A Proactive Scheme for QoS Enhanced Alternate Path ... - CiteSeerX

A Proactive Scheme for QoS Enhanced Alternate Path Discovery in a Super-Peer Architecture Thierry Rakotoarivelo a,b,c,d, Patrick Senac c,d, Aruna Seneviratne b, Michel Diaz d a

University of New South Wales, Sydney, Australia National ICT Australia (NICTA), Sydney, Australia {thierry.rakotoarivelo, aruna.seneviratne}@nicta.com.au c ENSICA, Toulouse, France d LAAS-CNRS, Toulouse, France {senac, diaz}@laas.fr b

Abstract - In the next generation Internet, the network should evolve from a plain communication medium into an endless source of services available to the end-systems. We name these services “Overlay Applications”. They would be composed of multiple cooperative distributed application elements that would build a dynamic communication mesh, namely “Overlay Association”. In a former contribution, we proposed an unstructured Super-Peer architecture (SPAD) that provides enhanced Quality of Service (QoS) between end-points within an Overlay Association. This architecture aims at discovering and utilizing composite alternate end-to-end paths that experience better QoS than the path given by the default IP routing mechanisms. This paper presents a proactive information dissemination scheme that complements SPAD’s mechanisms and significantly improves its performances. I. INTRODUCTION Demand for mobile network-enabled devices has steadily increased in recent years. These devices collectively form a pervasive computing and networking environment around the user, informing her, supporting her communication needs, and performing various tasks on her behalf. In that regard, these resource-limited portable devices would no longer need extensive local applications, computing or storage resources: service providers at the edge of the network would provide them with these now distributed resources. End-systems would then view the network as an endless source of services, and would act mainly as input/output devices. This approach would benefit aspects such as device cost, mobility or energy consumption. These service-oriented networks would provide services, which will be composed of multiple cooperative distributed software elements [1]. These elements will perform generic tasks and communicate with each other, forming dynamic overlay networks above the existing Internet infrastructure as required. We term “overlay application” the distributed application composed by use of such generic software elements.

Within an overlay application, data flows no longer travel between two end-points. They may instead traverse multiple peer end-points (hosting processing application elements) and be produced/consumed by several other peers. For example, an audio flow in a distributed Voice Over-IP service [2] might pass through several peers providing elementary services such as firewall traversal, or codec/quality adaptation. This defines a new peer-to-peer communication paradigm, complementing the traditional point-to-point, or point-to-multipoint communication paradigms, namely a set of connections between software elements within an overlay application. This set of connections is referred to as an “overlay association” [3]. This concept of overlay association allows the design of mechanisms that improve and manage the Quality of Service (QoS) experienced by the end-users of an overlay application as a whole (e.g. reducing latency in the above VoIP service). These mechanisms would perform global resource optimization on an overlay association, rather than less efficient local resource management decisions. More precisely, these mechanisms would be part of a middleware framework [3] that would provide unified means of managing the communication and QoS needs of any overlay application, thus reducing their implementation complexity. This middleware framework would mediate between the software elements involved in an overlay application and the network. Super-Peer based Alternate path Discovery (SPAD) [4] is a distributed peer-to-peer scheme that enhances the QoS between two peers of an overlay association. It is a key part of our middleware framework for overlay networks. The fundamental idea behind SPAD is to discover and utilize alternate composite Internet paths [5] that provide better QoS than the default path given by the IP routing, similar to what is discussed in [6]. We use the term “QoS Enhanced Alternate Paths” (QEAPs) to refer to such alternate paths. They exist mainly because of non-QoS optimal BGP routing policies between Internet Autonomous Systems (AS) [5].

The current SPAD system allows the discovery of QEAPs that provide better delay between end-points. However, it could be adapted to discover QEAPs that enhance other QoS parameters (e.g. bandwidth, loss). This paper presents an extension to SPAD’s alternate path discovery mechanisms. This extension significantly improves its performance by reducing the message cost and search latency associated with a given QEAP discovery request. Within the original SPAD, cooperative end-points belong to an unstructured super-peer network [7], where normal-peers (NPs) originate requests for information on desired alternate paths. Super-peers (SPs) receive and process these requests: forwarding them to other neighbor SPs, exchanging connectivity information related to their associated NPs, and returning back to the requesting peer the filtered relevant information concerning the desired alternate paths. In the proposed extension, SPs would execute a probabilistic flooding algorithm during their idle time. This background algorithm would allow the proactive exchange between SPs of connectivity information, as opposed to the reactive exchange triggered upon request processing. As a result, the overall community’s connectivity information would be progressively disseminated among all SPs. A given QEAP request would then pass through fewer SPs in order to generate the same amount of relevant responses as in the original SPAD, hence an improvement in per-request message cost and search latency. Due to the dynamic behavior of peer-to-peer architectures and the probabilistic nature of the proposed extension, complete information dissemination might not be achievable among SPs. Thus, preventing the ideal case where a request would not require any forward. However, our evaluations show that even with partial information dissemination, the proposed scheme significantly improves SPAD’s performance. The remaining of this paper is organized as follows. In section II, we discuss some related works. Section III presents an overview of SPAD and its current limitations. We then describe the proposed proactive SPAD extension in section IV, and evaluate it in section V. Section VI concludes this paper with some directions on our future works. II. RELATED WORK Savage et. al [5] discussed the existence and benefits (enhanced or controlled QoS and robustness) of alternate Internet paths. They found that QEAPs exist for up to 80% of the node pairs in their North-American dataset. Following contributions such as RON [8], and Q-RON [6] proposed methods and architectures to discover and utilize such paths. All these frameworks involve either a central entity (RON) or several distributed third-party brokers (Q-RON) that “sell” QEAPs to end-users. In contrast, SPAD is a fully distributed system that allows a community of users to directly discover and utilize QEAPs. Within such a distributed system, nodes play both roles of clients and servers, hence the choice of a Peer-to-Peer (P2P) approach in SPAD’s design. Research on P2P systems has

focused primarily on file/cpu sharing, content distribution networks, or scalability improvement techniques [9]. To the best of our knowledge, no previous research contributions have attempted to use P2P systems for QEAPs discovery. The proposed proactive scheme is based on background information dissemination among SPAD SPs. Percolationbased techniques, such as probabilistic flooding [10], provide efficient information dissemination with lower bandwidth usage than classic flooding techniques, and without any membership management as in Gossip-based techniques [11]. Use of probabilistic flooding in power-law unstructured P2P networks was studied in [12] and shown to be effective. SPAD extends this work, using probabilistic flooding in its proactive information exchange scheme. Percolation-based random-walk also has low bandwidth requirements. However, it achieves full information dissemination at a higher latency than probabilistic flooding. III. SPAD: A P2P APPROACH TO QEAP DISCOVERY A. SPAD Overview To design SPAD, we made the following assumptions: i) quasi-symmetry of Internet delays, ii) existence of low cost measurement methods such as King [13], iii) low processing latency at relay nodes as demonstrated by TCP stack processing analysis [14]. We refer the reader to [3, 4] for discussions supporting these assumptions. Based on unstructured P2P system measurement studies [9], we also made the assumption that SPAD SPs are self-organized into a power-law topology. In this topology, the average node degree follows a power-law distribution: P(k)=Ck−α , with P(k) the probability of a node to have k edges, α the powerlaw exponent, and C a normalizing constant. SPAD is based on a community of cooperative end-points grouped in an unstructured Super-Peer network [7]. When joining this community, an end-point would by default act as a NP, and may evolve as a SP during its lifetime. SP selection/election is an ongoing research issue not discussed in this paper [9]. During its join phase, a NP A contacts a set of SPs {Si } that provide it with a finite set of other random SPAD nodes. Using these bootstrap nodes, A constructs a fixed size list of potential candidate relay nodes: a Candidate Relay (CR) list. This list contains the selection of “closest” (in term of delay) bootstrap nodes to A (A needs to evaluate its delay towards all the bootstrap nodes). Then A uploads its CR list to its associated SP S (randomly selected among the {Si }). Entries in A’s CR list are of the form: . We note that if nodes A and X are within the same AS, they would probably share the same gateway towards a remote node B, thus the paths AtoB and XtoB would be very similar, and the chances of a QEAP from A to B via X would be very low. Therefore, we used a simple mechanism based on IP-to-AS mapping (not described in this paper due to space constraint) to ensure node diversity in the CR lists. Finally, based on delay constancy behavior [15],

B. Motivation for SPAD extension One limitation of the previously described scheme is the fact that its performance is a function of the reach of a QEAP request during the forwarding process. Indeed, the more SPs a request reaches, the more potential relay nodes will be known to the request’s source (provided information on these nodes exists in the community). In a SP network with a power-law topology, if we fix the number of SPs, and their minimum node degree, the reach of a request depends on its TTL [7]. Therefore, to increase its chances to discover QEAPs, a source node should set high TTL values to its requests. This behavior implies more request/response forwarding between SPs, thus increasing the message cost and the overall search latency. The proposed proactive scheme addresses this limitation by allowing SPs to perform an information dissemination algorithm during their idle time. This algorithm allows the exchange of connectivity information, namely LET entries, between SPs. As a result, a given SP would eventually have in a local cache all the existing connectivity information related to its associated NPs. A QEAP request would then need to be forwarded to only a few SPs in order to generate the same amount of 1 This requires admission control techniques and policies on potential relay nodes. These necessary mechanisms are not discussed in this paper.

100 Scenario (N ; m ; TTLD) (100 ; 3 ; 3) (100 ; 3 ; 4) (100 ; 4 ; 3) (100 ; 4 ; 4) (1000 ; 3 ; 3) 70 (1000 ; 3 ; 4) (1000 ; 4 ; 3) 60 (1000 ; 4 ; 4) 90

Amount of reached nodes (%)

and its future interaction with other peers, A updates its CR list regularly and forwards these updates to S. Each SP has a finite set of associated NPs, and stores local copies of their corresponding CR lists in its Local Entry Table (LET). When a node A looks for a QEAP towards a node B, it sends a request (TTL: Time To Live) to its SP S. Upon receiving this request, S selects all matching entries in its LET. This process is explained in details in [4], and aims at selecting entries that involve nodes that could potentially act as relay on a QEAP from A to B. S stores these selected entries as its own contribution to the response. Then if TTL > 0, S decrements it, forwards the request to all its connected SPs and wait for their responses. S aggregates the received responses with its own, performs a filtering algorithm on the whole response set, and returns the result to the source of the request. Each SP on the request path recursively executes these procedures. The filtering process (described in [4]) aims at gradually removing redundant and irrelevant entries along the request reverse path. When this search process is complete, A receives a response set containing entries of the form (with {X or Y} = {A or B}). A first analyzes this list to search for “trivial” QEAPs. For example, cases where the list contains delay_AtoZ and delay_ZtoB, with their sum smaller than delay_AtoB. If such case exists, A sends a query message to the potential relay node Z. Otherwise, it sends query messages in parallel to all the nodes in the response list. These query messages allow A to detect if the path A_X_B is a QEAP, and if so, to ask X if it would like to be a relay1. When A eventually finds a QEAP, it constructs, uses, and monitors it as described in [4].

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Figure 1. Amount of reached nodes for different values of (PD ; TTLD), and different network topology (N ; m)

relevant responses as in the original SPAD. This would result in lower per-request message cost and search latency. IV. EXTENDING SPAD WITH A PROACTIVE INFORMATION DISSEMINATION SCHEME A. Probabilistic Flooding and Power-Law Networks Probabilistic flooding derives from the bond-percolation theory [10]. In this scheme, a node forwards new generated or received information to its direct neighbors with a probability p, and drops that information with the complementary probability (1-p). It also drops already processed or forwarded information (i.e. infect-and-die policy per new information). Results from the bondpercolation theory demonstrate that for a given connected network, there exists a threshold dissemination probability PC at which the information statistically reaches all nodes at a minimum message cost. When this threshold is reached, the network is reduced to a minimum connectivity state that provides full reachability without any redundant paths (i.e. information does not reach a same node twice). In [12], the authors studied the application of that scheme to request forwarding in power-law networks. They provided an analytic expression of PC based on the power-law exponent α of the network being considered. They demonstrated that PC could be smaller than 1. However their expression assumes infinite TTL for the request/information. Extending their study, we analyzed the dissemination probability in regard to the propagation TTL and the amount of reached nodes. We used BRITE [16] to generate 1000 power-law topologies (α ≈ 2.8) based on the Barábasi-Albert model. For each topology, we randomly selected a node from which we started propagation simulation. Figure 1 shows the amount of nodes reached by the information for different values of dissemination probability (PD) and dissemination TTL (TTLD), as well as different numbers N of SPs with minimum node degree m. This figure confirms two points: i) for a given network, propagation reach depends on both PD and dissemination TTLD; ii) higher minimum node degree allows faster information propagation. For a power-law topology of 100 nodes, m={3, 4}, and TTLD=4 (network diameter), the classic flooding strategy (i.e. PD=1 in figure 1) disseminates the information to 100% of the nodes. However, with a dissemination probability of PD=0.6 for m=4, and PD=0.8 for

m=3, the information has already reached 94.18% and 98.03% of all nodes. These results demonstrate that in power-law networks, an information dissemination scheme using probabilistic flooding can achieve near full propagation at a lower message cost (20–40% less in the above example) and a similar dissemination TTL than classic flooding (i.e. when PD=1). We note that these results do not allow any conclusions on the scalability characteristics of probabilistic flooding. This issue is the subject of ongoing studies [12].

The choice of PD and TTLD determines the information reach, and is a function of the topology characteristics. In [17], the authors provide a brief study of the average distance between any two nodes in random graphs. The following analysis is based on their problem formulation. For simplicity, we consider a graph of N nodes, with a fixed node degree (that we note M+1) equals to 3. The following analysis remains valid for graphs with arbitrary node degree distribution, such as power-law distribution (M+1 would then represent the average node degree). Figure 2 shows this graph, where each node represents a SP. We select node A as the dissemination source of a new piece of information. We can then represent the graph as a tree structure; where A is the root (rank 0), and where B, D, E (A’s direct neighbors) are one level below (rank 1). Following the graph’s topology, we add each node’s direct neighbors in the tree until all nodes are visited, with the only constraint that a tree node at rank k cannot have its parent (rank k-1) as one of its direct children (rank k+1). We note that a given node from the graph can appear several times within the tree. For example, node C appears for the first time at rank 2, then many times at rank 3. This is due to the fact that a node has several neighbor nodes in the graph; hence it could be the child of several parent nodes in the tree. Furthermore, we also note that A has M+1 children nodes, and any node at rank k, with k>0, has M children nodes. We number the nodes according to their sequence of inclusion in the tree. For example, node A has the number 1, node C has the numbers 8, 12, 21. We define tk as the last node number at rank k. If we build the dissemination tree using a probabilistic flooding strategy with a probability p, we have: 2

(1)

using iterative simplification and fixing Mp ≠ 1, we obtain: tk =

(M + 1)M k p k +1 − ( p + 1) (Mp − 1)

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We define f(t) as the total number of unique nodes in the tree after the tth node (Nt) has been added. For example, f(4)=4, and f(10)=7. Then f(tk) – f(tk-1) represents the number of unique nodes in the tree at rank k. We define δt:

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Figure 2. Graph and tree examples for the theoretical analysis of SPAD’s information dissemination strategy.

B. Selection of PD and TTLD

t1 = 1 + (M + 1) p , and t 2 = 1 + (M + 1) p + (M + 1)Mp

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with δt = 1 if Nt is a new node, and δt = 0 otherwise. The probability that Nt is a new node is then P(δt=1), and: P(δ t = 1) =

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We define F(t) as the expected value of f(t), and we take the expectation on both side of (3). Using (4), we obtain: F (t) − F (t − 1) =

N − F (t − 1) N

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then we solve (5) iteratively (using f(0)=0) to obtain: F (t) = N 1 −

N −1 N

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which represents the expected value of the total number of unique nodes in the tree after the inclusion of the tth node. From this result, we can estimate the number of unique nodes reached by a message that was issued by node A and was disseminated through the graph using a probabilistic flooding strategy. Indeed for a given pair of PD and TTLD (respectively corresponding to p and k), equation (2) gives a node number tTTLD that we can report in equation (6) to obtain an estimation of the mean number of distinct reached nodes. Therefore, in SPAD information dissemination scheme, if we assume that a given SP knows NS, the maximum number of SPs2, and that it can estimate the average number of direct neighbors M+1; then it can analytically compute estimates of PD and TTLD that would allow its message to reach a given fraction x (close to 1) of all the SPs at a minimum message cost. To verify the model provided by (2) and (6), we generated 103 BRITE power-law topologies (with N=103 nodes and a minimum node degree m=3), and performed probabilistic flooding simulations with different PD and TTLD. For these topologies, we measured an average network diameter of 5, and an average M+1 ≈ 5.92 (±6.77). For a TTLD=5, figure 3 presents the comparison of experimental dissemination on these generated topologies and the theoretical propagation 2 NS could be a system-wide parameter, set during initial SPAD deployment and passed-on to new super-peers during their initialization.

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Figure 3. For TTLD=5, Comparison of information dissemination on experimental topologies versus theoretical model implied by (2) and (6).

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Figure 4. Pseudo-code of the Incoming Entry Processing algorithm executed by SPs.

implied by (2) and (6), using the measured value of M+1. According to these results, the estimation given by (2) and (6) of the average numbers of distinct nodes in the network at the kth rank (e.g. k=5=TTLD) is slightly smaller than the experimental values. Therefore, when using (2) and (6) to determine optimal values of PD and TTLD, a SPAD SP will obtain conservative values. As presented on figure 3, PD=0.6 and TTLD=5 will theoretically guarantee a reach of at least 60%; which is confirmed by experimentations showing an average reach between 78% and 80%. C. Integration of Probabilistic Flooding in SPAD The previous subsection provides an analytical model (equations (2) and (6)) to dynamically compute PD and TTLD. We use this model in the following SP bootstrap mechanism to include the probabilistic flooding scheme into SPAD. The accuracy of this model depends on the value of M+1. In a stationary topology, where the number of SPs remains constant after a given time, M+1 can be analytically computed using the topology’s power-law distribution (not described here due to space constraint). However, in a dynamic P2P network, where SPs join and leaves randomly, each SP needs to dynamically estimate the value of M+1. The following bootstrap mechanism allows such estimation. As part of its bootstrap phase, a SP SX retrieves the maximum number NS of allowed SPs in its SPAD community (e.g. from an already existing neighbor SP). It also measures mSX the number of its direct neighbor SPs. To compute an estimation of M+1, SX communicates its measured value mSX to all of its direct neighbors SIs, and receives back their measured values mSIs. Then it takes the average of its mSX and all the received mSIs as its estimation of M+1. Finally, SX uses the values of NS and M+1 as input parameters into the equations (2) and (6). This mechanism allows each SPs to dynamically compute optimal PD and TTLD in a distributed manner. Furthermore upon receiving the value mSX from SX, each SI updates its estimation of M+1, and recalculates its PD and TTLD. This allows dynamic updates of these parameters as the SPAD network topology evolves. A given SP S uses its idle time to perform the functions associated with the dissemination scheme. S is idle whenever

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Figure 5. Amount of discovered QEAPs for different Query TTL and information dissemination reach (D) (Topology: 15 SPs and minimum node degree m=3).

it is not processing a QEAP request. As mentioned earlier, the entries in SPs’ LETs are the information to propagate. The first step for S is to communicate its LET to its directly connected neighbors. S initially sends its entire LET. When its LET subsequently changes due to updates from associated normal-peers, S will send only the modified entries to its neighbors. LET propagation is done following the probabilistic flooding technique. The second step is the processing of incoming LET entries, as described in figure 4. After receiving an incoming entry E and deciding to process it (line 2-6), S compares E with the entries from its own LET (line 7-11). If E matches one of the LET entries, then it contains information potentially relevant to QEAP requests from S’s associated NPs. Therefore, S retains E and stores it in a Remote Entry Table (RET). S also compares E to its existing RET entries, to determine if E could potentially provide more information to one of them (line 12-15). S does not propagate its RET entries to its neighbors. Indeed, via LET propagation, they may already have received the raw information on which they would probably have made a different selection than S. As dissemination progresses, S would cache locally more and more entries (from further SPs) relevant to its associated NPs. Each SP fixes the size of its own RET table based on its available resources. When S receives a QEAP request from a node A towards another node B, it processes it as described in section III.A with the following two modifications. First, S includes its RET entries in the selection process that builds its part of the response. Therefore, its part of the response contains matching entries from both its LET and RET. The second modification concerns the request forwarding to other SPs. Depending on the state of the dissemination process, S might already have in its RET all the existing information relevant to the request. In such case, S would not need to forward the request to its neighbor SPs. However, due to the dynamic character of the peer-to-peer SPAD community, and the probabilistic nature of the dissemination scheme, this ideal case might not be reached yet. Therefore, S might still need to forward the request, but with a lower TTLQ than the original SPAD system. We propose the following simple decision process: if the amount of entries within S’s local part of the response is over a certain threshold (e.g. 10 entries), S decides that its local part of the response already

TABLE I. MESSAGE COST AND SEARCH LATENCY FOR DIFFERENT QUERY TTL (TOPOLOGY N=15, m=3)

VI. CONCLUSION

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951.9

contains enough entries, and it does not forward the request. If not, S forwards it with a TTLQ inversely proportional to the size of its local part of the response. We will enhance this decision process in our future work. V. EVALUATION To evaluate the proposed SPAD extension, we performed trace-based simulations on delay measurements from the PlanetLab All-Pair-Ping project [18]. We randomly selected 15 SPs among the 177 available PlanetLab nodes (NS=15), and assigned the remaining nodes as associated NPs (about 11 NPs per SPs). Using BRITE [16], we organized the SPs in a power-law topology. Then, we built all the CRlists (with a fixed size of 10) and the LETs, and performed information dissemination with different target reaches, using the model from section IV.B. Finally, at a random timestamp, we selected random nodes as source and destination of a QEAP request, and started the search process for different query TTL (TTLQ). Figure 5 shows the averaged results over 104 trials. For a given TTLQ, a SPAD system with the information dissemination scheme allows the discovery of more QEAPs than a SPAD system without it. Moreover, a higher dissemination reach provides a higher amount of discovered QEAPs. Assuming that SPs initially set PD and TTLD to aim for a 100%-reach, starting from a state of 0%reach, dissemination reach will increase as time progresses and the super-peer network remains quasi-stable. For example, an achieved dissemination reach of 75% allows the discovery of 66.21% of existing QEAPs for TTLQ=1, while only 55.18% are discovered without the dissemination scheme (labeled “No Diss.” on figure 5). For one QEAP request processing and different values of TTLQ, table I presents the average number of messages generated by SPs, and the average QEAP search latency. This latency takes into account the request forwarding delay, and the response delay on the reverse path. It does not account for processing time on SPs. According to figure 5 and table I, if we assume a SPAD community with NS =15, m=3, and sufficient initial time to have a 50%-reach dissemination, the information dissemination scheme allows the discovery of about 64% of existing QEAPs at an average cost of 6.17 messages and a latency of 190.9 ms. Achieving a similar performance without the proposed scheme requires 12.11 messages, and a latency of 380.5ms.

This paper presents an extension to SPAD, a previously proposed architecture [4]. SPAD aims at enhancing QoS between two end-points within an overlay association. It provides a distributed scheme to discover and utilize QoS Enhanced Alternate Paths (QEAPs). The proposed extension adds a background information dissemination scheme to SPAD. This scheme allows the proactive exchange of connectivity information between SPAD SPs during their idle time. In comparison to the original SPAD system, this additional scheme results in a gain in terms of message cost and search latency per QEAP discovery request. However, it increases the complexity and processing load on SPs. This is an acceptable trade-off in the context of super-peer networks. Indeed, by definition SPs are altruistic peers that in general have more resources at their disposal and therefore handle more duties than NPs. We are currently implementing a SPAD prototype for more comprehensive evaluations, potentially involving network emulation tools or test-beds such as PlanetLab [18]. We also continue our investigations on distributed QEAP discovery methods, and their integration within an overlay middleware framework. REFERENCES [1] B. Raman, et al. The SAHARA Model for Service Composition across Multiple Providers. IEEE Pervasive Computing, August 2002. [2] Skype, see http://www.skype.com [3] T.Rakotoarivelo, P. Senac, A. Seneviratne, and M.Diaz. Enhancing QoS Through Alternate Path: An End-to-End Framework. IEEE International Conference on Networking (ICN05), April 2005. [4] T.Rakotoarivelo, P. Senac, A. Seneviratne, and M. Diaz. A Super-Peer based Method to Discover QoS Enhanced Alternate Paths. IEEE AsiaPacific Conference on Communications (APCC05), October 2005. [5] S. Savage, A. Collins, E. Hoffman, J. Snell, and T. Anderson. The Endto-End Effects of Internet Path Selection. ACM SIGCOMM, 1999. [6] Zhi Li and P. Mohapatra. QRON: Qos-Aware Routing in Overlay Networks. IEEE Journal on Selected Areas in Communications, 2004. [7] B. Yang, H. Garcia-Molina. Designing a Super-Peer Network. In Proc. of the IEEE Conference on Data Engineering, 2003. [8] D. G. Andersen, H. Balakrishnan, F. Kaashoek, R. Morris. Resilient Overlay Networks. In Proc. 18th ACM SOSP, Banff, Canada, 2001. [9] E.K. Lua, J. Crowcroft, M. Pias, R. Sharma, and S. Lim. A Survey and Comparison of Peer-to-Peer Overlay Network Scheme. IEEE Communications Survey and Tutorial, March 2004. [10] D. Stauffer, and A. Aharony. Introduction to Percolation Theory. Taylor and Francis, 1992. [11] A.J. Ganesh, A-M. Kermarrec, and L. Massoulie. Peer-to-Peer Membership Management for Gossip-Based Protocols. IEEE Transactions on Computers. Vol 52 No 2. 2003. [12] F. Banaei-Kashani, and C. Shahabi. Criticality-based Analysis and Design of Unstructured Peer-to-Peer Networks as Complex Systems. In Proc. of Intl. Symposium on Cluster Computing and the Grid, 2003. [13] P. Gummadi, S. Saroiu and S.D. Gribble. King: Estimating Latency between Arbitrary Internet End Hosts. ACM SIGCOMM-IMW, 2002. [14] D. Clark, V. Jacobson, J. Romkey, and H. Salwen. An analysis of TCP processing overhead. IEEE Communication, vol. 27 No6, 1989. [15] Y. Zhang, N. Duffield, V. Paxson, and S. Shenker. On the Constancy of Internet Path Properties. SIGCOMM Internet Measurement 2001 [16] BRITE Topology Generator, http://www.cs.bu.edu/brite [17] Q. Zhang, F. Yang, W. Zhu, and Y.Q. Zhang. A Construction of Locality-Aware Overlay Network: mOverlay and its performance. In IEEE Journal on Selected Areas in Communications,Vol.22-No.1, 2004. [18] PlanetLab All Pair-Pings, see http://pdos.csail.mit.edu/~strib/pl_app/