Efficient Content Distribution in Wireless P2P Networks
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- George Peregrine Walters
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1 Effcent Content Dstrbuton n Wreless P2P Networs Qong Sun, Vctor O. K. L, and Ka-Cheong Leung Department of Electrcal and Electronc Engneerng The Unversty of Hong Kong Pofulam Road, Hong Kong, Chna {oansun, vl, cleung}@eee.hu.h ABSTRACT Wth the development of wreless communcaton technologes and the popularty of the P2P applcatons, an mportant problem s to determne how to dstrbute data effcently n wreless P2P networs. However, data dstrbuton n wreless P2P networs faces many challenges compared wth that n the tradtonal wred networs. One of the challenges s the contenton problem. In ths paper, we propose a conflct-free broadcastng scheme to address the problem of fle sharng n wreless P2P networs. Ths scheme not only maes use of the broadcastng nature of the rado channel, but also schedules multple transmssons smultaneously to tae advantage of the frequency reuse of a mult-hop wreless networ. It can mnmze the completon tme experenced by the users. We also deduce a lower bound of the completon tme. Our smulaton results show that our algorthm s promsng. Categores and Subect Descrptors C.2.4 [Cmputer-Communcaton Networs]: Dstrbuted systems - Clent/server, Dstrbuted applcatons. General Terms Algorthm, Desgn, Performance. Keywords Broadcastng, Content dstrbuton, Peer-to-peer. 1. INTRODUCTION Nowadays, peer-to-peer (P2P) fle sharng applcatons are very popular. Snce the shared fles do not resde n a fxed remote server, P2P fle sharng technology allows faster fle transfer and thus conserves the networ bandwdth. Due to the sgnfcant performance mprovement wth fle sharng, there are many successful P2P applcatons such as Permsson to mae dgtal or hard copes of all or part of ths wor for personal or classroom use s granted wthout fee provded that copes are not made or dstrbuted for proft or commercal advantage and that copes bear ths notce and the full ctaton on the frst page. To copy otherwse, or republsh, to post on servers or to redstrbute to lsts, requres pror specfc permsson and/or a fee. Qshne08 July 28-31, 2008, Hong Kong, Chna BtTorrent [1], Gnutella [2], Kazza [3], and Napster [4]. However, they are desgned for wred networs and cannot be employed drectly over wreless networs due to the unque features of the wreless medum, such as the lmted bandwdth and transmsson range at a node, lmted battery power, error-prone channels, and so on. Due to the unque nature of wreless networs, we need to consder two more aspects n addton to those consdered for the wred networs, namely, how to mae full use of the networ resources, and how to avod contenton durng data dstrbuton. In ths paper, we employ the hop-based contenton model [15]. The broadcastng nature of the wreless medum and space dversty are utlzed to fnd as many sender and recever pars as possble n each dstrbuton. Our maor contrbutons are summarzed as follows: 1) A hop-based contenton graph s constructed to acheve a conflct-free schedule for data dstrbuton among nodes. 2) The content dstrbuton schedulng algorthm utlzng the broadcastng nature of wreless medum s developed n order to mnmze the total completon tme for fle sharng. 3) A theoretcal lower bound of the requred transmsson tme s derved. 4) Our proposed algorthm s shown n our smulaton to outperform other exstng algorthms. The rest of ths paper s organzed as follows. Secton 2 descrbes the related wor. An analytcal model, together wth the model assumptons, s presented n Secton 3. Our proposed algorthm s descrbed and analyzed n Secton 4. Secton 5 shows the smulaton results. Future wor and conclusons are summarzed n Secton RELATED WORK There has been much wor on the development of the practcal P2P applcatons mentoned above and on academc research n mprovng P2P performance. Peer selecton and chun selecton are two crucal factors that affect the effectveness of the content dstrbuton process [8]. In [12, 13, 15], peers are selected by bandwdth probng, path length estmaton, and so on. Snce the estmates are generally updated perodcally, they may become stale and the performance suffers. However, n our
2 P2P algorthm, we do not select nodes based on the above estmates, so we do not need perodcal updates. Regardng chun selecton, Bt Torrent employs the rarest element frst (REF) algorthm, n whch chuns lacng n most peers are downloaded frst. REF s good at ncreasng the avalablty of chuns n the networ. However, the smulaton results n [6] show that the performance of REF s far from optmal snce REF does not tae nto account whch peer(s) should have hgher prortes as recpents accordng to ther demands (number of chuns needed). Whle n most demandng node frst (MDNF) algorthm, a node wth the most demands wll be satsfed frst. In other words, REF focuses on chun selecton whle MDNF deals wth peer selecton. Although our algorthm only accounts for chun rarty and dstrbutes the rarest chuns frst, t enables multple nodes to dstrbute smultaneously utlzng the nature of the wreless medum. The smulaton results show our algorthm outperforms REF and MDNF. The problem of broadcastng a shared content as a sngle chun n heterogeneous networs has been nvestgated n [5, 11, 14]. It has been shown that the problem of fndng an optmal broadcast schedule that mnmzes the maxmum completon tme s NP-complete. However, these studes only analyze the problem of dstrbutng ust one chun, whereas a content s generally dvded nto multple chuns and dstrbuted chun-by-chun n P2P content dstrbuton systems. In our model, we consder how to dstrbute multple chuns by fndng the best broadcastng schedule. 3. PROBLEM FORMULATION To focus on the fundamental ssues, our model s based on several smplfyng and assumptons: 1) All the nodes n the networ are homogeneous. That s, all nodes have the same uploadng and downloadng bandwdths. 2) There s only a sngle channel for each node. Ths means that a node cannot transmt and receve smultaneously. In addton, a recepton falure may occur due to pacet collsons. 3) A fle s parttoned nto multple chuns wth the same sze. The transmsson tme of one chun between any par of nodes s the same (say, one tme slot). 4) The dstrbuton networ s quas-statc, so that networ topology and channel status changes only at the boundary between any two successve tme slots. Assumpton 1 and 2 wll generally hold n most wreless networs. Assumpton 4 wll hold n those wreless networs n whch the status of a networ generally changes n a tme scale much larger than the duraton of a tme slot. 3.1 Content Dstrbuton Model The analytcal model conssts of two parts. The frst s a networ model, whch can provde connectvty and contenton relatonshp among nodes. The other s a content processng model, whch provdes a schedule on how each peer dstrbutes a chun based on the nformaton from the networ model Networ Model Gven the condtons of a wreless P2P networ at tme slot n, we can get the connectvty graph Gv ( n ), and thus, buld the correspondng contenton graph Gc ( n ). Constructon of connectvty and contenton graph The connectvty graph G ( n) ( V, E) s bdrectonal, as v shown n Fgure. 1. Let V be the set of nodes and E be the set of edges to ndcate whch par of nodes s connected. Two nodes are consdered to be connected when one node s wthn the transmsson range of the other. G ( ) (, ) c n U L represents the contenton graph, where U s the set of nodes and L s the set of edges to ndcate whch par of nodes contend wth each other. Bascally, two nodes can send data n the same tme slot wthout contenton f and only f they are more than two hops away from each other. In wreless networs, nodes manly suffer from two types of conflcts [7, 10]. The prmary conflct occurs when more than one node transmt to the same destnaton, whereas the secondary conflct occurs when a node recevng a transmsson s also wthn the nterference range of another transmsson not ntended for t. Thus, two nodes wthn two hops n a connectvty graph Gv ( n) wll be connected by an edge from L n ts correspondng contenton graph Gc ( n ). Broadcastng set For the effcent utlzaton of channels, we permt several nodes wthout contenton to transmt wthn the same tme slot. A set of nodes that can send n the same slot wthout conflct s called a broadcastng set, and there s no contenton edge between any two nodes n the set n the correspondng contenton graph. A maxmal broadcastng set s a broadcastng set such that addng any other node to the set wll result n of a contenton edge between a par of nodes n the set. A maxmum broadcastng set s a maxmal broadcastng set wth the largest cardnalty. It has been shown [14] that the problem of fndng a maxmum broadcastng set n a networ s NPcomplete [9]. In our paper, the maxmum weghted broadcastng set s used to select broadcasters and dstrbute chuns. For a gven contenton graph and wth weghts assgned to each node, a maxmum weghted broadcastng set s a maxmal broadcastng set such that ts weght s maxmum among all maxmal broadcastng sets. For example, the connectvty graph and the contenton graph of a networ are shown n Fgures 1 and 2, respectvely. The maxmal broadcastng sets are {A, E}, {B}, {C, D}, and {C, E}. {A, E} and {C, D} are the
3 maxmum weghted broadcastng sets, snce the weghts of both sets are three. {M1,M3} Fle={M1,M2,M3,M4,M5} A C {M2,M3} B {M2,M4} {M1,M2,M4} D E {M3,M5} Fgure 1. A connectvty graph. W(A)=2 A C W(C)=1 B W(B)=1 W(D)=2 D E W(E)=1 Fgure 2. A contenton graph Content Processng Model Chuns are scheduled and dstrbuted among peers based on the content possesson nformaton and peers locatons n the connectvty graph. Chun possesson vector and matrx: In a gven wreless P2P networ scenaro, let the total number of nodes be N. The shared fle F s dvded nto M peces such that F ( F, 1,2,..., M ). Each node possesses a subset of F. We use a chun possesson vector V (, n) to represent possessons of each node n tme slot n. V (, n)[ ] cp s used to represent the elements n V (, ) cp n whch s defned as: 1, f node has chun F V (, n)[ ] cp 0, f node does not have chun F The chun possesson nformaton of all nodes at tme slot n n can be shown n an N M matrxcp, nown as the chun possesson matrx. In the example llustrated n Fgure 1, M=N=5. Intally (n=0), the chun possesson matrx s: cp CP At tme slot 0, row of CP 0 s the content possesson vector of node. Chun dstrbuton vector: Based on the chun possesson vector from 1-hop neghbors, for each node we can construct a chun dstrbuton vector V (, n ), whch ndcates the total number of requests for each chun possessed by node by ts neghbors. The element s defned R, f chun F possessed by node V (, n)[ ] s requred by R neghbors 0, f node does not have chun F In Fgure 1, V ( A, n) ( 2, 0, 1, 0, 0) means that F 1 and F 3 are requested by two and one neghbors of node A, respectvely. The maxmal element of V (, n) shows whch chuns of node are requested the most number of neghbors. We defne C ( n) max( V (, n)[ ], 1,..., M ) to ndcate whch chun has the largest value n V (, n ) and ths chun wll be broadcasted by node. So for node A, chun 1 wll be broadcasted, snce C( n) max{ V ( A, n)} ( F (2)) MAX-SERVING ALGORITHM Snce we focuse on content dstrbuton, we assume that ether there s a central controller who nows the entre networ topology and the requrements of each node or each node nows the global nformaton by exchangng control messages. The am of our algorthm s to fnd an optmal schedule for each tme slot so as to attan the fnal K chun possesson matrx CP wth all ts elements equal to 1 n the mnmum number of tme slots K. The algorthm s executed once at the boundary of each tme slot. 4.1 MaxSer Schedulng Algorthm Our proposed algorthm MaxSer s shown n the followng. In ths algorthm, each node s assumed to have nformaton from ts 1-hop neghbors. MaxSer Algorthm wth 1-hop Informaton: In tme slot n, do: 1. Gven a networ, the 1-hop connectvty graph G 1 v ( n )
4 of the networ and ts correspondng contenton graph Gc ( n) can be constructed. 2. Based on the contenton graph, all maxmal broadcastng sets of the networ can be obtaned [16, 17]. For node, we can get a set S ( n) {(, ) has no contenton wth,1 N}. 3. Wth the connectvty graph G 1 v ( n ), we can get the chun possesson vector Vcp (, n) and the chun dstrbuton vector V (, n) and C ( n) for each node. 4. Sum each element (of set S ( n )) C ( n ) together and get C ( n) so that all maxmal broadcastng sets can s be converted nto ther correspondng maxmal weghted broadcastng sets, and the weght of whch s wrtten as Cs ( n ). 5. Defne Ws ( n) max( C ( ), 1,..., ) s n N. S s the maxmum weghted broadcastng set, then each node n set S s selected to be broadcaster n tme slot n and the correspondng chun s sent accordng to C ( n ). If more than one set have the same max( Cs ( n )), say, W ( n) W ( n) max( C ( n)), we wll s sl s randomly choose one set to be the broadcaster set. 6. If each element of the chun possesson vector V (, n) s one, the schedulng process stops; cp otherwse, repeat 1-6 n tme slot n+1. Bascally, wth more nformaton, the schedulng algorthm would perform better and the completon tme for content dstrbuton can be reduced. In order to dstrbute more contents wthn the followng tme slots, we should consder more than 1-hop nformaton. It s easy to acheve an optmal soluton by extendng MaxSer. We ust need to collect request nformaton of all neghbors wthn more hops and then apply MaxSer. However, t tae more tme to exchange messages among nodes. Thus, there s a tradeoff between better performance and more communcaton overheads for exchangng control nformaton among nodes. Moreover, the topology of a wreless P2P networ can be very dynamc. The connectvty relatonshp among nodes may vary over tme. Therefore, the schedulng protocol should be desgned manly based on 1-hop networ nformaton n a dynamc envronment. 4.2 Performance Analyss In ths subsecton, we wll analyze the lower bound of the number of tme slots K for completng the content dstrbuton among all nodes. In our algorthm, each node can ether broadcast one chun or receve one chun wthn each tme slot. For a gven networ connectvty graph and an ntal chun possesson matrx CP 0 for all nodes partcpatng n the networ, we can analyze the lower bound K from two aspects: the nodes (rows of CP 0 ), and the chuns (columns of CP 0 ). 1) Nodes (rows of CP 0 ) Snce each node can receve at most one chun from one of ts neghbors n each tme slot, the total number of tme slots for each node s equal to ts correspondng number of the mssng chuns. The total number of 0s across row s r, where r M 0 (1 CP ) 1. Therefore, K max( r ) (1) 2) Chuns (columns of CP 0 ) For the dstrbuton of a certan chun, n each tme slot, the chun cannot serve more than Dmax nodes, where Dmax s the maxmum degree of each node. Let c be the total number of 1s along column. Thus, c N CP. 1 We can fnd the mnmum number of 1s along all columns c mn mn (1,... M ) c. The chun wth cmn wll need the most number of tme slots for dstrbuton. Q s defned as the number of nodes whch can broadcast ths chun smultaneously n each tme slot. After one tme slot, there wll be at most ( cmn Q Dmax ) 1s along ths column. At tme slot K, there wll be c Q D K 1s along ths column, whch s mn max greater than or equal to N. Thus, N c K Q D mn max 3) Combned lower bound of K Based on the above dscusson, the lower bound of the value K s the maxmum value of the two lower bounds derved above. N c K mn max( rmax, ) Q Dmax 5. SIMULATION RESULTS We randomly generate some problem nstances to evaluate our algorthm. In these problem nstances, we choose four representatve networ topologes, as shown n Fgure 3. The frst one s a grd topology wth 9 nodes. The second 0 (2) (3)
5 one s a star topology wth 10 nodes. The last two are hybrd topologes wth 24 and 35 nodes, respectvely. The number of chuns or chun sze s 10, 50 and 200, and the probablty of any node possessng a certan chun s 0.2 and 0.5, respectvely, n the two scenaros consdered. Under these dfferent topologes and chun possesson matrces, we compare our algorthm wth two classcal algorthms RPF/REF and MDNF [6]. In the smulaton, we focus on tme slots needed for complete dstrbuton. The smulaton results show that our algorthm outperforms the others. 1) Probablty of 1s n CP s 0.2 Fgure 4 shows the performance comparson of the three algorthms wth dfferent chun szes. In all cases, the tme slots needed for content dstrbuton by MaxSer are smaller than the other two algorthms. The performance mprovement of MaxSer over RPF and MDNF ncreases wth chun sze. The reason s that MaxSer chooses the broadcastng set whch allows more nodes to be served n each tme slot, whch helps dstrbute the content as qucly as possble. 2) Probablty of 1s n CP s 0.5 Fgure 5 shows the performance comparson of three algorthms by varyng node sze. In all cases, the tme slots used by MaxSer are smaller than the other two algorthms. The number of tme slots used by MaxSer does not change greatly wth ncreasng peer sze. Ths demonstrates that the proposed algorthm s scalable wth the number of peers. In addton, we fnd the number of tme slots wth ten nodes s larger than that wth 24 nodes. Ths s not only because there are more broadcastng sets wth 24 nodes, but also the maxmum degree n the 24 node graph s more than that n the ten node graph. Wth a gven number of chuns, our proposed algorthm s effectve n reducng the number of tme slots needed for networs wth more broadcastng sets and hgher node degrees. As shown n the smulaton results, our algorthm performs better n most cases. The results also show that both the networ topology and the ntal dstrbuton of chuns wll greatly mpact the tme needed for dstrbuton n the wreless networs. 6. CONCLUSION In ths paper, we address the content dstrbuton problem n wreless P2P networs. We formally defne the content dstrbuton problem wth the chun possesson matrx and contenton graph. The broadcasters n each tme slot are selected by determnng the maxmum weghted broadcastng set of the contenton graph. Therefore, the number of tme slots needed to complete content dstrbuton s mnmzed and hence the overall system performance s mproved. The lower bound of the number of tme slots requred s deduced. Our smulaton results show that the proposed MaxSer algorthm outperforms other exstng algorthms n most cases. Therefore, the proposed MaxSer algorthm s a promsng canddate for content dstrbuton schedulng n wreless P2P networs. In our model, to focus on the fundamental ssues of content dstrbuton, we mae some assumptons such as no power constrant, homogeneous nodes, and so on. Therefore, n the future wor, we would le to relax these assumptons to mae t more realstc. We shall also mae our model applcable to more dynamc networ scenaros by ncorporatng moblty models of wreless nodes. Fgure 3 (a). A networ topology wth 9 nodes. Fgure 3 (b). A networ topology wth 10 nodes. Fgure 3 (c). A networ topology wth 24 nodes. Fgure 3 (d). A networ topology wth 35 nodes.
6 Fgure 4. Number of tme slots versus chun sze. Fgure 5. Number of tme slots versus node sze. 7. REFERENCES [1] The offcal BtTorrent webste, [2] The offcal Gnutella webste, [3] The offcal Kazaa webste, [4] The offcal Nepster webste, [5] BHAT, P.B., RAGHAVENDRA, C.S., and PRASANNA, V.K Effcent Collectve Communcaton n Dstrbuted Heterogeneous Systems. Journal of Parallel and Dstrbuted Computng, Vol. 63, No. 3, pp , March [6] CHAN, J.S., LI, V.O.K. and LUI, K.S Performance Comparson of Schedulng Algorthms for Peer-to-Peer Collaboratve fle dstrbuton. IEEE Journal on Selected Areas n Communcatons, Vol. 25, pp , January [7] EPHREMIDS, A. and TRUONG, T.V Schedulng Broadcasts n Multhop Rado Networs. IEEE Transactons on Communcaton. Vol. 38, pp , Aprl, [8] FELBER, P. and BIERSACK, E.W Cooperatve Content Dstrbuton: Scalablty Through Self-Organzaton. In Lecture Notes n Computer Scence, Vol. 3460, pp , May [9] GAREY, M.R. and JOHNSON, D.S Computers and Intractblty-A Gude to the Theory of NP Completeness. W. H. Freeman. [10] HUNG, K. and YUM, T Far and Effcent Transmsson Schedulng n Multhop Pacet Rado Networs. In Proceedngs of IEEE GLOBECOM 1992, pp. 6 10, November [11] KHULLER, S. and KIM, Y.A On Broadcastng n Heterogeneous Networs. In Proceedngs of ACM- SIAM SODA 04, pp , January [12] LEUNG, K.H. and KWOK, Y.K An Effcent and Practcal Greedy Algorthm for Server-Peer Selecton n Wreless Peer-to-Peer Fle Sharng Networs. In Lecture Notes n Computer Scence, Vol. 3794, pp , December [13] NG, T.S.E., CHU, Y.H.S. and ZHANG, H Measurement- Based Optmzaton Technques for Bandwdth-Demandng Peer-to-Peer Systems. In Proceedngs of IEEE INFOCOM 2003, Vol. 3, pp , 30 March 3 Aprl [14] RAMASWAM, R. and PARHI, K.K Dstrbuted Schedulng of Broadcasts n a Rado Networ. In Proceedngs of IEEE INFOCOM 1989, Vol. 2, pp , Aprl [15] SYAL, M., BREITBART, Y. and VINGRALEK, R Selecton Algorthms for Replcated Web Servers. Readng n ACM SIGMETRICS Performance Evaluaton Revew, Vol. 26, No. 3, pp , December [16] TSUKIYAMA, S., IDE, M., SHIRAKAWA, I A New Algorthm for Generatng All the Maxmal Independent Sets. SIAM Journal on Computng, Vol. 6, pp , [17] YU, C.W. and CHEN, G.H Generate All Maxmal Independent Sets n Permutaton Graphs. Internatonal Journal of Computer Mathematcs, Vol. 47, pp. 1-8, 1993.
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