REPLICATION IN BANDWIDTH-SYMMETRIC BITTORRENT NETWORKS. M. Meulpolder, D.H.J. Epema, H.J. Sips

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1 REPLICATION IN BANDWIDTH-SYMMETRIC BITTORRENT NETWORKS M. Melpolder, D.H.J. Epema, H.J. Sips Parallel and Distribted Systems Grop Department of Compter Science, Delft University of Technology, the Netherlands ABSTRACT The poplar and well-known BitTorrent peer-to-peer protocol offers fast file distribtion in a highly scalable way. Several stdies have investigated the properties of this protocol, mostly focsing on heterogeneos end-ser environments sch as the Internet, with asymmetric connections. In this paper however, we focs on the sage of the BitTorrent protocol in homogeneos local environments with symmetric bandwidth properties. Compared with a traditional client-server setp, the se of BitTorrent in sch settings can offer hge benefits in performance and scalability, allowing bandwidth sharing and high speed file distribtion. We aim to improve the performance of sch networks with a novel mechanism for replication sing so-called replicators, which replicate a sbset of the files in the system. A mathematical model of the reslting Replicated BitTorrent is presented and validated by emlation. Frthermore, we present simlation reslts that provide insight in the performance of Replicated BitTorrent networks with dynamic peer arrivals and departres. The reslts show that Replicated BitTorrent significantly improves download times in local bandwidth-symmetric BitTorrent networks. 1. INTRODUCTION Over the last few years, the BitTorrent [1] protocol has become widely sed and has grown into a topic of increasing interest in the research commnity. Among the present day peer-to-peer (P2P) protocols, BitTorrent is clearly the most poplar, especially for file sharing over the Internet. The most important reasons for its poplarity are its otstanding scalability characteristics, as well as its tit-for-tat mechanism [2] which ensres that while downloading a file, sers are atomatically sharing parts of the file with others. Recently, varios papers have been pblished [, 4, 5] which contain theoretical models, simlations, and measrements considering the BitTorrent protocol, its performance, and its sage patterns. Up ntil now, however, the focs regarding the application of BitTorrent and the research into its properties have been centered arond file sharing by heterogeneos end-sers on the Internet. A very important consideration in sch environments is the often asymmetric natre of Internet connections sch as ADSL. Since the BitTorrent protocol is based on the mtal exchange of file pieces by crrent downloaders, as well as on a certain amont of altrism by finished downloaders, the asymmetry in download and pload speeds of end-ser connections is an important assmption in the analysis of the performance and scalability of the protocol. Frthermore, the behavior of peers in a general file sharing context is very hard to predict. This paper is based on a different kind of environment for the application of BitTorrent: local environments with symmetric end-ser connections. Important examples are corporate and academic LANs, in which P2P techniqes have hardly been applied so far. Yet, in sch environments BitTorrent cold prove to be the ideal protocol for rapid local file distribtion in a highly scalable way. De to the BitTorrent protocol, sers who are downloading the same file at the same time gain a hge profit from each other. As presented in [6], the reslting download times are almost constant with respect to the nmber of downloaders. Even thogh there are no tailored implementations of BitTorrent for this context yet, many interesting possibilities can be imagined, sch as high-qality mltimedia services which se BitTorrent in the backgrond for the actal content distribtion. In or work, we consider local environments in which a collection of files is available for all sers in the network. In the case of a psh model, where a centralized athority decides at a specific point in time to distribte specific files, network-level mlticasting techniqes cold be applied. However, we focs on a pll model, where sers can decide when to download and what to download ot of the collection. A practical example is a niversity camps, where edcational materials

2 and mltimedia files have to be available for all stdents. Crrently, the common approach is to make all files available at a (collection of) central server(s), from where they can be downloaded sing the FTP or HTTP protocol. Instead, we consider the se of the BitTorrent protocol for sch transfers, in sch a way that both the server(s) and the end-ser machines transparently act as peers in the reslting peer-to-peer network. As or main contribtion, we present, analyze, and simlate a novel replication mechanism which highly improves the performance and scalability of sch bandwidth-symmetric BitTorrent networks: Replicated BitTorrent. We introdce the concept of replicators, which are special peers that replicate a sbset of the files in the system, thereby increasing system performance. A model is devised in order to analyze the inflence of these replicators, and is validated by emlation sing real BitTorrent clients. Frthermore, we provide insight in the performance of Replicated Bit- Torrent in networks with dynamic arrivals and departres of peers. We have simlated Replicated BitTorrent networks with both homogeneos and Zipf-distribted file poplarities. We have assessed varios network configrations in order to compare client-server, BitTorrent, and Replicated BitTorrent performance. The reslts show that replicators significantly increase the performance, leading to download speeds that are many times higher than those in a reglar BitTorrent system. 2. REPLICATED BITTORRENT In this section, we present or replication mechanism for bandwidth-symmetric BitTorrent networks. It has to be noted that throghot the rest of this paper, we make se of standard BitTorrent [1] terminology that can be fond in many other pblications on the sbject. We will briefly introdce the relevant concepts of BitTorrent to those not yet familiar with the sbject: in BitTorrent a file is divided into chnks, which are then bartered between peers that are interested in the file; a leecher is a peer who is in the process of downloading a file bt has not yet finished; a seeder is a peer in possession of the whole file and sharing it with the network; a swarm associated with a file is the collection of peers leeching or seeding that file. Peers discover other peers in the network by reqesting IP addresses from the tracker, the only central component in a BitTorrent network. The tracker keeps track of the seeders and leechers of each file. As mentioned in the introdction, we consider local BitTorrent environments in which a collection of files has to be available for all sers in the network. Some of the peers, the sorces, provide a central point for injecting content and ensre that at least one copy of every file is file A replicator file B sorces file C replicator Figre 1: Example of a simple Replicated BitTorrent system with a few sorces, three active swarms associated with three different files, and two replicators which seed varios files. available. We now distingish three types of seeders: (1) the sorces, that seed all files and are assmed to be always online, (2) the peers that have finished a download and remain online for a certain amont of time, and () replicators. A replicator is a peer that is manally added to the network, and that is seeding a sbset of the files that are available in the system. In Figre 1, an example of a simple Replicated BitTorrent system with replicators is displayed. At the BitTorrent level of a particlar file swarm, a replicator is not different from a general BitTorrent seeder. However, we focs on the system as a whole and seek to inflence the nmber of seeds of particlar files, in sch a way that the reslting download speeds in the system are as high as possible. The mechanism of replicators is designed to inflence which files are seeded by which nmber of seeders based on the file poplarity in the system, withot changing the BitTorrent protocol itself. In a small network, replicators can be sed to redce the load of the network as a whole. In a larger network, consisting of different segments with possibly different file poplarity characteristics, replicators can be placed in the different segments to specifically redce the load of the each segment in an optimal way. The contents of the replicators depend on the poplarity of files in the system or network segment. In or crrent implementation, replicators are notified of the file reqests in the system by the tracker, which is extended to provide this fnctionality (the overhead as compared to reglar tracker fnctionality is very small). Based on these file reqests replicators monitor the file poplarity and decide which files to seed according to their replication policy. We evalate different file poplarity distribtions with varying reqest arrival rates and different replication policies.

3 . ANALYSIS In this section we present a model to analyze the performance of Replicated BitTorrent in a given system with known swarm properties. We validate the model by emlation sing real BitTorrent clients..1. Model We consider a Replicated BitTorrent system with a fixed nmber of sorces and a fixed nmber of replicators. Each of the sorces seeds all of the files available in the system. Each of the replicators seeds a sbset of the available files. In the model, different replicators can seed different sbsets of files, thogh the nmber of files seeded is constant over all replicators. In Section.4, we discss the restricted case in which all of the replicators seed the same files. We introdce the following notation: F The set of files seeded by the sorces. F The size of F. S The nmber of sorces. N f The nmber of peers downloading file f. M f The nmber of finished peers still seeding f. R The nmber of replicators. Q The nmber of files seeded by each replicator (Q F ). c s The pload bandwidth of the sorces. c r The pload bandwidth of the replicators. c The pload/download bandwidth of reglar peers. β f The fraction of replicators seeding file f. We assme that a peer is downloading at most one file at a time so that its fll download bandwidth is available for each single download. Frthermore, we do not take bartering overhead into accont, that is, we assme that the bandwidth sed for bartering flly reslts in effective download bandwidth. Since we assme that each sorce seeds the same files, we can withot loss of generality assme that there is only one sorce (S = 1)..2. Scalability of the nmber of leechers We will show that in the case of bandwidth symmetry, the effective download bandwidth of a leecher is independent of the nmber of leechers in a swarm. Theorem 1 Let in a bandwidth-symmetric BitTorrent swarm of a file f the total available bandwidth of all seeders be. Sppose that the leechers of this file are not seeding or leeching any other files. Then the fol seeders Figre 2: Illstration of the proof of Theorem 1 for a swarm with leechers. lowing holds for the download speed d of any leecher: d = min{, c}. Theorem 1 makes sense intitively, since all bandwidth that is received by a leecher can be made available to other leechers. The proof is stated below. An illstration of the proof is displayed in Figre 2. Proof of Theorem 1 Sppose that the nmber of leechers in a particlar swarm is n, and that every leecher obtains a download speed of /n from the seeders. We assme first that c. Since there are only (n 1) leechers to barter with, not more than a bandwidth of (n 1)(/n) can be sed effectively for bartering with the other leechers. The maximm download speed then becomes d = n + (n 1) n =. When we do not take bartering overhead into accont, and when all peers have at least one chnk to share, we can assme this maximm is reached. It follows that when a total speed of c is obtained from the seeders, the download speed of a leecher is maximal. Hence, > c will always lead to an effective download speed of c... Analysis of the download speed In crrent BitTorrent implementations, the pload bandwidth of a peer is evenly shared among all files that it seeds or leeches. Since this also holds for the sorces, each sorce provides a bandwidth of c s /F to each swarm in the system. With S = 1, it follows from Theorem 1 that any leecher of any file obtains an effective download speed from the sorce of d = min{ c s /F, c }. The total available amont of bandwidth to a swarm of a specific file f consists of three contribtions. First

4 of all, the swarm receives its share of bandwidth from the sorce, which is c s /F. Secondly, there are M f peers that have finished downloading and are now seeding file f. Finally, there is the bandwidth contribtion from the replicators. For a file f, there are β f R replicators that are seeding f, each of which divides its bandwidth over the Q files that it is seeding. Becase of Theorem 1, each of the leechers in the swarm will obtain an effective download speed that eqals the total available bandwidth of all seeders. Hence, the effective download speed d f of a leecher in the swarm of file f is d f = min{ c s F + M f c + β f R c r, c }. (1) Q..1. Optimal nmber of replicators Since the download bandwidth of the downloading peers is bonded by c, the increase in bandwidth de to the replicators is maximized when ( β f R (1 M f )c c ) s Q. (2) F c r If the nmber of replicators is sch that given a certain β f, the reslting download bandwidth for file f is maximized, we call the replicator configration optimal for f. If the configration is optimal for all f, we call the configration optimal. We define the optimal nmber of replicators R opt as the minimm integer vale of R sch that Eq. (2) holds for all f with β f >...2. Speedp of a swarm We calclate the speedp s f of a leecher of file f as the fraction d f /(d f R= ). According to Eq. (1) this reslts in s f = min{ 1 + β f RF c r Q(c s + F M f c),... Speedp of the system F c }. () c s + F M f c If we want to consider the system as a whole, we have to take into accont all leechers in all swarms. The average speedp ŝ over all leechers in the system is then f F ŝ = N f s f f F N. (4) f.4. Special case In order to provide more insight into the practical implications of the model, we consider the special case in which all of the following assmptions hold: (1) all peers in the system have the same speeds (c s = c r = c); (2) finished downloaders immediately leave the system, which implies that M f = for all f; () the replicator configration is homogeneos, i.e., all replicators seed the same files. A file f is therefore seeded by all or by none of the replicators. Hence, for every f it holds that either β f = 1 or β f =. Let N be the total nmber of downloaders for all files. For the homogeneos configration, we define the replication fraction α Q/F as the fraction of the available files that is seeded by the replicators. Eq. (4) is now redced to ŝ = N {f:β f =1} { R } N f min α, F 1 (5) According to Eq. (2), the speedp in this case is maximal if R R opt = α(f 1)..5. Model validation In the previos sections we have analyzed the download speed in a single swarm of file f, and the speedp of the system achieved with the replicators. In order to validate the model, we have performed emlations of real swarms sing real BitTorrent clients. We have bilt a swarm emlator for this prpose, which is based on the simlator sed in [7]. The emlator creates an artificial BitTorrent swarm and initiates a BitTorrent download. We have emlated swarms with varios nmbers of replicators. In every emlation there is a single sorce (S = 1) that seeds 8 files (F = 8), and all speeds are homogeneos (c = c r = c s = 5 MB/s). Finished peers do not remain in the system (M f = for all f). We se only one leecher in every emlation, since the download speed in a swarm is independent of the nmber of leechers. The emlation reslts for different swarms are combined to determine the system speedp for α = 1/8, 1/4, 1/2 and 1, each with a varying nmber of replicators. The reslting vales are compared with the vales predicted by Eq. (5). In Figre, the system speedp is plotted, as well as the speed of leechers that reside in a swarm with replicators. The corresponding vales along with the theoretical predictions are displayed in Table 1. It can be observed in the table that the vales for the speedp reslting from the emlations are very close to the vales predicted by the model. It is reasonable to expect a small bartering overhead, as well as an error margin in the emlations. Note that when R R opt, the emlation vales remain practically constant, as predicted by the model.

5 Speedp alpha = 1/8 alpha = 2/8 alpha = 4/8 alpha = 1 System speedp nmber of replicators Speed (MB/s) Speeds in swarm with replicators alpha = 1/8 alpha = 2/8 alpha = 4/8 alpha = nmber of replicators Figre : The system speedp (left) and the download speed of leechers in a swarm with replicators (right) for varios vales of the replication fraction α. α 1/8 1/4 1/2 1 R sim model sim model sim model sim model Table 1: The system speedp with varying nmbers of replicators. The cases where the replicator configration is (theoretically) optimal are printed in boldface. 4. EVALUATION The validated model as presented in the previos section offers an accrate way to determine the speeds in a system where the specific swarm properties for every file f are known. We now want to provide insight in the behavior of a realistic system in which swarms and download speeds dynamically change de to arriving and departing peers. We have performed simlations of varios configrations of bandwidth-symmetric networks, both with and withot replicators. In this section we describe the simlation setp and we present the simlation reslts Simlation setp We have simlated a bandwidth-symmetric BitTorrent network with one sorce (S = 1) that has F = 4 files available. There are 1 replicators (R = 1) that seed a fraction α = 1/4 of these files. The replicators are homogeneos: each replicator seeds the same set of files. Given these parameters, the nmber of replicators is optimal (R = R opt ). All files have a size of 5 MB and all pload and download bandwidths in the system are set to 5 MB/s. In the system, peers reqesting a file arrive according to a Poisson process with arrival rate λ. We have performed simlations for vales of λ between 1 and 48 arrivals/hor. In each of the simlations we have measred the download time of a file as soon as a steady state was reached, i.e., a state in which the available download speed for the file no longer changed over time. Each incoming reqest is associated with a specific file according to a given file poplarity distribtion. We have simlated two different file poplarity scenarios: a homogeneos file poplarity where every file has an eqal probability of being reqested, and a Zipf-distribted file poplarity. In both cases, the file poplarity does not change over time. In the homogeneos case, the replicators seed the same set of 1 arbitrary files. In the Zipfdistribted case, we have evalated the system with varios replication policies. We have assessed five different network configrations: (1) A client-server network (CS); (2) A BitTorrent network withot replication where all peers leave immediately after finishing their download (BT); () A Replicated BitTorrent network where

6 Steady-state download time (homogeneos poplarity) Steady-state download time (zipf poplarity) Download time (s) CS BT RBT BT-15 RBT-15 Download time (s) CS BT RBT BT-15 RBT Reqest arrival rate (per hor) (a) Reqest arrival rate (per hor) (b) Figre 4: The download times in different bandwidth-symmetric BitTorrent networks with (a) homogeneos file poplarity, and (b) Zipf-distribted file poplarity. 5 4 no replication replicate most poplar files replicate medim poplar files replicate least poplar files 4 5 Download time (s) 2 System speedp Reqest arrival rate (per hor) % 1% 2% % 4% 5% 6% 7% 8% 9% 1% Replication fraction Figre 5: Comparison of different replication policies nder a Zipf-distribted poplarity distribtion. all peers leave immediately as well (RBT); (4) A BitTorrent network with 15 mintes seeding of each finished peer (BT-15); (5) A Replicated BitTorrent network with 15 mintes seeding of each finished peer (RBT-15) Reslts In Figre 4, the steady state download times are displayed for the two poplarity distribtions and the varios network configrations. In these reslts, the replication policy is sch that the 1 most poplar files are seeded by the replicators. It can be observed that the client-server download time stays low ntil the arrival rate reaches a certain threshold, after which it explodes. This is to be expected since if reqests arrive with a higher rate than the rate with which they can be finished by the server, the download speed drops to zero. The plain BitTorrent con- Figre 6: Inflence of the replication fraction on the speedp of a system with 1 replicators and a Zipf distribted file poplarity with 24 reqests per hor. The replicator policy is to seed the most poplar files. figration shows a far better scaling behavior in which the download time converges to 4 seconds. This again is intitive since with a high enogh arrival rate, swarms will be active for each of the 4 files continosly and the bandwidth of the sorce will be divided eqally over these swarms. With a reslting bandwidth of 5/4 MB/s, a download of 5 MB natrally takes 4 seconds. For both file poplarity distribtions, the configrations with replicators perform mch better than the other configrations. The most significant speedp is obtained in the Zipf case with immediate leave of finished peers, where replication leads to download times that are close to 25% of those in a network withot replication. If finished downloaders are seeding as well, download times are still only 5% of the times withot replication. In the

7 homogeneos case, the trends sggest that in a configration where finished downloaders remain in the system, the effect of replication will eventally diminish. This is intitive since replicators are seeders, and if the nmber of other seeders in the system grows, the relative contribtion of the replicators becomes less significant. Figre 4 (a) shows a decreasing download time when finished peers remain seeding, since the total contribtion in bandwidth of finished peers natrally grows with the arrival rate of new peers. In Figre 5, the download speeds for three different replication policies are displayed for a Zipf distribted file poplarity scenario with no seeding of finished peers: (1) replicating the most poplar files; (2) replicating medim poplar files; () replicating the least poplar files. As can be expected, replicating the most poplar files yields the best reslts. The swarms of more poplar files are bigger and therefore the speed with which these swarms are served benefits larger nmbers of peers. This policy performs far better than the others while there seems hardly a difference between replicating a set of medim poplar files or the set of least poplar files. This can be explained by the natre of the long tailed Zipf distribtion where the difference in poplarity between the most poplar files and medim poplar files will be far greater than the difference in poplarity between medim poplar files and the least poplar files. In Figre 6, the inflence of the replication fraction on the system speedp is displayed for a system with 1 replicators, a Zipf distribted file poplarity, and 24 reqest arrivals per hor. It is important to observe that when the replication fraction is larger than 5%, the 1 replicators case a speedp that exceeds 11, the vale that wold be expected at first sight. This can be explained by the fact that all reglar BitTorrent clients divide their bandwidth eqally over all files that they are seeding (instead of over all peers that are downloading from them). As a reslt, the bandwidth available for the most poplar swarm is eqal to the bandwidth available to the least poplar swarm. With 1 replicators, more swarms will obtain a maximm download speed which will case a more efficient overall BitTorrent distribtion. Overall, it is clear from the reslts that replication highly increases the performance of bandwidthsymmetric BitTorrent networks, both with homogeneos and Zipf-distribted file poplarity. 5. DISCUSSION In or model and experiments, we have taken varios assmptions of the network environment and file poplarity conditions. We will discss the most important assmptions and their implications in a more general way here Bandwidth homogeneity It is assmed throghot the model that all peers have bandwidth symmetry, and that this bandwidth is homogeneos throghot the system. Even thogh bandwidth symmetry is realistic for most LANs, there might in reality be bandwidth bottlenecks in the network. First of all, different segments of the network might be connected by backbones that form a bottleneck. Secondly, organizations might be spread over mltiple bildings or locations, connected via the Internet. In these sitations, the scalability of Theorem 1 will be limited by pper bonds depending on the location of the varios peers in a swarm. When a specific network strctre is known, the model can be adapted to this network by incorporating scalability limitations in the eqations. It follows natrally that as long as the pper bonds are not reached by the sorces and the downloaders, the download speeds can be increased by sing replicators Replicator contents Since we have analyzed the replicators in a general context, we have assmed homogeneos replicators which all seed the same files. In a real system however, it might be highly advantageos to allow different replicators to replicate different files. Especially when replicators have different locations in the network, replicators can be dedicated to replicate files that are poplar in specific network segments. Sch systems are hard to analyze a-priori withot knowing the details of the context, since many complex assmptions wold have to be made abot the network strctre, the poplarity of different files within different network segments, and the location of replicators throghot the system. However, when the environment and conditions are known in detail, or general model can first be applied separately to each segment of the network, after which the reslting sb-models can be joined in a more complex, system-wide model. Simlations can then be performed in order to determine optimal placement and policies of the replicators. 6. RELATED WORK As mentioned in the introdction, most papers on BitTorrent focs on heterogeneos end-sers sharing files on the Internet. A notable exception is the work presented in [6] and [8], where BitTorrent-based data distribtion on LAN-based desktop grids is stdied. The athors

8 show by experiments that BitTorrent clearly otperforms FTP for the dissemination of large files over a LAN, and present an enhancement of the protocol that improves the performance for small file distribtion as well. However, replication mechanisms sch as the one we present in this paper are not considered. Replication and caching have been widely researched in a variety of contexts. In the context of P2P however, research ntil now has focsed on (earlier) P2P protocols that are based on searching an instance of a reqested file and directly transferring it from a particlar location. In [9], the effect of the nmber of replicas on search performance in nstrctred P2P networks is investigated. This work is contined in [1] and [11], where it is arged that a proportional replication scheme minimizes the download time, the workload, and the sed network bandwidth. The athors frthermore show that near-proportional replication can be obtained by sing an LRU cache replacement policy. In [12], varios replication strategies are compared as well and a sqare-root replication strategy is presented, which is arged to be better than both niform and proportional replication. In [1] and [14], the effect of varios replication strategies on file availability and reliability is stdied. 7. CONCLUSIONS In this paper, we have presented a novel mechanism for replication in bandwidth-symmetric BitTorrent networks: Replicated BitTorrent. The concept of replicators is presented, which are peers that are added to a BitTorrent network, and that atomatically replicate a sbset of the files that are available in the system, thereby increasing the download speeds of downloaders in the system. We have presented and validated a mathematical model of Replicated BitTorrent which allows s to compte the download speeds and assess the benefit of replicators. Frthermore, we have simlated Replicated BitTorrent in a dynamic setting where download speeds and swarm properties change de to arriving and departing peers. The simlation reslts clearly demonstrate the significant speedp of Replicated BitTorrent over reglar BitTorrent. References [1] BitTorrent. [2] B. Cohen. Incentives bild robstness in bittorrent. In Workshop on Economics of Peer-to-Peer Systems, Berkeley, USA, May 2. [] D. Qi and R. Srikant. Modeling and performance analysis of bittorrent-like peer-to-peer networks. In Proc. of ACM SIGCOMM 24, Portland, Oregon, USA, Agst 24. [4] J.A. Powelse, P. Garbacki, D.H.J. Epema, and H.J. Sips. The bittorrent p2p file-sharing system: Measrements and analysis. In Proc. of the 4th Int l Workshop on Peer-to-Peer Systems (IPTPS 5), Febrary 25. [5] A.R. Bharambe, C. Herley, and V.N. Padmanabhan. Analyzing and improving a bittorrent network s performance mechanisms. In Proc. of IEEE Infocom 26, Barcelona, Spain, April 26. [6] B. Wei, G. Fedak, and F. Cappello. Collaborative data distribtion with bittorrent for comptational desktop grids. In Proc. of the The 4th International Symposim on Parallel and Distribted Compting (ISPDC 5), pages , Washington, DC, USA, 25. IEEE Compter Society. [7] P. Garbacki, A. Iosp, D. Epema, and M. van Steen. 2Fast: Collaborative downloads in p2p networks. In Proc. of the 6th IEEE International Conference on Peer-to-Peer Compting, Cambridge, September 26. [8] B. Wei, G. Fedak, and F. Cappello. Schedling independent tasks sharing large data distribted with bittorrent. In Grid Compting Workshop, pages IEEE Compter Society, 25. [9] S. Tewari and L. Kleinrock. Analysis of search and replication in nstrctred peer-to-peer networks. In Proc. of ACM SIGMETRICS 25, 25. [1] S. Tewari and L. Kleinrock. On fairness, optimal download performance and proportional replication in peer-to-peer networks. In Proc. of IFIP Networking 25, pages , 25. [11] S. Tewari and L. Kleinrock. Proportional replication in peer-to-peer networks. In Proc. of IEEE INFO- COM 26, 26. [12] E. Cohen and S. Shenker. Replication strategies in nstrctred peer-to-peer networks. In Proc. SIG- COMM 2, Pittsbrgh, USA, Agst 22. [1] G. On, J. Schmitt, and R. Steinmetz. The effectiveness of realistic replication strategies on qality of availability for peer-to-peer systems. In Proc. of the rd International Conference on Peer-to-Peer Compting (P2P ), 2. [14] R. Bhagwan, D. Moore, S. Savage, and G. Voelker. Replication strategies for highly available peer-topeer storage. In Proc. of FDiCo: Ftre directions in Distribted Compting, 22.