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Understanding Disconnection and Stabilization of Chord
April 2011 (vol. 22 no. 4)
pp. 650-661
Zhongmei Yao, The University of Dayton, Dayton
Dmitri Loguinov, Texas A&M University, College Station
Previous analytical work [16], [17] on the resilience of P2P networks has been restricted to disconnection arising from simultaneous failure of all neighbors in routing tables of participating users. In this paper, we focus on a different technique for maintaining consistent graphs—Chord's successor sets and periodic stabilizations—under both static and dynamic node failure. We derive closed-form models for the probability that Chord remains connected under both types of node failure and show the effect of using different stabilization interval lengths (i.e., exponential, uniform, and constant) on the probability of partitioning in Chord.

[1] R. Albert and A. Barabási, "Topology of Evolving Networks: Local Events and Universality," Physical Rev. Letters, vol. 85, no. 24, pp. 5234-5237, Dec. 2000.
[2] R. Arratia, L. Goldstein, and L. Gordon, "Two Moments Suffice for Poisson Approximations: The Chen-Stein Method," The Annals of Probability, vol. 17, no. 1, pp. 9-25, Jan. 1989.
[3] J. Aspnes, Z. Diamadi, and G. Shah, "Fault-Tolerant Routing in Peer-to-Peer Systems," Proc. ACM Symp. Principles of Distributed Computing (PODC), pp. 223-232, July 2002.
[4] N. Balakrishnan and M.V. Koutras, Runs and Scans with Applications. John Wiley & Sons, 2002.
[5] F.E. Bustamante and Y. Qiao, "Friendships That Last: Peer Lifespan and Its Role in P2P Protocols," Proc. Int'l Workshop Web Content Caching and Distribution, Sept. 2003.
[6] M. Castro, M. Costa, and A. Rowstron, "Performance and Dependability of Structured Peer-to-Peer Overlays," Proc. Int'l Conf. Dependable Systems and Networks (DSN), June 2004.
[7] B.-G. Chun, B. Zhao, and J. Kubiatowicz, "Impact of Neighbor Selection on Performance and Resilience of Structured P2P Networks," Proc. Int'l Workshop Peer-to-Peer Systems (IPTPS), pp. 264-274, Feb. 2005.
[8] H. Frank, "Maximally Reliable Node Weighted Graphs," Proc. Third Ann. Conf. Information Sciences and Systems, pp. 1-6, Mar. 1969.
[9] P.B. Godfrey, S. Shenker, and I. Stoica, "Minimizing Churn in Distributed Systems," Proc. ACM SIGCOMM, Sept. 2006.
[10] K. Gummadi, R. Gummadi, S. Gribble, S. Ratnasamy, S. Shenker, and I. Stoica, "The Impact of DHT Routing Geometry on Resilience and Proximity," Proc. ACM SIGCOMM, pp. 381-394, Aug. 2003.
[11] M.F. Kaashoek and D. Karger, "Koorde: A Simple Degree-Optimal Distributed Hash Table," Proc. Int'l Workshop Peer-to-Peer Systems (IPTPS), pp. 98-107, Feb. 2003.
[12] A.K. Kelmans, "Connectivity of Probabilistic Networks," Automation and Remote Control, vol. 29, pp. 444-460, 1967.
[13] S.G. Krantz, Handbook of Complex Variables. Birkhäuser, 1999.
[14] S. Krishnamurthy, S. El-Ansary, E. Aurell, and S. Haridi, "A Statistical Theory of Chord under Churn," Proc. Int'l Workshop Peer-to-Peer Systems (IPTPS), pp. 93-103, Feb. 2005.
[15] S.S. Lam and H. Liu, "Failure Recovery for Structured P2P Networks: Protocol Design and Performance Evaluation," Proc. ACM SIGMETRICS, pp. 199-210, June 2004.
[16] D. Leonard, V. Rai, and D. Loguinov, "On Lifetime-Based Node Failure and Stochastic Resilience of Decentralized Peer-to-Peer Networks," Proc. ACM SIGMETRICS, pp. 26-37, June 2005.
[17] D. Leonard, Z. Yao, X. Wang, and D. Loguinov, "On Static and Dynamic Partitioning Behavior of Large-Scale Networks," Proc. IEEE Int'l Conf. Network Protocols (ICNP), pp. 345-357, Nov. 2005.
[18] J. Li, J. Stribling, T.M. Gil, R. Morris, and M.F. Kaashoek, "Comparing the Performance of Distributed Hash Tables under Churn," Proc. Int'l Workshop Peer-to-Peer Systems (IPTPS), pp. 87-99, Feb. 2004.
[19] J. Li, J. Stribling, R. Morris, M.F. Kaashoek, and T.M. Gil, "A Performance vs. Cost Framework for Evaluating DHT Design Tradeoffs under Churn," Proc. IEEE INFOCOM, pp. 225-236, Mar. 2005.
[20] D. Liben-Nowell, H. Balakrishnan, and D. Karger, "Analysis of the Evolution of the Peer-to-Peer Systems," Proc. ACM Symp. Principles of Distributed Computing (PODC), pp. 233-242, July 2002.
[21] P. Maymounkov and D. Mazieres, "Kademlia: A Peer-to-Peer Information System Based on the XOR Metric," Proc. Int'l Workshop Peer-to-Peer Systems (IPTPS), pp. 53-65, Mar. 2002.
[22] G. Pandurangan, P. Raghavan, and E. Upfal, "Building Low-Diameter Peer-to-Peer Networks," IEEE J. Selected Areas in Comm., vol. 21, no. 6, pp. 995-1002, Aug. 2003.
[23] L. Plissonneau, J.-L. Costeux, and P. Brown, "Analysis of Peer-to-Peer Traffic on ADSL," Proc. Passive and Active Measurement Conf. (PAM), pp. 69-82, Mar. 2005.
[24] S. Rhea, D. Geels, T. Roscoe, and J. Kubiatowicz, "Handling Churn in a DHT," Proc. USENIX Ann. Technical Conf., pp. 127-140. June 2004.
[25] A. Rowstron and P. Druschel, "Pastry: Scalable, Decentralized Object Location and Routing for Large-Scale Peer-to-Peer Systems," Proc. IFIP/ACM Int'l Conf. Distributed Systems Platforms (Middleware), pp. 329-350, Nov. 2001.
[26] I. Stoica, R. Morris, D. Liben-Nowell, D.R. Karger, M.F. Kaashoek, F. Dabek, and H. Balakrishnan, "Chord: A Scalable Peer-to-Peer Lookup Protocol for Internet Applications," IEEE/ACM Trans. Networking, vol. 11, no. 1, pp. 17-32, Feb. 2003.
[27] D. Stutzbach and R. Rejaie, "Understanding Churn in Peer-to-Peer Networks," Proc. ACM Internet Measurement Conf. (IMC), pp. 189-202, Oct. 2006.
[28] K. Sutner, A. Satyanarayana, and C. Suffel, "The Complexity of the Residual Node Connectedness Reliability Problem," SIAM J. Computing, vol. 20, pp. 149-155, 1991.
[29] G. Tan and S. Jarvis, "Stochastic Analysis and Improvement of the Reliability of DHT-Based Multicast," Proc. IEEE INFOCOM, pp. 2198-2206, May 2007.
[30] X. Wang, Z. Yao, and D. Loguinov, "Residual-Based Estimation of Peer and Link Lifetimes in P2P Networks," IEEE/ACM Trans. Networking, vol. 17, no. 3, pp. 726-739, June 2009.
[31] X. Wang, Z. Yao, and D. Loguinov, "Residual-Based Measurement of Peer and Link Lifetimes in Gnutella Networks," Proc. IEEE INFOCOM, pp. 391-399, May 2007.
[32] R.W. Wolff, Stochastic Modeling and the Theory of Queues. Prentice Hall, 1989.
[33] Z. Yao, X. Wang, D. Leonard, and D. Loguinov, "Node Isolation Model and Age-Based Neighbor Selection in Unstructured P2P Networks," IEEE/ACM Trans. Networking, vol. 17, no. 2, pp. 144-157, Apr. 2009.
[34] Z. Yao, D. Leonard, X. Wang, and D. Loguinov, "Modeling Heterogeneous User Churn and Local Resilience of Unstructured P2P Networks," Proc. IEEE Int'l Conf. Network Protocols (ICNP), pp. 32-41, Nov. 2006.

Index Terms:
Peer-to-peer networks, graph disconnection, stabilization of Chord.
Citation:
Zhongmei Yao, Dmitri Loguinov, "Understanding Disconnection and Stabilization of Chord," IEEE Transactions on Parallel and Distributed Systems, vol. 22, no. 4, pp. 650-661, April 2011, doi:10.1109/TPDS.2010.114
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