, which is our preset deay bound for effective interactive conferencing experience. The average end-to-end oss rate for a sessions are at most 1%-2% upon system stabiization. The overa operation overhead of Ceerity in the 4-party Internet experiment is around 3.9%. In particuar, the packet overhead accounts for 3.4%, and the ink-rate contro and ink-state report overhead is around.5%. 7. CONCLUDING REMARKS With the proiferation of front-facing cameras on mobie devices, muti-party video conferencing wi soon become an utiity that both businesses and consumers woud find usefu. With Ceerity, we attempt to bridge the ong-standing gap between the bit rate of a video source and the highest possibe deay-bounded broadcasting rate that can be accommodated by the Internet where the bandwidth bottenecks can be anywhere in the network. This paper reports Ceerity soution as a first step in making this vision a reaity: by combining a poynomia-time tree packing agorithm on the source and an adaptive rate contro aong each overay ink, we are abe to maximize the source rates without any a priori knowedge of the underying physica topoogy in the Internet. Ceerity has been impemented in a prototype system, and extensive experimenta resuts in a tough dumbbe LAN testbed and on the Internet demonstrate Ceerity s superior performance over the state-of-theart soution Simucast and Mutuacast. As future work, we pan to expore source rate contro mechanisms beyond the 2-hop tree-packing imitation in Ceerity to further improve its performance without incurring excessive overhead. 8. 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10 Simucast Ceerity Mutuacast (a) Sending Rate of Node A (Hong Kong) Simucast Ceerity Mutuacast (b) Sending Rate of Node B (Hong Kong) Mutuacast Simucast Ceerity (c) Sending Rate of Node C (Redmond) Simucast Mutuacast Ceerity (d) Sending Rate of Node D (Toronto) Ceerity Mutuacast Simucast (e) Tota sending rate of a sessions Utiity Simucast Ceerity Mutuacast (f) Tota utiity of a sessions end to end deay(s) end to end oss rate average deay from node A to node B average deay from node A to node C average deay from node A to node D average oss rate from node A to node B average oss rate from node A to node C average oss rate from node A to node D end to end deay(s) end to end oss rate average deay from node C to node A average deay from node C to node B average deay from node C to node D average oss rate from node C to node A average oss rate from node C to node B average oss rate from node C to node D (g) Average end-to-end deay and oss rate from(h) Average end-to-end deay and oss rate from(i) Average end-to-end deay and oss rate from node A to other nodes node C to other nodes node D to other nodes end to end deay(s) end to end oss rate average deay from node D to node A average deay from node D to node B average deay from node D to node C average oss rate from node D to node A average oss rate from node D to node B average oss rate from node D to node C Figure 7: Performance of four-party conferences over the Internet, running prototype systems of Ceerity, Simucast, and the scheme in [4]. (a)-(d): Throughput of individua sessions. (e): Tota throughput of a sessions. (f): Utiity achieved by different systems. (g)-(h): End-to-end deay and oss rate of session A, C, and D for the Ceerity system. wide-area internet bottenecks, in Proc. of the 3rd Internet Measurement Conference, 23. [1] N. Hu, L. E. Li, Z. M. Mao, P. Steenkiste, and J. Wang, Locating internet bottenecks: Agorithms, measurements, and impications, in Proc. of ACM SIGCOMM, 24. [11] V. Vazirani, Approximation agorithms. Springer Verag, 21. [12] X. Chen, M. Chen, B. Li, Y. Zhao, Y. Wu, and J. Li, Ceerity: A ow-deay muti-party conferencing soution, The Chinese University of Hong Kong, Hong Kong, Tech. Rep., 211. [Onine]. Avaiabe: [13] J. Mo and J. Warand, Fair end-to-end window-based congestion contro, IEEE/ACM Trans. Netw., no. 5, pp , Oct. 21. [14] L. Guo and I. Matta, QDMR: An efficient QoS dependent muticast routing agorithm, in Proc. IEEE Rea-Time Technoogy and Appications Symposium, Canada, [15] L. Lovasz, On two minimax theorems in graph theory, Journa of Combinatoria Theory, Series B, vo. 21, no. 2, pp , [16] Y. Wu, M. Chiang, and S. Kung, Distributed utiity maximization for network coding based muticasting: A critica cut approach, in Proc. IEEE NetCod 26, 26. [17] K. Arrow, L. Hurwicz, H. Uzawa, and H. Chenery, Studies in inear and non-inear programming. Stanford university press, [18] A. Nedić and A. Ozdagar, Subgradient methods for sadde-point probems, Journa of optimization theory and appications, vo. 142, no. 1, pp , 29. [19] R. Bruck, On the weak convergence of an ergodic iteration for the soution of variationa inequaities for monotone operators in Hibert space, Journa of Mathematica Anaysis and Appications, vo. 61, no. 1, pp , [2] F. Key, Fairness and stabiity of end-to-end congestion contro, European Journa of Contro, vo. 9, no. 2-3, pp , 23. [21] S. H. Low, L. Peterson, and L. Wang, Understanding vegas: A duaity mode, Journa of ACM, vo. 49, no. 2, pp , 22. [22] D. P. Bertsekas, Noninear programming. Athena Scientific Bemont, MA, [23] J. Park, M. Gera, D. Lun, Y. Yi, and M. Medard, Codecast: a network-coding-based ad hoc muticast protoco, Wireess Communications, IEEE, vo. 13, no. 5, pp , 26. [24] R. Ahswede, N. Cai, S. Li, and R. Yeung, Network information fow, IEEE Trans. on Information Theory, vo. 46, no. 4, pp , 2. [25] X. Chen, M. Chen, B. Li, Y. Zhao, Y. Wu, and J. Li, Ceerity: Towards ow-deay muti-party conferencing over arbitrary network topoogies, in ACM NOSSDAV, 211.