A Resource-trading Mechanism for Efficient Distribution of Large-volume Contents on Peer-to-Peer Networks

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1 A Resource-tradng Mechansm for Effcent Dstrbuton of Large-volume Contents on Peer-to-Peer Networks SmonG.M.Koo,C.S.GeorgeLee, Karthk Kannan School of Electrcal and Computer Engneerng Krannet School of Management Purdue Unversty, West Lafayette, IN Abstract In recent years, the rapd growth of peer-to-peer P2P networks has provded a new paradgm for content dstrbuton. To mprove the effcency of a P2P system, t s mportant to provde ncentves for the peers to partcpate and contrbute ther resources. Varous attempts have been made to reward/penalze peers by provdng servce dfferentaton based on a requestng peer s hstory or reputaton. However, n a truly dstrbuted, non-cooperatve envronment, mantanng and preventng the untruthful revealng of such nformaton wthn the communty mpose larger computaton and communcaton overheads to the system. These problems are further magnfed when large-volume contents are beng dstrbuted because of the length dstrbuton processes and the update of hstory or reputaton has to keep up wth the dstrbuton process. In ths paper, we address the ncentve provsonng problem for dstrbuton of large-volume content n P2P networks, and present a seeng-s-belevng ncentve-compatble mechansm protocol n whch a peer wll decde how much resources wll be assgned to whch neghbors based on what t has experenced. The protocol apples a utlty-based resource-tradng concept where peers wll maxmze ther contrbutons for a far or better return, and we show that by adoptng ths protocol, the system wll acheve Cournot Equlbrum. Furthermore, our protocol s lght-weght, completely decentralzed, and cheatproof. Expermental results llustrate sgnfcant mprovements on the dstrbuton effcency of our protocol over other adopted alternatves. I. INTRODUCTION The foundaton of peer-to-peer P2P systems s based on the contrbuton of resources from peers and such contrbuton plays a sgnfcant role n the effcency and performance of the system. A lot of efforts have been made to avod free-rdng and tragedy of the commons [1], two of the major problems n P2P networks. Varous desgns have been proposed to provde ncentves for peers so that they are more wllng to share ther own resources wth the communty, and resources of nterest may nclude processng power, dsk space, fles, and bandwdth. Peer-to-peer content dstrbuton systems PCDS e.g., [2], [3] are among those whose performance depends hghly on peers bandwdth contrbutons. Recent survey shows that PCDS are takng over and ganng popularty over fle-sharng systems lke Kazaa [4]. Whle both systems share and dstrbute contents n a P2P fashon, fle-sharng systems emphasze more on effectve content searchng and locatng, and PCDS focus more on dstrbuton effcency. Ths separaton makes PCDS a better canddate for sharng/dstrbutng largevolume contents when the overhead of locatng content s neglgble relatve to the dstrbuton process. PCDS also provde a low-cost alternatve to Content Dstrbuton Networks CDN [5] for content provders snce CDN could ncur a hgh cost of operaton when many customers want the content. Currently, Lnux dstrbutors lke Deban and Mandrake use PCDS to dstrbute ther verson of Lnux. However, the problem of provdng ncentves for peers to contrbute s not an easy one because t s very dffcult to montor the actvtes of each and every peer n the communty and account for ther contrbutons to the communty. Attempts have been made to reward/penalze peers n P2P networks by provdng servce dfferentaton based on a requestng peer s contrbuton hstory or reputaton [6], [7], [8]. However, n a truly dstrbuted, non-cooperatve envronment, mantanng and preventng the untruthful revealng of such nformaton wthn the communty have resulted n a costly computaton and communcaton overhead. These problems are further magnfed when the contents beng dstrbuted are large n volume because the dstrbuton process lasts relatvely longer and the update of hstory/reputaton has to keep up wth the dstrbuton process. Furthermore, wth dstrbuton effcency beng the prmary objectve, t s not suffcent just to measure a peer s contrbuton by how much data one has sent but also the rate one transmts data. Dstrbuton effcency s also affected by network condton and peers connectvtes so both should be consdered when evaluatng contrbutons. Most exstng mechansms are desgned to handle the fle-sharng scenaros and do not take network traffc and data rate nto consderaton. Another approach to provde ncentve s through mcropayment. Once agan, many new problems ncludng account management, transacton securty, and user credblty, etc. are assocated wth the mechansm, and Odlyzko [10] provded a strong argument aganst the use of mrcopayments. A better soluton s to let the peers make the decson based

2 on what they experenced. In that stuaton, all the problems that are assocated wth reputaton exchange and securty are removed. In ths paper, we address the ncentve provsonng problem for dstrbuton of large-volume content n PCDS, and present a seeng s belevng mechansm protocol n whch a peer wll decde how much capacty wll be assgned to whch neghbors based on what t has experenced. Our protocol apples a utlty-based Cournot adjustment process where peers wll maxmze ther contrbutons for a far or better return, and we show that by adoptng ths utlty-based protocol, the system wll acheve Cournot Equlbrum [11]. Nonetheless, our protocol also enhances dstrbuton effcency, and because t does not rely on any reputaton exchange, the overhead t mposes on the system s mnmal. Expermental results confrm that our protocol performs better than wdelyadopt counterparts n terms of user satsfacton and dstrbuton effcency, The rest of the paper s organzed as follows: We wll present our resource-tradng protocol n Secton II. Incentvecompatble consderaton on the protocol s dscussed n Secton III. Experments to evaluate the performance of our proposed protocol s presented n Secton IV. A dscusson on the strength and lmtaton of our protocol s presented n Secton V. We summarze the conclusons n Secton VI. II. RESOURCE-TRADING PROTOCOL In ths secton we present our resource-tradng protocol n PDCS. We consder the stuaton where a large fle that s beng dstrbuted s cut nto smaller peces and peers who are downloadng these peces are also concurrently uploadng to the communty wth the peces they already posses. Ths scenaro has been wdely adopted by many PDCS and s proven to be benefcal to the dstrbuton effcency [12], [13]. We assume that peers have gone through the neghborselecton process [14] and have already dentfed a set of neghbors who are downloadng the same content. The mechansm to exchange nformaton about whch content peces each peer has s also assumed see [2] for example of such mechansm. The problem s to determne how much capacty a peer s gong to assgn to each of ts neghbors f the peer has somethng to contrbute. For peers who are new to the system have nothng to contrbute or unable to contrbute because of content avalablty ther neghbors already have what they have, there s no decson to be made and they wll just wat untl they receve somethng from a neghbor that s nterested by the others. Furthermore, we assume all peers are ratonal and selfsh, and ther prmary objectve s to receve the complete content n the shortest perod, so they are wllng to contrbute up to ther lmt for maxmum downloadng capacty. A. Notatons and Defntons We consder the followng: for a peer s, t has a set of N neghbors. We denote the capacty that s receves from neghbor = {1, 2,...,N} at tme t to be λ t and the capacty that s assgns to neghbor at tme t to be µ t. Peer Uλ n kbps ω = 0.9 ω = 0.7 ω = 0.5 ω = λ n kbps Fg. 1. Effect of ω on Uλ. In ths example λ max = 1.5Mbps and µ max = 256kbps s has a maxmum n-bound and out-bound capacty of λ max and µ max, respectvely. These can also be the declared lmts of a peer nstead of the physcal lmts, but we wll show later that there are ncentves for peers to reveal ths truthfully. For ease of dscusson, we wll assume the uplnk and downlnk are separate, whch means that peer s can receve up to λ max and send up to µ max at the same tme. For elastc applcatons lke fle transfer n PDCS, the general form of utlty functon of capacty s strctly concave because of a dmnshng margnal rate of performance enhancement [15]. We defne for peer s the utlty functon of capacty receved from neghbor as: U s λ t = λ t s µ max λ s max where ω s s the wllngness-to-pay of peer s and 0 <ω s < 1. A larger ω means that a peer s wllng to contrbute more for the same amount of capacty t receved from ts neghbors. Fgure 1 shows how the functon changes wth dfferent ω s. The unt of the utlty functon s defned to be n contrbuton capacty. Therefore, from the perspectve of peer s, a desrable trade requres 1 µ t U s λ t 2 We take ths defnton of utlty functon for the followng reasons: a t s strctly concave, whch agrees wth [15]; b t can accommodate dfferent levels of wllngness-topay, whch s a user-dependent parameter; c t elmnates the need to use dfferent utlty functons for receved and contrbuted capacty; and d t s upper bounded by µ max when λ t = λ max, whch also concurs wth the prmary goal, where a peer s wllng to contrbute up to ts lmt to maxmze the downloadng rate. It should be noted that our protocol does not requre the utlty functon to be defned as Eq. 1 and t wll work for

3 all strctly concave utlty functons that s bounded between 0 and λ max. We wll use Eq. 1 as the utlty functon n the remanng of the paper for llustratve and analytcal purposes. B. Decson Mechansm Intally, λ 0 s set to zero for all. For ease of dscusson, we wll drop the tme-dependent notaton on the transfer rate because we are nterested n the capacty assgnment based on the nstantaneous transfer rate observed. Ths allows us to wrte λ and µ nstead of λ t and µ t. If a peer has nothng to contrbute to ts neghbor for any reason, there s no decson to be made and t wll just wat untl t receves somethng from a neghbor that s also nterested by the others. If a peer has already fnshed downloadng and stays n the system to be a seeder, the decson strategy s smply pckng a random subset of neghbors and to serve them for a perod of tme, and then pck another random subset and repeat the process. Algorthm 1 Capacty Assgnment Update CAU 1: for =1to N do 2: f λ < λ then 3: x µ {= U λ} 4: else 5: x Uλ 6: end f 7: end for 8: y k the ndex of the k th largest λ 9: {If λ = λ j, the order s randomly pcked.} 10: reman cap = µ max 11: for j =1to N do 12: f xy j reman cap then 13: µ yj xy j 14: reman cap reman cap - xy j 15: else f reman cap > 0 then 16: µ yj reman cap 17: reman cap 0 18: else 19: µ yj 0 {No more capacty avalable.} 20: end f 21: end for If a peer s has somethng to contrbute to ts neghbors, and t has not yet downloaded the complete content, t wll run the Capacty Assgnment Update CAU algorthm and decde the amount of capacty dedcated to ts neghbors. The algorthm frst computes the desred contrbuton to each neghbor usng the observed nstantaneous capactes λ s and Eq. 1. If λ s smaller than some threshold λ, whch means neghbor s ether havng nothng to contrbute or contrbutng slowly, the algorthm wll assgn µ = U s λ to t f there s capacty avalable. The algorthm then sorts all the λ s n descendng order and starts provdng µ = U s λ to the neghbors that are contrbutng wth the hghest nstantaneous capactes. As a boundary case, one neghbor may be assgned less than U s λ µ or λ s Utlty functon for peer s Utlty functon for neghbor Cournot Equlbrum λ *, µ * = µs *, λs * λ or µ s Fg. 2. Illustraton of the Cournot adjustment process and the convergence to Cournot Equlbrum. because of resource lmtaton. The rest of the neghbors f there are any wll be assgned zero capacty. The ntroducton of the threshold value λ and correspondngly µ n CAU algorthm has two purposes. Frst, t serves as the seedng capacty for newcomers. For peers that are not able to contrbute or contrbute slowly for any reason lack of content or neghbors not nterested n content downloaded, the mechansm ensures that they wll receve a mnmum amount µ of data rate to buld up ther nventory and start contrbutng, provded that ther neghbors stll have capacty remaned after assgnng to other contrbutors. The second purpose that µ serves s to trgger the Cournot adjustment process [16]. Intally, λ = 0 for all. Iftwo neghbors each has content peces that are nterested by the others, contrbutng µ by one party wll jumpstart the tradng process. A graphcal llustraton s outlned n Fgure 2. Consder the case where peer s starts contrbutng µ to neghbor, and neghbor wll respond by contrbutng U µ back to peer s n the next run of CAU. Peer s, after recevng U µ from peer, wll respond by provdng U s U µ to neghbor. By repeatng CAU algorthm perodcally, the process wll contnue untl ether one party cannot keep up because of resource lmtaton the boundary case or Cournot Equlbrum [11] s reached. Ether way, both partes consder the trade desrable and are able to get the most out of each other. Cournot adjustment process s not lmted to two peers but s applcable to n peers n general, so CAU algorthm wll yeld the Cournot Equlbrum of an n-player game. In addton to achevng Cournot Equlbrum, perodcally runnng CAU algorthm wll also allow the peers to adapt to the latest network condton, and the dynamc jon/leave of neghbors. The computatonal complexty of CAU algorthm s ON log N step 8 n the algorthm, where N s the number of neghbors a peer s connected to. Therefore, runnng CAU wll mpose a very low computaton overhead on the peer.

4 III. INCENTIVE COMPATIBILITY In ths secton, we nvestgate the ncentve-compatblty ssues n our mechansm. We consder the ncentves to follow the CAU algorthm, the truthful revealng of the utlty functon parameters, and the problem of free-rdng. A. Followng the CAU algorthm As we have seen n Secton II, tradng accordng to the utlty functon defned n Eq. 1 s consdered to be a desrable trade by a peer. However, Uλ s the maxmum amount of capacty a peer s wllng to pay for λ, so the queston becomes what the gan s f any f a peer contrbute a value less than Uλ back to a neghbor that provdes λ except the boundary case where there s not enough resources to do so. CAU algorthm ranks the nstantaneous capacty provded by each neghbor, and those that share more wll be gven a prorty to receve contrbutons n return. If peer m for malcous returns U m λ c to neghbor nstead of U m λ accordng to CAU algorthm, t may be ranked lower than t should be. If the new rankng s stll hgh enough and c s not too large, peer m may stll receve λ from neghbor. However, peer m has no nformaton about the utlty functon of neghbor, whch has a drect effect on how large c can be; nor does t know about the condton of neghbor s neghbors. Therefore, by returnng U m λ c, peer m faces the possblty of recevng a smaller λ, f not zero, than t should. As the prmary objectve of the peers s to completely download the content n the shortest tme, any acton that s not gong to ncrease neghbors contrbuton s not a desrable acton for the peer. Besdes, peer m has no nformaton about where the Cournot equlbrum between neghbor and tself les, so by truthfully returnng U m λ, t may get a larger λ n the next perod because of the Cournot adjustment process. B. Truthful revealng of utlty parameters Another ncentve ssue that s nterestng to know s that f there s any ncentve for the peer to truthfully reveal ts λ max, µ max, and ω, whch determne ts utlty functon. We consder agan wth peer m and ts neghbor. If truthfully revealed, the utlty functon for peer m s: µ = U m λ =λ m µ max,m λ m max,m and that for neghbor s: µ m = U λ m =λ µ max, m 4 λ max, At equlbrum, λ = µ m and λ m = µ, Eq. 4 becomes or µ = λ = µ 3 µ max, λ max, 1 λ λ 1 ω max, 5 µ max, Settng λ = λ and µ = µ n Eq. 3 and combnng t wth Eq. 5, we have λ m µ max,m λ max,m m = Takng logarthm on both sdes, 1 ω m log λ + log = 1 1 ω log λ ω log λ λ max, µ max, µ max,m λ m max,m 1 1 ω 6 λ max, µ max, After smplfcaton, we have, λ k 1 k 2 =exp ω 1 ω m where µ max,m k 1 = log 9 λ m max,m 1 λ max, k 2 = log 10 1 ω µ max, Snce two peers wll not trade beyond the Cournot Equlbrum level, t s obvous that peer m wants to maxmze λ, the equlbrum and maxmum capacty neghbor would contrbute. From Eq. 8 we can see that λ s an ncreasng functon of k 1, and from Eq. 9, k 1 s a decreasng functon of λ max,m and an ncreasng functon of µ max,m. Therefore, n order to maxmze λ, peer m should set λ max,m to the smallest desrable value and µ max,m to the largest desrable value. There s absolutely no ncentve for any peer to declare a λ max that s smaller than ts physcal lmt because that wll restrct the amount of ncomng capacty. There s also no ncentve to declare a µ max to be larger than a peer can physcally supply, because for the same λ, Uλ, µ max, <Uλ, µ max,j for all µ max, >µ max,j, and Cournot Equlbrum also can never be reached f µ max s set to a value greater than one s physcal lmtaton. As a result, revealng the true λ max,µ max s the best strategy for any peer to acheve maxmum λ. The relatonshp between λ and ω and can be obtaned by dfferentatng Eq. 8 wth respect to ω. Once agan, the parameter s postvely related to λ, and over-declarng s clearly undesrable, so the best strategy for a peer s revealng ts true ω. 7 C. Threshold values λ and µ The CAU algorthm requres the peers to contrbute µ to one s neghbors that are observed to be provdng λ or less capacty, f there s capacty remanng. The effect of noncomplance to these values by some malcous peers has only mnor setback to the system performance. Peers wth lttle or no content to contrbute wll have to wat for a longer perod to

5 get ther seed content from complyng peers. From a peer s perspectve, settng a low µ wll slow down the Cournot adjustment process, whch results n an undesrably longer downloadng tme for tself. Furthermore, a low µ wll also receve a lower rankng n CAU algorthm on the neghbors end, whch leads to low servce prorty from the neghbors. IV. COMPUTER SIMULATIONS In ths secton we mplemented the CAU algorthm and compared ts performance aganst wdely-adopted alternatves. We selected BtTorrent BT as the benchmark for comparson because of ts dstrbuton effcency as a PCDS and ts popularty [4]. Please refer to [2] for the mplementaton detals of BT. A. Smulaton Setup We used the expermental setup descrbed n [14] to evaluate the performance of the CAU algorthm usng ns-2. In the setup, peers could be one of the followng three classes: Class 1: 10 Mbps b-drectonal lnk, representng campus LAN hosts. Class 2: 128 kbps uplnk and 1.5 Mbps downlnk, representng ADSL hosts. Class 3: 56 kbps b-drectonal lnk, representng roughly dal-up hosts. The number of peers n each class was exogeneously set. Results reported n ths paper were obtaned assumng that 30% of peers were Class 1, 50% were Class 2, and 20% were Class 3. We have also smulated other peer compostons, and the smulaton results shown n ths secton demonstrate the typcal trend. The arrval pattern of these peers was taken from real traffc traces from a tracker runnng on the Internet, and the departure of peers after completon of download followed an exponental dstrbuton. In the smulaton, we consdered a Class-1 peer to be the seeder, whch has a fle sze of 700 MB volume of a CD-ROM, dvded nto 1400 peces 512 kb each to dstrbute. The smulaton s repeated multple tmes for 150 smulaton-hours each to obtan statstcal sgnfcant results. More than 2000 nodes are generated n each of the experments, and there are about 400 to 500 nodes concurrently downloadng the content at any tme after the ntal seedng phrase. For the model of ntermedate network, we adopted the one used n [17] where t s assumed that the capacty bottleneck was always at the last hop, that s, ether the outgong capacty of the sender or the ncomng capacty of the recever was the cause of end-to-end congeston. Each peer can be connected to at most 20 neghbors. We also assumed the presence of a generc BT tracker essental for BT to functon, but only needed by CAU for selectng neghbor peers, and the bandwdth of the tracker was assumed abundant. We mplemented the CAU algorthm and the generc BT tt-for-tat mechansm n the peers, and they followed the selected exchange mechansm once they are assgned to ther neghbors. TABLE I AVERAGE DOWNLOADING TIME IN MINUTES. VARIANCES ARE SHOWN IN PARENTHESES. BT CAU Class Class Class The wllngness-to-pay for each peer ω n the experment s unformly dstrbuted between 0.1 and 0.9, and the value of λ max and µ max are set to the respectve maxmum. These values are only used by CAU. BT does not need them. B. Smulaton Results Two metrcs were utlzed for comparson: percentage gan n utlty P gan and uplnk and downlnk utlzaton. The percentage gan n utlty s defned as the rato of the total net utlty receved to the total contrbuton. Equvalently, P gan = Uλ t µ tdt µ 100% 11 tdt Ths metrc measures the satsfacton of a peer throughout the whole process. Fgure 3 shows the dstrbuton of P gan measured from the experment. Snce n the CAU algorthm peers only trade when t s desrable, except for seedng the newcomers, t s not surprsng that the majorty of peer experence a postve P gan. On the other hand, even though BT provdes ncentves for peers to contrbute by servng the hghest contrbutors frst, t does not consder the absolute amount of contrbuton. For example, f 10 neghbors are connected to a peer, and 9 of them servng 1kbps, the tenth one wll be gven the hghest prorty f t s servng 2kbps. As a result, a peer may over-contrbute and receve negatve utlty. The average value of P gan for CAU clents s 30% and that for BT clents s -1280%! Ths result also explans why n realty many BT clents prefer to lmt ther upload capacty to a value lower then µ max, as they are gettng negatve utlty from the communty. The average downloadng tme requred by each class of peers to download the complete content s shown n Table I. Smulaton results show that for the same class of nodes, those that use CAU have a lower average than ther counterparts. Such gan can be explaned as a result of better lnk utlzaton. V. DISCUSSIONS The strength of the CAU algorthm s that t does not requre any nformaton exchange among peers except those on content avalablty, whch s requred by almost all P2P networks. The nformaton one reles on can be obtaned locally by measurng or estmatng the ncomng capactes receved from one s neghbors. Ths s partcularly useful n a fully-dstrbuted envronment, where cooperaton among peers s not guaranteed. However, how to measure or estmate nstantaneous capacty s a problem that has long been consdered and no vastly acceptable model s avalable. In our experments, we adopt a

6 Occurance percentage Fg. 3. BT CAU Percentage gan n utlty Dstrbuton of percentage gan n utlty n BT and CAU. peer wll decde how much capacty wll be assgned to whch neghbors based on what t has experenced. We appled the Cournot adjustment process where peers wll try to maxmze ther contrbutons for a far or better return, and we showed that by adoptng CAU, the system wll acheve the Cournot Equlbrum. We also showed through analyss that there are ncentves to comply wth the CAU algorthm, and CAU encourages peers to reveal ther true wllngness-to-pay and uplnk/downlnk capactes. Because the CAU algorthm does not rely on any reputaton/hstory exchange, the overhead t mposes on the system s mnmal, and the algorthm tself runs n ON log N tme, where N s the number of neghbors a peer connects to. Smulaton results confrmed that CAU performs better than wdely-adopt counterparts lke BtTorrent n terms of both user satsfacton and dstrbuton effcency, the prmary objectve of a PCDS. smplstc approach used by many other researchers, and that s to use the amount of data receved from a neghbor, take the average over tme, and use the value as the nstantaneous capacty. Ths tme-average estmaton s not the optmal measure, but t provdes mportant nsghts to the study. It s also nterestng to know, BtTorrent, one of the most popular P2P applcatons nowadays, takes on a specal case of the CAU algorthm, by settng λ to be λ max and µ to be K µ max, where K s the number of neghbors that the peer s gong to send data to. BtTorrent assgns all of a peers outbound capacty to the K hghest contrbutng neghbors plus another peer under optmstc unchokng [2], whch s randomly pcked by the peer to serve, so t should have a hgh dstrbuton effcency under a homogeneous, hghspeed network. But as Secton IV suggests, n a heterogeneous envronment where some peers have faster lnks than the others, BtTorrent protocol becomes nsuffcent whle CAU wll better utlze the peers capacty to acheve a hgher effcency. Also, BtTorrent does not provde ncentve for peers to reveal ther true connectvtes. Throughout the experment we assumed there s a data ntegrty checkng mechansm to avod data polluton [18]. The desgn of such mechansm s out of the scope of ths paper, but the mechansm s an mportant guard to malcous users who want to defeat the system. For example, f a new peer who doesn t have any content peces wants to get the fle faster, t may send junk data to ts neghbors at a hgh rate, and get a much better servce rate n return. Wth a smple checkng mechansm see [2] for the one used n BtTorrent, peers wll be able to verfy the ntegrty of the content peces receved from ther neghbors, gnore the polluted data, and nullfy the false contrbutons. VI. CONCLUSIONS In ths paper, we addressed the ncentve provsonng problem for dstrbuton of large-volume contents n PCDS, and presented a seeng-s-belevng protocol CAU n whch a REFERENCES [1] G. Hardn, The Tradegy of the Commons, Scence, vol. 162, pp , [2] B. Cohen, Incentves Buld Robustness n BtTorrent, n Proc. of the Frst Workshop on Economcs of Peer-to-Peer Systems, Berkeley, CA, June [Onlne]. Avalable: [3] edonkey 2000, [Onlne] [Onlne]. Avalable: [4] J. Borland, Survey: Move-swappng up; Kazaa down, CNET News.com. [Onlne] [5] J. Dlley, B. Maggs, J. Parkh, H. Prokop, R. Staraman, and B. Wehl, Globally Dstrbuted Content Delevery, IEEE Internet Computng, pp , Sep Oct [6] S. Buchegger and J.-Y. le Boudec, A Robust Reputaton System for P2P and Moble Ad-hoc Networks, n Proc. of the Second Workshop on Economcs of Peer-to-Peer Systems, Cambrdge, MA, [7] R. T. B. Ma, S. C. M. Lee, J. C. S. Lu, and D. K. Y. Yau, An Incentve Mechansm for P2P Networks, n Proc. of the 24 th Intl. Conf. on Dstrbuted Computng Systems ICDCS 04, Tokyo, Japan, Mar. 2004, pp [8] T. Moreton and A. Twgg, Tradng n Trust, Tokens, and Stamps, n Proc. of the Frst Workshop on Economcs of Peer-to-Peer Systems, Berkeley, CA, June [9] A. Odlyzko, The Case Aganst Mcropayments, n Fnancal Cryptography 2003, J. Camp and R. Wrght, Eds. Sprnger, [10] D. G. Luenberger, Mcroeconomc Theory. McGraw-Hll, [11] D. Qu and R. Srkant, Modelng and Performance Analyss of BtTorrent-Lke Peer-to-Peer Networks, n Proc. ACM SIGCOMM, Portland, OR, Sept. 2004, pp [12] X. Yang and G. de Vecana, Servce Capacty of Peer to Peer Networks, n Proc. of INFOCOM 2004, Hong Kong, Mar [13] S. G. M. Koo, C. S. G. Lee, and K. Kannan, A Genetc-Algorthm- Based Neghbor-Selecton Strategy for Hybrd Peer-to-Peer Networks, n Proc. of the 13 th IEEE Internatonal Conference on Computer Communcatons and Networks ICCCN 04, Chcago, IL, Oct. 2004, pp [14] S. Skenker, Fundamental Desgn Issues for the Future Internet, IEEE Journal on Selected Areas n Communcatons, vol. 13, no. 7, pp , Sept [15] C. Buragohan, D. Agrawal, and S. Sur, A Game Theoretc Framework for Incentves n P2P Systems, n Proc. of the Thrd Intl. Conf. on Peerto-Peer Computng P2P 03, 2003, pp [16] S. G. M. Koo, C. Rosenberg, and D. Xu, Analyss of Parallel Downloadng for Large Fle Dstrbuton, n Proc. of the 9th IEEE Internatonal Workshop on Future Trends of Dstrbuted Computng Systems FTDCS 2003, San Juan, Puerto Rco, May 2003, pp [17] J. Lang, R. Kumar, Y. X, and K. Ross, Polluton n P2P Fle Sharng Systems, n Proc. of INFOCOM, Mam, FL, Mar

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