Content Reserve Utility Based Video Segment Transmission Scheduling for Peer-to-Peer Live Video Streaming System

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1 Cotet Reserve Utility Based Video Segmet Trasmissio Schedulig for Peer-to-Peer Live Video Streamig System Zhu Li 1, Jiawei Huag 2, ad Aggelos K. Katsaggelos 3 1,3 Multimedia Research Lab, Motorola Labs, Schaumburg, IL, USA, 2 Dept of Ifo Egieerig, Chiese Uiversity of Hog Kog, Chia 3 Dept of EECS, Northwester Uiversity, Evasto, IL, USA Abstract Peer-to-Peer (P2P) distributio has becomig a popular solutio for IPTV applicatios. I this wor, we defie a utility fuctio over the play bac buffer cotet reserve, ad develop a utility gradiet based video segmet trasmissio schedulig algorithm for uploadig badwidth allocatio i P2P live streamig system, with the goal of miimizig play bac freezes. Simulatio results demostrated the effectiveess of the proposed solutio. I. INTRODUCTION The advace of iteret ifrastructure maes Peer to Peer (P2P) live streamig a viable solutio for IPTV [Jai] services with medium quality video. Compared with the traditioal cliet-server system, which does ot scale well with large ad dyamic viewig cliets, a P2P system is cheaper to deploy for cotet providers ad offers more cotet choices to ed cosumers. P2P scheme utilizes uploadig badwidth ad buffer storage capacity of participatig peers i a collaborative fashio. It turs the passive cotet cosumers i cliet-server system ito active cotet providers ad maes fully use of the idividual users resources, thus is much more scalable ad robust. Despite the great success of may P2P streamig systems, e.g., PPLive [PPLive, He6], CoolStream [Zhag], PPStream [PPLive], there does ot exist much wor aalyzig the operatio ad tradeoff of such systems. Recetly, [Kumar7] aalyzes the pull-based P2P streamig systems based o fluid model, ad costructs a simple 2-hop schedulig algorithm for a buffer-less system. A system with buffer is also studied usig extesive simulatios. For multicast tree based P2P streamig systems, [Padmaabha3] cosiders a simple tree maagemet algorithm that improves the resiliece of the system utilizig path diversity i the etwor. However, oe of these wor givse a aalytical model of the P2P streamig system uder heterogeeous buffer occupacies. P2P dowloadig system, lie Bit Torret [Qiu4] has bee extesively studied. However, P2P dowloadig system does ot cosider real time playbac costrait ad thus does ot have the playbac buffer uderflow issues as is addressed i this paper. I a P2P streamig system, it is desirable to miimize the probability of freezes durig the live video playbac. I other words, the extra buffered cotet (i.e., cotet reserve level) of each peer should be ept positive. Here we use the well ow α -fair utility fuctio [Mo] to model users satisfactio level of their curret cotet reserve levels, ad we allocate etwor resources (i.e., trasmissio rates) to differet users to maximize the total etwor utility.. It ca be show that the optimal solutio ca balace the buffer occupacy level amog users. Fially, we propose a greedy heuristic solutio that achieves the desirable result with low complexity. peers x 2 t 2 y time lie (gop) Figure 1. 6 peer playbac buffer states The paper is orgaized ito the followig sectios. I Sectio II, we preset defiitios ad formulatios of the problem, I Sectio III, we develop the utility gradiet based schedulig algorithm. I Sectio IV, simulatio results are preseted alog with some discussios, ad i Sectio V, we summarize the results ad propose future wor. II. DEFINITIONS AND FORMULATIONS A. Defiitios ad Formulatios Cosider a P2P System with a video source ad peers, with upload capacities, C, C 1,., C. Let the cotet to be

2 streamed over all peers with a costat bit rate (CBR) R. Each peer s ( 1 ) play bac buffer is therefore characterized by the buffer state tuple, S = x, t, y } (1) { where the buffer cotet startig poit ad edig poit are x ad y, ad the curret playbac time is t. The cotet reserve level is calculated as y -t. This is illustrated by a example i Fig. 1, where the play bac buffer occupacy states of 6 peers are plotted as horizotal bars. The curret playbac video segmet t, or Group of Picture (GoP), is mared for each peer by ^. Each GoP cosists of. secod of video segmet coded i IPBP patter, ad for CBR video it cosists of R /2 bits. The play bac buffer state, {x 2, t 2, y 2 } for peer 2 is mared. A importat cosideratio for P2P live video streamig system is to maage/allocate peer upload badwidths to prevet peer buffers from uderflow, ad therefore causig upleasat freezes i the playbac. Ituitively, a peer with a playbac time stamp t close to the ed of buffer y should be allocated more resources. To characterize this we defie a utility fuctio over the cotet reserve, U(y -t,), where the utility fuctio has the form of, 1 α x U ( x) =, < α < 1, (2) 1 α Examples of this utility fuctio are plotted i the Fig 2 below. Notice that the parameter α cotrols the property of the utility fuctio. Whe α is close to 1, it leads to proportioal fair allocatio of resource, ad whe it is close to, it leads to total buffer occupacy maximizatio. U(x) 2 1 a=.2 a=.4 a=.6 a= x Figure 2 Utility fuctios The problem of upload badwidth allocatio is therefore formulated as a costraied optimizatio problem. For the schedulig period, T, the obective is to allocate upload badwidth for each peer, R, such that the total utility over the play bac buffer cotet reserve is maximized, T max U ( R + ( y t )), s. t. R C + C (3) R R 1 1 I Eq. (3), we assume the upload badwidth {C } remais costat for the schedulig period. This is a typical total resource costraied utility maximizatio problem. From the radio resource pricig cotrol wor for wireless video over multi-access chael [Li6], it is ow that at the optimal allocatio of resources, each user s utility gradiet should be the same. I the cotext of this wor, sice all user are usig the same utility fuctio, it meas all peer s cotet reserves will coverge to the same size at optimal allocatio. If all buffer states iformatio are ow, the Eq. (3) ca be explicitly solved [Li6] for the optimal allocatio {R *}. T C + C + ( y t ) * R 1 1 R R = y + t. T Oce we have the allocatio, the actually trasmissio of video segmets eed to be scheduled. For small schedulig itervals, gradiet based schedulig algorithms has bee show to maximize the total etwor utility i various cases, such as hybrid ARQ based TDMA systems [Huag], CDMA systems [Agr2], ad OFDMA systems [Huag7]. The ituitive is to always serve the pacet with the largest utility gradiet i the queue. However, the P2P system is differet from wors i [Li6], [Huag], [Huag7]. The resource costraits are actually more complicated. The allocated rate R is provided by multiple peers, = R r, where for peer, the additioal cotet reserve is obtaied by pullig from servig peers with rate r,. The P2P servig rates are subected to upload capacity, r, C (4) ad cotet availability costraits, r, =, if y y () The costraits i () are depedet o the curret peer buffer states. For example, r 1, = for ={3,, 6}, for buffer states i Fig. 1. A optimal rate schedulig will be difficult due to the complexity of costraits i (4) ad (). I a practical pullbased system, the rate allocatio ad schedulig are discrete, ad ca be viewed as a video segmet trasmissio schedulig problem. At each schedulig, each peer will request a set of video segmets, or GoPs startig with time offset y +1, to fill the playbac buffer. For a upload badwidth of C, ad schedulig iterval T, the umber of GoPs ca be trasmitted by peer is m. Each peer ca allocate, upload capacity to peer, if they are available. The schedulig formulatio is therefore give as,

3 max U (, s. t.,,, + ( y if t y m, m =, )), TC = R / 2 < y This is a combiatorial optimizatio problem, with total umber of possible solutio, 1 m 1 m1 m2 m L = 1 m1 m2 m3 m A exhaustive search will icur prohibitive cost i computatio. Istead, we develop a greedy algorithm i the ext sectio. (6) III. UTILITY GRADIENT DRIVEN SCHEDULING SOLUTION I a practical solutio, we assume a peer with good throughput ad computig capabilities is radomly selected to act as a coordiator of a small sub-set of peers. The trasport is the best-effort based UDP scheme. The upload capacities, {C }, stay roughly costat durig the playbac, ad are ow at the coordiator. At each schedulig iterval, the play bac buffer status { S } are commuicated to the coordiator. Based o this iformatio, the coordiator computes a GoP trasmissio list for each peer that approximates the optimal solutio to Eq. (6). Algorithm I: GoP Schedulig Collect buffer states {S } Compute upload capacities {m }, ad total capacity M, Compute GoP request list G, sort by utility gradiet U, gopct= m ; i=1; WHILE (gopct >) Fid peers P={ m >, x <= g <= y } IF P is empty % ot serviceable, Cotiue. ELSE * = arg mi y gi P m * =m * - 1 Add GoP g to peer * s servig schedule gopct=gopct 1 i=i+1 END Ed Figure 4. GoP Schedulig Algorithm The GoP servig priority is based o the requested GoP s locatio i each peer s buffer. The utility gradiet for requested GoP y + of peer is computed as, U ', = U ( y t + ) U ( y t + 1) (7) I a greedy schedulig for (6), it meas the requested GoP with largest utility gradiet should be scheduled first. From the buffer status updates, the coordiator ca compute the followig requested GoP umber list with its associated utility gradiet, G { g = y + U ' } (8) : i, U mi The size of the GoP request list ca be adusted accordig to the schedulig iterval / total GoP servig capacity, with the utility gradiet threshold U mi. The algorithm assigs each GoP i the request list G to a feasible servig peer, i the order of descedig utility gradiet, util all uploadig capacities i the schedulig iterval are exhausted. The servig peer is selected through a closest buffer ed first heuristic. For a requested GoP with time offset g i, oly peers with y >= g i ca serve this request. If we sort all servig peers by y, the upload badwidth of the peer with the latest cotet are the most desirable oe, i.e., it ca serve all peers with older cotet. Therefore, their badwidth should be coserved, ad we eed to select the peer with y closest to the requested QoP g i. The greedy algorithm is summarized i Fig. 4. IV. SIMULATION RESULTS To verify the performace of the proposed algorithm, we set up P2P video sessios with the followig costats i system settig. Let the system average upload badwidth be, = C C =. I the first test, we experimeted our GoP greedy schedulig algorithm with a = 6 peer system. The system settigs are summarized i Table 1. The schedulig iterval is set as T=4 (GoPs). For a total of 3 iteratios, or 6 sec playbac, the resultig play bac buffer cotet reserve i umber of GoPs are plotted. Table 1. P2P system settigs Parameter Value Commets R (bps) 3 Video playbac rate L(sec) 6 Video cotet legth Upload badwidth C std (pbs) 4 variatios Cotet access widow W (sec) 3 size Utility fuctio α.6 parameter The results for average upload badwidth C=322.8bps are plotted i Fig. a, ad those of C=384.bps, or 1.28R, are plotted Fig. b. Notice that i both cases, the cotet reserve sizes are quicly coverged, ad at later case the cotet reserve size stabilizes. To compare we also developed a utility blid schedulig algorithm that ust serves GoP request o a first-come-first serve (FCFS) basis. The cotet reserve sizes are plotted i Fig. c. It is clear that the system is ot stable ad the reserve sizes do ot coverge, some peers ed up with more reserves while others are starved ad have umerous freezes i play

4 bac. =6 C=33.6 bps R =3. bps T=4 GoP 3 =16 C=368.6 bps R =3. bps T=2 GoP 3 2 playbac buf reserve (GoP) 2 1 playbac buf reserve (GoP) 1 playbac buf reserve (GoP) iteratio (a) C=33.6 =6 C=384. bps R =3. bps T=4 GoP iteratio (d) C=368.6bps Figure. Peer Buffer Cotet Reserve States I a secod system, we icrease the umber of peer to =16, source upload rate to 2.R, ad reduces the schedulig iterval to T=2 (GoP). The system show stable reserve cotet sizes at a average upload badwidth of C=368.6bps. The icrease of the size of locally coordiated P2P group does improve the performace. For time varyig upload badwidth, the system ca also adapt to the chages ad effectively provide the service. For the same 6 peer set up, the performace of cotet reserve size is plotted i the Fig. 6a below. The correspodig upload capacity chages ad the average capacity C over schedulig iteratios are plotted i Fig. 6b. 3 =6 C=38.3 bps R =3. bps T=4 GoP iteratio 3 3 (b) C=384.bps =6 C=384. bps R =3. bps T=4 GoP playbac buf reserve (GoP) 2 1 playbac buf reserve (GoP) iteratio (a) Performace with time-varyig upload badwidth iteratio (c) C=384.bps, FCFS schedulig

5 upload capacity peer upload capacity chages [Padmaabha3] V.N. Padmaabha, H.J. Wag, ad P.A. Chou, Resiliet Peero-to-Peer Streamig, IEEE Iteratioal Coferece o Networ Protocols, 3. [PPLive] PPLive system, URL: [PPStream] PPStream, URL: [Qiu4] D. Qiu ad R. Sriat. Modelig ad Performace Aalysis of BitTorret-Lie Peer-to-Peer Networs, Proc. ACM SIGCOMM, Portlad, OR, Sept. 4. [Zhag] CoolStreamig/DONet: A Data-drive Overlay Networ for Peer-to-Peer Live Media Streamig, X Zhag, J Liu, B Li, TSP Yum - Proc. IEEE Ifocom, iteratios (b) upload badwidth chages Figure 6. Performace with time-varyig upload badwidth Notice that the performace is similar to Fig. b, ad the average upload badwidth chage over time is plotted as solid lies i Fig. 6b, while each peer s upload badwidth chages are plotted i dotted lies. V. CONCLUSION AND FUTURE WORK I this paper we developed a utility gradiet based video segmet schedulig algorithm for P2P live video streamig solutio. The simulatio results demostrated the effectiveess of the proposed solutio. I the future we will ivestigate a combiatorial optimizatio solutio, study the utility fuctio parameter ad its impact o covergece speed, ad iclude the ed-to-ed GoP trasmissio delays ito the system modelig ad simulatio. REFERENCES [Agr2] R. Agrawal ad V. Subramaia, Optimality of Certai Chael Aware Schedulig Policies, Proc. of 2 Allerto Coferece o Commuicatio,Cotrol ad Computig, Oct. 2. [Huag] J. Huag, R. Berry ad M. L. Hoig, "Wireless Schedulig with Hybrid ARQ", IEEE Trasactios o Wireless Commuicatios, vol. 4, o. 6, pp , Nov.. [Huag7] J. Huag, V. Subramaia, R. Agrawal, ad R. Berry, "Dowli Schedulig ad Resource Allocatio for OFDM Systems", Proc. Coferece o Iformatio Scieces ad Systems (CISS), Priceto Uiversity, NJ, USA, March 6. [Hei6] Xiaou Hei, Chao Liag, Jia Liag, Yog Liu ad Keith Ross, "Isight ito PPLive: A Measuremet Study of a Large-Scale P2P IPTV System", Proc of WWW 6 worshop of IPTV services over World Wide Web. [Jai] R. Jai, I Wat My IPTV, IEEE Multimedia, vol. 12(3),. [Kumar7] R. Kumar, Y. Liu ad K. Ross, Stochastic Fluid Theory for P2P Streamig Systems, IEEE INFOCOM 7 [Li6] Z. Li, J. Huag, ad A. K. Katsaggelos, Pricig Based Collaborative Mutli-User Video Streamig over Power Costraied Wireless Dow Li, oral paper, IEEE It l Coferece o Acoustics, Speech ad Sigal Processig (ICASSP), Toulouse, Frace, 6. [Mo] J. Mo ad J. Walrad, Fair ed-to-ed widow-based cogestio cotrol, IEEE/ACM Trasactios o Networig, vol. 8, o., pp. 6-67,