AN early generation of unstructured P2P systems is

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1 1078 IEEE TRANSACTIONS ON PARALLEL AND DISTRIBUTED SYSTEMS, VOL. 16, NO. 11, NOVEMBER 2005 Dynamic Layer Management in Suereer Architectures Li Xiao, Member, IEEE, Zhenyun Zhuang, and Yunhao Liu, Member, IEEE Abstract Suereer unstructured P2P systems have been found to be very effective by dividing the eers into two layers, suerlayer and leaf-layer, in which message flooding is only conducted among suerlayer and all leaf-eers are reresented by corresonding suereers. However, current suereer systems do not emloy any effective layer management schemes, so the transient and lowcaacity eers are allowed to act as suereers. Moreover, the lack of an aroriate size ratio maintenance mechanism on suerlayer to leaf-layer makes the system s search erformance far from being otimal. We resent one workload model aimed at reducing the weighted overhead of a network. Using our roosed workload model, a network can determine an otimal layer size ratio between leaf-layer and suerlayer. We then roose a Dynamic Layer Management algorithm, DLM, which can maintain an otimal layer size ratio and adatively elect and adjust eers between suerlayer and leaf-layer. DLM is comletely distributed in the sense that each eer decides to be a suereer or a leaf-eer indeendently without global knowledge. DLM could effectively hel a suereer P2P system maintain the otimal layer size ratio and designate eers with relatively long lifetime and large caacities as suereers, and the eers with short lifetime and low caacities as leaf-eers under highly dynamic network situations. We demonstrate that the quality of a suereer system is significantly imroved under the DLM scheme by comrehensive simulations. Index Terms Unstructured eer-to-eer, suereer architecture, layer management, workload analysis, adative algorithms. æ 1 INTRODUCTION AN early generation of unstructured P2P systems is urely unstructured, such as Gnutella [8], where all the eers are involved in the query flooding rocess without excetion. However, eers can be very different from each other in bandwidth, CPU ower, duration times, shared files, and interests [6], [9]. In ure P2P systems, all eers, regardless of their caacities, act equal roles and take the same resonsibilities for all the oerations. As the network size increases, the weak eers will seriously limit the scalability of P2P systems. To address this roblem, suereer architectures were roosed, which have been attracting more and more users in unstructured P2P communities. For examle, KaZaA and early Morheus [15], based on FastTrack structure, have dominated the to downloads lists for most of 2001 and are continuing to increase in oularity in 2002 [9], [3]. Schemes are also roosed to introduce Ultra-eers into Gnutella rotocol [22]. The advantages of suereer systems are well discussed in [26]. However, current suereer systems do not exloit any effective layer management schemes; thereby, they leave the following three roblems unsolved: First, how many suereers are referred to exist in the network? In other words, what is the otimal size ratio of leaf-layer to suerlayer? Second, assuming an otimal value of layer size ratio exists for a network, how can this layer size ratio be. L. Xiao and Z. Zhuang are with the Deartment of Comuter Science and Engineering, 3115 Engineering Building, Michigan State University, East Lansing, MI {lxiao, zhuangz1}@cse.msu.edu.. Y. Liu is with the Deartment of Comuter Science, Hong Kong University of Science and Technology, Kowloon, Hong Kong. liu@cs.ust.hk. Manuscrit received 31 July 2004; revised 17 Dec. 2004; acceted 21 Dec. 2004; ublished online 21 Set For information on obtaining rerints of this article, lease send to: tds@comuter.org, and reference IEEECS Log Number TPDS maintained? Current suereer aroaches lack an aroriate size ratio maintenance mechanism and make the system s search erformance far from otimal. Third, what tyes of eers should be elected to suerlayer? This roblem has not been effectively solved yet. As far as we know, no efficient mechanism is given to ensure that the suereers have large-caacity and long-lifetime. Since no global knowledge is available in distributed P2P systems, it is imossible to tell what values can be high or long enough, esecially under highly dynamic environments. This roblem is even more difficult to solve when the network needs to consider more metrics besides caacity and lifetime. In this aer, we resent one workload model to solve the first question mentioned above and resent one dynamic layer management algorithm (DLM) to solve the other two questions. The main contributions of this aer are as follows:. First, we discuss the imortance for a suereer P2P system to have an aroriate size ratio on suerlayer to leaf-layer and obtain the otimal size ratio by modeling suereer systems based on existing studies and our observations.. Second, we roose a fully distributed dynamic layer management algorithm, DLM, which can adatively elect eers and adjust them between suerlayer and leaf-layer. DLM is comletely distributed in the sense that each eer is determined to be a suereer or a leaf-eer indeendently without global knowledge. DLM could effectively hel a suereer-p2p system maintain an aroriate layer size ratio and designate eers with relatively long lifetime and large caacities as suereers and the /05/$20.00 ß 2005 IEEE Published by the IEEE Comuter Society

2 XIAO ET AL.: DYNAMIC LAYER MANAGEMENT IN SUPERPEER ARCHITECTURES 1079 eers with short lifetime and low caacities as leafeers under highly dynamic network situations.. Third, we demonstrate that the quality of a suereer system is significantly imroved under the DLM scheme by comrehensive simulations. The rest of this aer is organized as follows: In Section 2, we discuss the related work. We resent our workload model to illustrate the trade-off between two workloads as a function of layer size ratio in Section 3. Using the workload model, we obtain an otimal layer size ratio value that can minimize the weighted workload. In Section 4, we describe the design rationale of DLM, along with different variations of it. We then evaluate the effectiveness of the workload model and DLM through simulations in Section 5 and discuss the side effects of DLM in Section 6. We conclude this aer in Section 7. 2 RELATED WORK To accurately understand P2P systems, many researchers have tried to model the behaviors of the eers and the network. Ge et al. [7] develoed a simle mathematical model to illustrate the erformance issues of P2P systems and aly the model to three different eer-eer architectures: centralized indexing, distributed indexing with flooded queries, and distributed indexing with hashdirected queries. For unstructured P2P systems, Menasce and Kanchanaalli [14] roosed a P2P rotocol and develoed an analytical model to analyze the erformance of the resented rotocol. The studied metrics include the success rates, the fraction of eers involved in a search, and the average number of hos required to find a directory entry. Cooer and Garcia-Molina [5] roosed a search/index links (SIL) model for P2P search networks and their simulation results suggest that the arallel search clusters are suerior to existing suereer networks under some metrics. Numerous structured P2P rotocols have also been resented, along with mathematical analysis [18], [23], [27], [17]. To cature the common design techniques of the various structured P2P mechanisms, a tree-based model was roosed in [10] and the routing adatively feature was analyzed. Xu et al. [24] studied the fundamental tradeoffs between the routing table size and the network diameter by modeling the P2P systems. Alications based on suereer architectures are consuming a large ortion of Internet traffic. In June 2002, for examle, KaZaA consumed aroximately 37 ercent of all TCP traffic, which was more than twice the Web traffic on the University of Washington camus network [9]. Sandvine also estimates that 76 ercent of P2P file sharing traffic belongs to KaZaA/FastTrack traffic and only 8 ercent comes from Gnutella in the US [2]. Thus, suereer architectures are attracting more and more attention in P2P research communities. To well understand the behavior of suereer systems, Yang and Garcia-Molina [26] examined the erformance trade-offs in suereer systems by considering suereer redundancy and toology variations. They also studied the otential drawbacks of suereer networks and reliability issues. To make the Gnutella network more scalable, Singla and Rohrs [22] described how ultraeers work in an ideal network with a static toology and a handshaking mechanism based on the Gnutella v0.6 rotocol, in which some requirements for suereers were roosed, such as not firewalled, suitable oerating system, sufficient bandwidth, and sufficient utime. Singh et al. [21] resented some incentives to deloy suereers and roosed a toic-based search scheme to increase the effectiveness of suereers. However, because KaZaA is rorietary and uses encrytion, little has been known about the rotocols, architectures, and behaviors of KaZaA, the most oular alication based on suereer architectures. With over three million users at any time, KaZaA has neither been documented nor analyzed. Since suereers and leaf-eers take different resonsibilities, eers need be assigned to aroriate layers through some well-designed layer management mechanism. But, as far as we know, no such mechanism is roosed to date. In this aer, we roose a dynamic layer management algorithm and evaluate its effectiveness. 3 WORKLOAD MODEL We first discuss the imortance of maintaining an aroriate layer size ratio in a suereer network. We then roose a workload model to analyze the erformance of suereer architectures in this section. Our model focuses on the amounts of workloads, both on suereers and the overall network, and we obtain an otimal layer size ratio by minimizing the weighted workload. 3.1 Imortance of Aroriate Layer Size Ratio In a suereer network, the search is mainly erformed by suereers, which actually form the backbone of the P2P network. Suereer systems take advantage of eers heterogeneity by dividing eers into two layers: suerlayer and leaf-layer, thereby scaling better by reducing the number of query aths [26]. The eers in the suerlayer are called suereers, which are resonsible for rocessing and relaying the queries that come from the leaf-eers and other suereer neighbors. Each suereer behaves like a roxy or an agent of its leaf-eers and kees an index of its leafeers shared data. The eers in the leaf-layer are called leafeers, which only kee a number of connections to suereers for the urose of reliability. In suereer systems, both suereers and leaf-eers can submit queries, but only suereers can relay queries and resonses. After receiving a query, a suereer first checks to see if the queried data is stored locally or in its leaf-eers (by checking the index of its leaf-eers objects). If some results are found in a eer, it sends a QueryHit message back to the query source along the inverse query ath. Comared with ure P2P systems, suereer systems have higher search efficiency because, instead of all the eers, only suereers are involved in search rocesses. Intuitively, an aroriate layer size ratio, i.e., the ratio of the number of leaf-eers to the number of suereers, is of great imortance. One roosed layer management mechanism [25] uses reconfigured values as the thresholds to

3 1080 IEEE TRANSACTIONS ON PARALLEL AND DISTRIBUTED SYSTEMS, VOL. 16, NO. 11, NOVEMBER 2005 Fig. 1. Inaroriate layer size ratio. select suereers which cannot maintain an aroriate size ratio and are exlained in Fig. 1. Suose that a system sets the bandwidth threshold to 50KB/s (the Ultra-eer Proosal in Gnutella 0.6 [1] recommends at least 15KB/s downstream and 10KB/s ustream bandwidth). Peers with bandwidths larger than 50KB/s can be selected as suereers. A network with good size ratio is shown in Fig. 1a, where the number inside a eer denotes its bandwidth value. However, after a certain time eriod, if most joining eers have high bandwidths, the system will soon have too many suereers, as shown in Fig. 1b. The system in this case will be more like a ure P2P system since most eers take art in the search rocess. If most joining eers are weak ones with low bandwidths, the system will behave like a centralized P2P system with too few suereers, as shown in Fig. 1c. A major drawback of a centralized P2P system is the single oint of failure. 3.2 Workload Model To better analyze the imact of layer size ratio on the system erformance, we model a P2P suereer system as follows: Consider a P2P network with n articiating eers, in which n s eers are suereers and n l eers are leaf-eers. Assume that each leaf-eer connects to m suereers and each suereer connects to k s other suereers and k l leafeers, on the average. We use to denote the layer size ratio of a suereer network, which is given by: ¼ n l n s. Theorem 1. On the average, each suereer connects to m leafeers and the number of suereers is given by n s ¼ n 1þ. Proof. Consider all the connections between the suerlayer and the leaf-layer. The out-degree from the suerlayer to the leaf-layer is n s k 1 and the out-degree from the leaflayer to the suerlayer is n l m. Since these two outdegrees are equal, we have k l ¼ nlm n s ¼ m. Also, since n s þ n l ¼ n and ¼ nl n s, we have n s ¼ n tu 1þ. We define two different tyes of workloads: the Workload on the Overall Network and the Workload on a Suereer. The Workload on the Overall Network, denoted as W on, is defined as the total traffic overhead required to erform a search task in a P2P network. The Workload on a Suereer, denoted as W s, is defined as the traffic overhead required on a suereer to erform a search task. The erformance of a network deends on the workloads on each eer and the overall network. The network administrators (or ISPs) are concerned more about W on, while the users are concerned more about W s. We use the number of messages needing to be rocessed to measure the amount of the workloads. Hence, each connection creation, query initiation, and query relay can be done using one message, resectively. Now, we analyze W on and W s as a function of. A suereer mainly erforms the following tasks: 1) maintaining the connections to the neighboring eers, 2) rocessing the queries initiated from its leaf-eers and itself, and 3) relaying the queries come from its suereer neighbors. Therefore, the workloads on a suereer and the overall network can be divided into three arts: Connection Workload, Query Workload, and Relay Workload. We now define and analyze each of them Connection Workload There are two kinds of connections in suereer networks the connections between suereers and the connections between leaf-eers and suereers. The Connection Workload of a eer is defined as the traffic overhead incurred to maintain the connections to the neighboring eers. The amount of connection workload on any eer is directly related to the size and stability of the neighboring eer set and is roortional to the number of neighbors and inversely roortional to the average u time of them. We use W s cw and W on cw to denote the ortions of connection workload in W s and W on, resectively. Thus, W s cw ¼ k l t l þ k s t l t s ¼ m þ k s t s and W on cw ¼ n lm þ n s ðk l þ k s Þ¼ mn þ nðm þ k sþ ; t l t s ð1 þ Þt l ð1 þ Þt s where k l is the average number of neighboring leaf-eers of a suereer, k s is the average number of neighboring suereers of a suereer, and t l and t s are the average lifetimes of neighboring leaf-eers and suereers, resectively Query Workload In a tyical query rocess, when a query is issued by a leafeer, the leaf-eer sends the query to its neighboring suereers. (In this aer, we assume that a leaf-eer sends a query to all of its suer neighbors.) This rocess contributes to W on and W s by the communication overhead between leaf-eers and suereers. Query Workload is defined as the traffic overhead incurred for a eer to rocess the queries generated by its leaf neighbors and itself. The amount of the query workload is roortional to the number of leaf neighbors and the query frequency of each eer. We use W s qw and W on qw to denote the ortions of query workload in W s and W on, resectively. Thus, we have, W s qw ¼ k l f ¼ mf and W on qw ¼ nmf 1 þ ;

4 XIAO ET AL.: DYNAMIC LAYER MANAGEMENT IN SUPERPEER ARCHITECTURES 1081 Fig. 2. Number of covered suereers. where f is the query frequency of a eer. Since, in reality, the query frequency of a eer does not have a correlation with its identity, we assume that all the eers have the same f values regardless of suereers or leaf-eers Relay Workload After receiving a query, suereers relay it to other suereers. In this rocess, the relaying communications are erformed among suereers only. Relay Workload is defined as the traffic overhead incurred to rocess queries relayed from the suereer neighbors. Since, in unstructured P2P systems, each eer indeendently decides what data to share, the search success rate heavily deends on how many eers are searched. To quantify the relay workload, we assume that each query should reach at least a certain number of eers to ensure a given query search scoe. We use to denote the number of eers that are queried (covered) in a search task. The following theorem secifies two bounds of the number of covered suereers as a function of : Theorem 2. In a suereer network with each leaf-eer connecting m suereers and each suereer connecting k 1 leaf-eers, to cover eers, the number of suereers that should be queried has a lower bound of ð1þk l Þ and an uer bound of m ðmþk l Þ on average. Proof. Since the queries are relayed and rocessed among suereers and each suereer stores the data indices of k l leaf-eers, a suereer can be viewed to reresent k l þ 1 eers (k l leaf-eers and itself). In Fig. 2, suose s suereers are queried and they are all located in the gray ellise zone, then the number of their connected leaf-eers is l ¼ s. One extreme case is that every leaf-eer, which is reresented by the s suereers, only connects to these s suereers, as shown in Fig. 2a. Since the total number of outgoing links connecting the leaf-layer is s k 1, which is equal to the number of incoming links l m from leafeers, we have s k l ¼ l m. This is the uer bound case. The other extreme case is that each leaf-eer, which is reresented by the s suereers, connects to only one of these s suereers, as shown in Fig. 2b. So, we have s k l ¼ l. This is the lower bound case. Thus, in general, we have s s k l ð s Þm, which is ð1þk lþ s m ðmþk. tu lþ Theorem 3. When s << n s, the robability of a leaf-eer connecting to more than one covered suereer is very close to zero. Proof. Consider a leaf-eer that connects to at least one covered suereer. Now, we comute the robability that it connects to more than one covered suereer. Suose that the eer already has one connection to a covered suereer and now it needs to make m 1 more connections to suereers. We can divide the rest of the n s 1 suereers into two grous: the covered grou (with size s 1) and the uncovered grou (with size n s s ). Let us use variable c to count the number of new connections to the covered grou. Since the m 1 more suereers are randomly selected (without relacement) from these two distinct grous, we can see that c follows the hyergeometric distribution. Thus, s 1 ns s 0 m 1 P ðc 1Þ ¼1 P ðc ¼ 0Þ ¼1 n s 1 m 1 ¼ 1 Ym 2 i¼0 ðn s s iþ ðn s i 1Þ : This value is very small when s << n s. For examle, when m ¼ 2, P ðc 1Þ ¼ s 1 n s 1 0. When m ¼ 3, P ðc 1Þ ¼1 ðn s s Þðn s s 1Þ ðn s 1Þðn s 2Þ 2 s n s 2 0: From Theorems 2 and 3, we can see that, when s << n s, the robability of a leaf-eer connecting to more than one suereer is very small. Thus, to cover eers, the number of covered suereers s is very close to the lower ð1þk lþ. By considering the two extremes illustrated above, we bound of give the uer and lower bounds of the number of messages used in a query task in Theorem 4. Theorem 4. To cover s ¼ messages ranges from mechanisms. ð1þk lþ ð1þk lþ suereers, the number of query 1 to k s ð1þk lþ, regardless of search Proof. In the suerlayer, the queries are relayed among suereers through various search mechanisms. Let us consider a network with five eers, which is shown in Fig. 3. The number associated with each link reresents the latency between the two eers of the link. Assume that eer O is the query source. The ideal search algorithm should only query each eer once. Therefore, to cover s suereers, it can only use ð s 1Þ messages, as shown in Fig. 3a. While, for an inefficient search algorithm such as blind flooding, some eers may be queried more than once with redundant messages, according to Gnutella rotocol, no eer will relay the same query to the same link more than once. Thus, each link relays the same query at most twice. In ut

5 1082 IEEE TRANSACTIONS ON PARALLEL AND DISTRIBUTED SYSTEMS, VOL. 16, NO. 11, NOVEMBER 2005 Fig. 3. Messages used to cover five eers. (a) Most efficient search. (b) Most inefficient search. Fig. 3b, all the links among other eers excet O will rocess the query twice. For s eers with each eer connecting k s other eers, the maximum number of links among them is sk s 2, so the maximum number of messages is s k s. Let s ¼ 1þk l,we can rove the theorem. tu Now, we analyze the average Relay Workload art of W s and W on. Suose that each query sent from suereers eventually uses g messages among suereers, which means that it will be relayed g times in the suerlayer in total. Also, since each eer in the network initiates f queries er time unit and each suereer receives ð1 þ k l Þf queries from itself and its leaf neighbors, the query frequency of the total network is ð1 þ k l Þn s f. From Theorem 4, we know that the number of messages ð1þk l Þ used by a query ranges from 1 to ks ð1þk l Þ. Thus, the lower and uer bounds of the ortions of the relay workload in W on are given by W on rwðminþ ¼ð1þk l Þn s f 1 ¼ n s fð 1 k l Þ 1 þ k l and ¼ nf ð 1 mþ 1 þ W on rwðmaxþ ¼ n s fk s ¼ fk sn 1 þ : Since the relay workload is distributed among all the ns suereers, on the average, Ws rw is 1 n s of W on rw and has the lower and uer bounds: W s rwðminþ ¼ð 1 mþf and W s rwðmaxþ ¼ fk s : Otimal Layer Size Ratio In a network with n eers, we want to find a highly suitable layer size ratio, that is, an otimal value. We deal with this roblem by considering both W s and W on. Since the total workload is the sum of the three workloads discussed above, we have, and W s ¼ W s cw þ W s qw þ W s rw W on ¼ W on cw þ W on qw þ W on rw : Thus, for the most efficient search algorithm, we have the lower bounds of W s and W on as W sðminþ ¼ m þ k s þ mf þð 1 mþf t l t s ¼ m þ k s þð 1Þf and t l t s W on ðminþ ¼ mn þ nðm þ k sþ þ nmf ð1 þ Þt l ð1 þ Þt s 1 þ þ nf ð 1 mþ 1 þ ¼ n m þ m þ k s þ f f : 1 þ t l t s For the most inefficient search algorithm, we have W sðmaxþ ¼ m þ k s þ mf þ fk s t l t s ¼ 1 þ f m þ k s þ fk s ; t l t s W onðmaxþ ¼ mn þ nðm þ k sþ þ nmf ð1 þ Þt l ð1 þ Þt s 1 þ þ fk sn 1 þ ¼ n m þ m þ k s þ mf þ fk s : 1 þ t l t s Ideally, the otimal value should minimize both of these two workloads. But, unfortunately, it is imossible to minimize these two workloads simultaneously. In fact, there is a trade-off between these two workloads. With more suereers in the network, W on will increase, but W s will decrease and vice versa. Thus, we use a weighted workload, W, to consider both W s and W on ; and it is given by W ¼ W s þ W on n ; ð1þ where and are weights of W s and W on, resectively, and we set þ ¼ 1. If a network concerns more on W s, we can set >, otherwise, we set >. Both and are reconfigured. Since both W s and W on are functions of, by differentiating (1), we can obtain the otimal value as rffiffiffiffiffiffiffiffiffiffiffiffiffi 0 B C ¼ 1; ð2þ A

6 XIAO ET AL.: DYNAMIC LAYER MANAGEMENT IN SUPERPEER ARCHITECTURES 1083 where, for the most efficient search algorithm, A ¼ m ;B¼ k s þ f f ; and C ¼ 1 þ 1 m; t l t s t l t s while, for the most inefficient search algorithm, A ¼ 1 þ f m; B ¼ 1 þ f k s ; and t l t s C ¼ 1 þ 1 þ f m: t l t s For a secific network, we assume that the values of,, m, and are all given by the rotocol and the values of k s, t l, and t s can be obtained from each eer s revious exeriences. Actually, these values are also evaluated by many studies [11], [9]. Therefore, on each eer, an otimal value of layer size ratio can be comuted indeendently. In KaZaA, suereers are found to have leafneighbors [12]. Since each leaf-eer normally kees connections to two to three suereers, the layer size ratio is exected to be several dozens. This value is very close to the values we comuted using our workload model, where the layer size ratio is also about several dozens in Section DESIGN OF DLM We roose a Dynamic layer management algorithm (DLM) that intends to deal with the following two roblems, which are not trivial to deal with since no eer has the global knowledge of the network: One roblem is how to maintain an otimal layer size ratio in a highly dynamic environment. The other roblem is which eers should be romoted (from leaf-layer to suerlayer) or demoted (from suerlayer to leaf-layer) when the system has more or less suereers than otimal. In other words, DLM should achieve two goals: 1) maintaining the size ratio of suerlayer to leaf-layer and 2) keeing the eers with larger lifetimes and caacities as suereers and the eers with shorter lifetimes and caacities as leaf-eers. Unfortunately, these two goals are not always comatible. For examle, at some time, the system may have a highly skewed layer size ratio and more suereers are heavily demanded, but the new joining eers all have low bandwidths. In this case, DLM needs to consider both goals and adatively romote some leaf-eers, though not owerful enough, to suerlayer. Moreover, to erform well under both stable and highly changeable network situations, DLM needs to dynamically adjust the romotion and demotion olicies adative to the changing environments. Ideally, the suereers should be more owerful and with a longer lifetime than average eers. To measure the eligibility of a eer, we define two metrics, Caacity and Age. Caacity is defined as the ability of a eer to rocess and relay queries and query resonses, while age is defined as the length of time u to now since a eer joined the network. We use Caacity(d) to refer to the caacity value of a eer d. The value of caacity can be comuted as CaacityðdÞ ¼ Xr i¼1 w i v i ðdþ; where r is the number of metrics affecting the eer s caacity, v i ðdþ is the value of ith metric, and w i ðdþ is the weight of the corresonding metric. Examles of the metrics affecting the caacity are bandwidth, CPU seed, and storage sace. We assume that a eer s caacity value does not change throughout its session and can be known at the time it is connected to the network. In this aer, for simlicity, we omit the comutation details of a eer s caacity and just use the bandwidth of a eer as its caacity, which does not affect the resentation of DLM algorithm. The lifetime of a eer is the eriod of time in which the eer articiates in the P2P network. The age is less than or equal to the lifetime of a eer by the definition. DLM will automatically romote the leaf eers with larger ages to suerlayer and demote the suereers with smaller ages to leaf-layer. Although the caacity value can be set at the time when the eer joins the system, there are no means to know the lifetime of a eer since a eer may leave the network at any time. One ractical way to infer the lifetime is by monitoring its age: The longer the eer lives, the more likely it is that the eer will live in the future. So, we use the age of a eer in DLM to redict its lifetime and use ageðdþ to denote eer d 0 s age value. 4.1 DLM-1 We resent the first aroach, DLM-1. In DLM-1, each eer first collects its neighboring eers information, which includes the caacities, ages, and number of neighboring leaf-eers (for a suereer neighbor). After rocessing the collected information, the eer will determine its own status. We describe DLM-1 in four stes Ste 1: Information Collection Peers first exchange information with their neighbors using messages. We design two airs of messages which are emloyed by a air of leaf-eers and suereers. The first air of the messages is neigh_num_request and neigh_num_ resonse messages; neigh_num_request is sent from a leafeer d to a suereer s to request the leaf neighbor number of s and we use l nn ðsþ to refer to this number. Message neigh_num_resonse is the resonse from the suereer. The second air of the messages is value_request and value_ resonse, which are sent between a suereer and a leaf-eer to query and resond to the leaf-eer s caacity and age. Note that these two airs of messages can also be iggybacked in other messages in some P2P rotocols. One issue is how often the eers exchange this information. Obviously, higher frequency means higher accuracy and more traffic overhead. In this design, we emloy an event-driven olicy in which information exchange is invoked whenever a eer finds that a new connection is created. In simulation, we have also evaluated other olicies, such as a time interval-based olicy where eers exchange information eriodically.

7 1084 IEEE TRANSACTIONS ON PARALLEL AND DISTRIBUTED SYSTEMS, VOL. 16, NO. 11, NOVEMBER Ste 2: Maintaining Aroriate Layer-Size-Ratio One of the goals of DLM is to maintain anaroriate layer size ratio. To achieve this goal, DLM first needs to estimate the extent of aroriateness of current layer size ratio. Current layer size ratio can be easily calculated if the global knowledge is known, but, in reality, no eer has this global knowledge. However, it is trivial for a eer to collect its neighbors information. Due to the randomness of the neighbor selection mechanism in suereer systems, to some extent, the current numbers of leaf neighbors of suereers can reflect the current layer size ratio. That is, if the suerlayer size is too small, the average number of leaf neighbors of a suereer will be larger than k l, the otimal leaf neighbor number; otherwise, it will be less than k l. Since each eer knows the otimal value of, the value of k l can be comuted by using k l ¼ m. Therefore, l nn, the leaf neighbor number of some suereer, can be used as a flag of the current layer size ratio when comared with the value of k l. To illustrate the comarison method, we now define the related set of a eer, denoted as G. For a suereer s, we define GðsÞ as the set of its current neighboring leaf-eers, while, for a leaf-eer l, we define GðlÞ as the set of suereers that it has connected within a eriod of time T l. The definitions of G on suereers and leaf-eers are different as a suereer normally kees connections to many leaf-eers, while a leaf-eer normally only connects to a few suereers. To accurately estimate the network condition, we hoe that the size of G is large enough, so that we consider all the suereers that a leaf-eer has contacted in a recent eriod of time. In simulation, G contains all the suereers that a leaf-eer has connected since it joins the network. For a suereer s, since it connects to some leaf-eers, it can directly use l nn ðsþ, while, for a leaf-eer l, it uses the average l nn value of the suereers in GðlÞ. We let denote the extent of inaroriateness of current layer size ratio comared to the otimal layer size ratio and it is comuted as ¼ logðl nn =k 1 Þ. We can see that a ositive value of, where l nn is larger than k 1, means that there are too few suereers in the system since suereers have more leaf-eer neighbors than normal., while a negative value of, where l nn is smaller than k 1, means that there are too many suereers. Furthermore, a larger absolute value of means a larger degree of inaroriateness. Thereby, the value of reflects the system requirement and it is used to adjust some other arameters, which determine the ossibility of a eer s being romoted or demoted Ste 3: Scaled Comarisons of Caacity and Age DLM automatically romotes the leaf-eers with large caacities and longer lifetimes to the suerlayer and demotes the suereers with small caacities and shorter lifetimes to the leaf-layer. The decision of romotion or demotion is based on the comarison results with other eers. One straightforward way of comarison is to directly comare the metric values of a eer with other eers. However, comaring in such a direct way may fail to maintain the layer size ratio successfully. Consider a scenario in which the system needs more suereers, but the leaf-eers all have larger metric values than the current suereers. The results of simle comarisons would forbid any leaf-eer being romoted; thereby, the system cannot adjust the layer size ratio at all. DLM imroves the direct comarison by using a scaledcomarison. Since the caacity and age metrics are disjoint, that is, a eer with high-caacity does not necessarily have larger age and vice versa, we analyze these two metrics individually. In the scaled-comarison, DLM introduces two scale arameters, X caa and X age, corresonding to the two metrics, resectively. These two scale arameters are adjusted dynamically by DLM based on the value of to reflect the system requirements. For each eer that runs DLM, it uses two counting variables, Y caa and Y age, corresonding to Caacity and Age metrics, resectively. A eer sets the value of these two counting variables by comaring its metric values with the eers in its related set, G. For a eer d, the seudocodes of the scaled-comarison are listed below. for all eer d i in GðdÞ if ðcaacityðd i Þ X caa > caacityðdþþ Y caa þ¼1=ðsize of GðdÞÞ; if ðageðd i Þ X age > ageðdþþ Y age þ¼1=ðsize of GðdÞÞ; We can see that Y caa and Y age store the fractions of eers that have larger metric values than those of d in GðdÞ. Y caa reflects the relative caacity value of a eer comared to the eers in the other layer, while Y age reflects the relative age value of one eer comared to the eers in the other layer. These two variables will be used to determine the eligibility of the eer s romotion or demotion. The values of X caa and X age are adjusted according to the value of. For a suereer, if it finds that the system needs more suereers, it will decrease the ossibility of its demotion by decreasing the two scale arameters. Otherwise, it will increase the ossibility of its demotion by increasing the scale arameters, while, for a leaf-eer, if it finds that more suereers are needed, it will decrease the scale arameters in hoing to increase the romotion ossibility; otherwise, it will increase the scale arameters to decrease the romotion ossibility Ste 4: Promotion or Demotion For a leaf-eer l, ify caa and Y age are small enough, it means that many suereers in GðlÞ have metric values smaller than it. Thus, l may assume that it has relatively large metric values and may decide to be romoted to suerlayer, while, for a suereer s,ify caa and Y age are large enough, it means that many leaf-eers in GðlÞ have metric values larger than it. Thus, s may assume that it has relatively small metric values and may decide to be demoted to leaf-layer. We use two threshold variables Z caa and Z age in the determination. For a leaf-eer l, ify caa and Y age are smaller than Z caa and Z age, resectively, it will be romoted to be a suereer. In romotion, the leaf-eer kees its current connections to other suereers. The scenarios before and after eer l 0 s romotion are illustrated in Figs. 4a and 4b.

8 XIAO ET AL.: DYNAMIC LAYER MANAGEMENT IN SUPERPEER ARCHITECTURES 1085 Fig. 4. Promotion of a leaf-eer. (a) Before romotion. (b) After romotion. Fig. 5. Demotion of a suereer. (a) Before demotion. (b) After demotion. For a suereer s, ify caa and Y age are larger than Z caa and Z age, resectively, it will be demoted to be a leaf-eer. In demotion, the suereer only kees m of its current connections to other suereers and dros the connections to leaf-eers. The scenarios before and after eer s 0 s demotion are illustrated in Figs. 5a and 5b. The values of threshold variables, Z caa and Z age, are also adjusted according to the value of. When more suereers are needed, suereers will increase the values of the threshold variables to reduce the demotion tendencies and leaf-eers will reduce the values of the threshold variables to increase the romotion tendencies. For the cases where there are too many suereers, inverse measures will be taken accordingly. To achieve the two goals we set in the beginning of Section 4, DLM needs to consider two factors: the layer-sizeratio factor () and the caacity-age factor. The first factor reflects the requirement of keeing the otimal layer size ratio and the second factor reflects the requirement of keeing large-caacity and large-age eers in the suerlayer. Since the two scale arameters, X caa and X age, are adjusted based on the values of the first factor, DLM can achieve the first goal: maintaining the otimal layer size ratio. Similarly, by using the scaled comarison method, DLM achieves the second goal: keeing large-caacity and large-age eers on the suerlayer. 4.2 DLM-2 In DLM-1, a suereer estimates the current layer size ratio by monitoring the number of its leaf neighbors and a leafeer does so by monitoring the numbers of leaf neighbors of its neighboring suereers. Because the numbers of leaf neighbors of different suereers may vary greatly in the network, the estimation results might not be very accurate; therefore, it may not reflect the exact layer size ratio. We roose letting neighboring suereers exchange information in DLM-2 to more accurately estimate the system condition. In this aroach, a suereer comutes the value of based on not only its own information, but also the information of its neighboring suereers. A leafeer, in turn, can get more accurate information from its suer neighbors through information exchanging. We roose three olicies to exchange information among suereers: Pushing Exchange, Pulling Exchange, and Periodic Exchange. In Pushing Exchange, each suereer sends its calculated system information to suereer neighbors whenever it runs DLM-1. In Pulling Exchange, whenever a suereer runs DLM-1, it requests its suereer neighbors to send back their system condition, while, in Periodic Exchange, each suereer sends out its estimation result eriodically. The Periodic Exchange method is much different from the first two. The erformance of Periodic Exchange varies according to different values of T. Larger T means fewer exchanges and overhead. Smaller T means more exchanges and overhead, but more information obtained for each eer. 4.3 DLM-3 In the first two aroaches of DLM, both suereers and leaf-eers run the algorithm and can romote or demote. In DLM-3, only suereers erform the estimation rocess. When one suereer infers that the network has too many suereers, it may decide to be demoted; this rocess is the same as that of DLM-1 and DLM-2. But, when it finds that more suereers are needed in the network, it will inform the most eligible leaf neighbor and romote it to suerlayer. One issue in the romotion of leaf neighbors is the olicy of selecting the most eligible leaf-eer. Similarly to DLM-1 and DLM-2, DLM-3 also uses the metrics of caacity and age in selection. We roose three different olicies to select the most eligible leaf-eer: Largest-Age, Largest-Caacity, and Weighted-Metric. The first two olicies are self-exlained and a suereer just selects the leaf-eer with the largest corresonding values. A similar lifesan-based mechanism is roosed in [4] to choose a eer s friends, and it is very

9 1086 IEEE TRANSACTIONS ON PARALLEL AND DISTRIBUTED SYSTEMS, VOL. 16, NO. 11, NOVEMBER 2005 TABLE 1 Simulation Parameters similar to our Largest Age olicy, while, in the Weighted- Metric olicy, we consider the two metrics, Caacity and Age, simultaneously. Since the two metrics of a eer are mostly disjoint, we roose measuring the eers eligibility by defining a combined metric Weighted Metric. We first calculate the weighted metric value of a eer d by WM d ¼ 1 CaacityðÞþ 2 AgeðÞ, where 1 and 2 are called Metric Weight Parameters, which are used to control the contribution weights of caacity and age, resectively. We also set 1 þ 2 ¼ 1. A suereer then selects the leaf-eer with the largest WM value as the most eligible suereer. We roose one Metric-Distribution mechanism to set i. Suose that all the eers have the same values on one metric, this metric may not be considered to be an influential metric in the eer selection. Thus, its Metric Weight Parameter will be set to zero. On the contrary, if the values of another metric are more sarsely disersed on these eers, this metric will be viewed as an influential one. Therefore, its Metric Weight Parameter will be assigned with larger value to reflect this diversity. The Metric-Distribution mechanism can also be alied to roblems with multile metrics, although, in DLM, it only considers two metrics. Consider a eer d in a suereer s Related-Set G and let us use V r;d to denote the value of metric r on d. The Metric-Distribution mechanism erforms through the following stes. First, we normalize the metric value to [0, 1] sace; this is done by V r;d ¼ Vr;d Vr;Min ðv, where V r;max V r;minþ r;min and V r;max are the minimal and maximal values of metric r, resectively. We then comute the standard variance of metric r, rffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi X r ¼ ðv r;d E½V r ŠÞ 2 ; d where E½V r Š is the normalized exectation of metric r. Last, letting r denote the weight arameter for metric r, it is set as r ¼ P r i i. 4.4 Alying DLM to Multilayer Architectures In general, the suereer architectures are secial cases of the k-layer architectures with k equals 2. The original flat architectures (for examle, Gnutella v0.4) are also secial cases of k-layer architectures with k equals 1. DLM can also be used on general k-layer architectures. If a eer in layer i ð1 i<kþ has larger caacity and age values, it will be automatically romoted to the uer layer, say, i þ 1. On the contrary, if a eer in layer i ð1 <i kþ has smaller caacity and age values comared with other lower layer eers, it will be demoted to the lower layer, say, i 1. When both romotion and demotion are requested, the eer needs to comare the necessities of romotion and demotion and act corresondingly. Thereby, the algorithm can make sure that the eers with longer lifetime and larger caability are in higher layer. 5 PERFORMANCE EVALUATION We use simulation to evaluate DLM and comare it to reconfigured algorithms. To collect real data, we imlement two Gnutella clients based on the ublicly available Mutella [16]. One client articiates in the network as an ultra-eer and the other acts as a leaf-eer. Using these two clients, we collect some first-hand data, such as the lifetimes of ultra-eers and leaf-eers, the number of oen connections, and the average query frequencies of eer. The collected data are consistent with the data resented in revious studies [19], [20], [9]. We configure our simulation environments based on the collected data and these studies, which are shown in Table 1. First, we test the workload model by measuring W on and W s on varying values. Using our roosed workload model, a network can determine an otimal layer size ratio between the leaf-layer and the suerlayer. Then, we evaluate the effectiveness of the different aroaches of Fig. 6. W s of most efficient search.

10 XIAO ET AL.: DYNAMIC LAYER MANAGEMENT IN SUPERPEER ARCHITECTURES 1087 Fig. 7. W s of most inefficient search. Fig. 10. Weighted workload of most efficient search ð ¼ 0:5; ¼ 0:5Þ. Fig. 11. Weighted workload of most inefficient search ð ¼ 0:5; ¼ 0:5Þ. Fig. 8. W on of most efficient search. Fig. 12. Weighted workload of most efficient search ð ¼ 0:3; ¼ 0:7Þ. Fig. 9. W on of most inefficient search. DLM. We also comare the workloads incurred by DLM-1 and reconfigured algorithm under given success rates. 5.1 Evaluation of Workload Model For the workload on a suereer, Fig. 6 and Fig. 7 illustrate the connection workload, query workload, relay workload, as well as the total workload W s with varying values of. Fig. 6 lots the minimum case of relay workload (for most efficient search) and Fig. 7 lots the maximum case (for most inefficient search). We can see that both the connection workload and query workload increase as increases. For the relay workload, in the minimum case, the amount decreases slightly when increases; however, in the maximum case, it almost says constant, regardless of different values. In both cases, the total workload on one suereer increases as increases. Those results are not surrising since a larger value means that each suereer reresents more leaf-eers. For the workload on the overall network, as shown in Fig. 8 and Fig. 9, W on decreases when increases. We can see that the main art of the total workload comes from the Relay and, comared to the Relay Workload, the amounts of the Connection Workload and Query Workload are negligible. To obtain the otimal layer size ratio, we first set ¼ ¼ 0:5 and measure the weighted workload as changes. The results are shown in Fig. 10 and Fig. 11. With the arameters listed in Table 1, we comute the otimal value using (2) in the following way: qffiffiffiffiffiffiffiffi For the most B C A efficient search algorithm, we have 1 0 ¼ 1 38, while, qfor ffiffiffiffiffiffiffiffithe most inefficient search algorithm, we have 1 0 ¼ The otimal values we obtained from B C A simulation are 35 and 45, resectively, and they are indicated in Fig. 10 and Fig. 11. We can see that the obtained values are very close to the theoretical ones.

11 1088 IEEE TRANSACTIONS ON PARALLEL AND DISTRIBUTED SYSTEMS, VOL. 16, NO. 11, NOVEMBER 2005 Fig. 13. Weighted workload of most inefficient search ð ¼ 0:3; ¼ 0:7Þ. Fig. 16. Layer sizes. Fig. 17. Layer size ratio under different aroaches of DLM. Fig. 15. Average caacity. We also obtain the otimal layer size ratio under different values of and. Our simulation and comutation show very close results. In Fig. 12 and Fig. 13, we resent the simulation results when ¼ 0:3 and ¼ 0:7. Comared with Fig. 10 and Fig. 11, we can see that both of the otimal values of in Fig. 12 and Fig. 13 are slightly larger. Since larger values indicate more weight on the network Overall Workload and larger values mean less flooding overhead among suereers, the otimal layer size ratio increases as decreases. 5.2 Effectiveness of DLM-1 We evaluate DLM-1 under various simulation environments. We first simulate a stable network by assigning new eers with caacity and lifetime values based on revious studies [19]. In a stable network, the simulation starts cold, i.e., without any eer. The size of the network increases, with new eers joining until it reaches the designated size. Then, with time assing, whenever a eer dies, a new eer is created and joins the network; therefore, the network size does not change. The new eer is always assigned to the leaf layer first and DLM will romote eligible leaf-eers to the suerlayer. The lifetime and caacity values of a new eer are generated based on the distributions we observed and shown in revious studies. We then simulate the dynamic networks by varying the means of the caacity and age distributions for new joining eers. For these two cases, the network sizes are not changed. We also evaluate DLM-1 on networks with different sizes. The results are consistent, so we only resent the results in dynamic environments in Fig. 14, Fig. 15, and Fig. 16. Starting from the 300th time unit, the lifetime values of new joining eers are generated using the method as described before, but with halved mean values. Thus, from that time, the new eers have smaller lifetime values. The results in Fig. 14 show that DLM-1 adatively romotes the eers with large caacities to suerlayers and the average caacity value of a suerlayer is always larger than that of a leaf-layer. Starting from the 1,000th time unit, the caacities of new joining eers are generated with doubled mean values; thereby, the new eers are more owerful than revious eers. Fig. 15 lots the average ages of each layer. As exected, the age of the suerlayer is much greater than that of the leaf-layer, regardless of the changing environments. The layer sizes of the network are shown in Fig. 16; we can see that an almost constant ratio is maintained throughout the simulation rocess, even though the network environment is changing. Note that the Y-axis of Fig. 16 is logarithmic.

12 XIAO ET AL.: DYNAMIC LAYER MANAGEMENT IN SUPERPEER ARCHITECTURES 1089 Fig. 18. Layer size ratio under different PE. Fig. 20. Average age comarison. Fig. 19. Layer size ratios on the same success rate. 5.3 Effectiveness of Different Aroaches and Policies We comare the effectiveness of different aroaches of DLM and the results are shown in Fig. 17, which is the scattered grah of the layer size ratio values. As exected, DLM-2 erforms the best since it emloys the information exchange mechanism between neighboring suereers. DLM-3 erforms the worst as it only runs on the suereers. Fig. 17 deicts the layer size ratio changes of the three aroaches. From this figure, we can see that DLM-2 has the denser distribution, which stands for more stable values, while DLM-3 is the one with most unstable size ratio. The erformances on the other two metrics, average caacity and average age, also show similar features. In DLM-2, Periodic Exchange (PE) is an effective information exchange olicy among suereers. It ensures the system information to be exchanged between suereers eriodically. However, different T values have large effects on the erformances. Fig. 18 shows the size ratio distribution curves of Periodic Exchange with different T values and Pushing Exchange (PU), the eak values corresonds to the otimal layer size ratio. We can see that, when T equals 5, the erformance of Periodic Exchange is better than Pushing Exchange, while, when T equals 30, it is worse than Pushing Exchange. 5.4 Effectiveness of DLM-1 over a Preconfigured Algorithm We comare DLM-1 with reconfigured algorithms under dynamic network situations where the new eers mean Fig. 21. Workloads on the same success rate. caacity values are eriodically changed. We comare the sizes and ages of two layers in DLM-1 and a reconfigured algorithm. The results are shown in Figs. 19, 20, and 21. We can see from Fig. 19 that the DLM-1 maintains the layer size ratio very well, while, in the reconfigured algorithm, the layer size ratio changes eriodically. For the average ages of suerlayer and leaf-layer, in DLM-1, they are sharly divided and the average age of the suerlayer is much larger than that of the reconfigured algorithm, as shown in Fig. 20. The comarisons of caacity values show similar results. We also comare the W on of these two algorithms. We comare the two algorithms under the same success rates. The normalized results are shown in Fig. 21. The success rate is set to be 10 ercent and we use an imroved k-walker [13] as the search mechanism. From the results, we can see that DLM-1 has a very stable W on, while the W on of the reconfigured algorithm fluctuates a lot and is much larger. 6 DISCUSSION ON THE SIDE EFFECTS OF DLM Introducing DLM to suereer systems does incur some traffic overhead, such as the traffic overhead for information exchanging among neighbors and the eer adjustment overhead. In this section, we discuss these issues in detail. 6.1 Overhead for Information Exchanging To imlement DLM, we roose adding two airs of messages described in Section 4 to the existing suereer P2P rotocol. We argue that the additional overhead on delivering these two airs of messages is negligible

13 1090 IEEE TRANSACTIONS ON PARALLEL AND DISTRIBUTED SYSTEMS, VOL. 16, NO. 11, NOVEMBER 2005 TABLE 2 Peer Adjustment Overhead Analysis comared to the search traffic costs in a P2P system for two reasons. First, these messages are only transferred between directly connected neighbors, so they can have very simle formats and only need a few bytes. As a result, these two airs of messages are quite light-weight. Second, these messages are only sent when new connections are created. Moreover, these two airs of messages may be iggybacked in other messages available, thus reducing the traffic overhead even more. Our collected data and studies in [19] found that each connection can kee active for at least several minutes on the average. Therefore, the frequency of DLM message transferring is quite low comared with that of other messages. 6.2 Peer Adjustment Overhead When a suereer is demoted to be a leaf-eer, it needs to cut the connections to the leaf-eers and the connections to some suereers because a leaf-eer only needs to kee a small number of links to suereers, say, m suereers. The leaf-eers disconnected by the demoted suereer will try to connect to another suereer instead. We call this kind of connection overhead Peer Adjustment Overhead (PAO). Note that the romotion rocess does not cause PAO because no eers are disconnected during the rocess. We analyze this overhead and find that the eer adjustment overhead is quite small. The results are shown in Table 2. We count the number of new eers, the number of suereers demoted as leaf-eers, and the number of disconnected leaf-eers caused by the demotions er unit time. The disconnected leaf-eers need to connect other suereers and incur the PAO. This rocess behaves like a new joining leaf-eer making connections to suereers. The difference is that each disconnected leaf-eer only needs to create one new connection to another suereer, while each new joining leaf-eer needs to create m new connections to suereers. Thus, the PAO for a disconnected leaf-eer is only 1=m of the connection overhead for a new joining eer. We call the connection overhead caused by new leaf-eers New Leaf-initiated Connection Overhead (NLCO). We also calculate the ratio of PAO and NLCO in Table 2. In Table 2, we can see that, as the network size increases, the ratio of PAO to NLCO decreases. The reason is that, as the network size increases, the number of leaf-eers each suereer connects to is more close to k l due to the randomness of connections between eers. Therefore, the robability of misjudgments is also decreased. We believe that in the real-world P2P networks with millions of eers, the ratio of PAO to NLCO is trivial. 7 CONCLUSION In this aer, we roose a workload model by analyzing the workloads on one suereer as well as on the total network. Based on this model, we obtain an otimal layer size ratio that can minimize the weighted workload of the network. We also roose a dynamic layer management algorithm, DLM, which can adatively elect eers and adjust them between suerlayer and leaf-layer. We resent three aroaches and address some technical issues of DLM. DLM can also be easily extended to multilayer architectures. Our simulation results show that DLM can maintain a given size ratio of suerlayer to leaf-layer and designate eers with long lifetime and large caacities as suereers and the eers with short lifetime and low caacity as leaf-eers under highly dynamic network situations. DLM is comletely distributed in the sense that each eer runs DLM indeendently. With the suort of our roosed management mechanism, the quality of a suereer system can be significantly imroved. ACKNOWLEDGMENTS This work is suorted in art by the US National Science Foundation under grants CCF and CCF and by Hong Kong RGC DAG 04/05.EG01. Some reliminary results of this work were resented in the Proceedings of the International Conference on Parallel Processing REFERENCES [1] The Gnutella Protocol Secification 0.6, htt://rfc-gnutella. sourceforge.net, [2] Regional Characteristics of P2P, htt:// [3] P. Backx, T. Wauters, B. Dhoedt, and P. Demeester, A Comarison of Peer-to-Peer Architectures, Proc. Eurescom Summit, [4] F.E. Bustamante and Y. Qiao, Friendshis that Last: Peer Lifesan and Its Role in P2P Protocols, Proc. Int l Worksho Web Content Caching and Distribution, [5] B.F. Cooer and H. Garcia-Molina, SIL: Modeling and Measuring Scalable Peer-to-Peer Search Networks, Proc. Int l Worksho Databases, Information Systems, and Peer-to-Peer Comuting, [6] N. Daswani, H. 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