Stochastic Modeling of Dynamic Distributed Systems with Crash Recovery and Its Application to Atomic Registers

  • Silvia Bonomi
  • Andreas Klappenecker
  • Hyunyoung Lee
  • Jennifer L. Welch
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 7702)

Abstract

In a dynamic distributed system, processes can join and leave the system. We consider such a system in which processes are subject to crash failures from which they may recover. Assuming a stochastic model for joining, leaving, crashing, and recovering of processes, we provide a probabilistic analysis of the long-term behavior of the system. As an example of the utility of our modeling, we provide a specification and implementation of an atomic register in such a system. The dynamic nature of the system can cause all active processes to leave or crash, leaving the system in a dormant state. We analyze the average time spent in dormant states that can give us some insight into the behavior of the register system.

Keywords

Stochastic Modeling Dynamic Distributed System Dynamic Atomic Register 

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References

  1. 1.
    Aguilera, M.: A pleasant stroll through the land of infinitely many creatures. SIGACT News 35(2), 36–59 (2004)CrossRefGoogle Scholar
  2. 2.
    Aguilera, M., Keidar, I., Malkhi, D., Shraer, A.: Dynamic atomic storage without consensus. J. ACM 58(2), 7:1–7:32 (2011)Google Scholar
  3. 3.
    Attiya, H., Bar-Noy, A., Dolev, D.: Sharing memory robustly in message-passing systems. J. ACM 42(1), 124–142 (1995)MATHCrossRefGoogle Scholar
  4. 4.
    Baldoni, R., Bonomi, S., Kermarrec, A., Raynal, M.: Implementing a Register in a Dynamic Distributed System. In: 29th International Conference on Distributed Computing Systems, ICDCS 2009 (2009)Google Scholar
  5. 5.
    Baldoni, R., Bonomi, S., Raynal, M.: Implementing a Regular Register in an Eventually Synchronous Distributed System Prone to Continuous Churn. IEEE Transaction on Parallel Distributed Systems 23(1), 102–109 (2012)CrossRefGoogle Scholar
  6. 6.
    Bhagwan, R., Savage, S., Voelker, G.M.: Understanding Availability. In: Kaashoek, M., Stoica, I. (eds.) IPTPS 2003. LNCS, vol. 2735, pp. 256–267. Springer, Heidelberg (2003)CrossRefGoogle Scholar
  7. 7.
    Brighten, G., Shenker, S., Stoica, I.: Minimizing churn in distributed systems. In: Proceedings of the 2006 Conference on Applications, Technologies, Architectures, and Protocols for Computer Communications, SIGCOMM 2006, pp. 147–158. ACM, New York (2006)Google Scholar
  8. 8.
    Chen, H., Yao, D.: Fundamentals of Queueing Networks – Performance, Asymptotics, and Optimization. Springer, New York (2001)MATHGoogle Scholar
  9. 9.
    Chockler, G., Gilbert, S., Gramoli, V., Musial, P., Shvartsman, A.: Reconfigurable distributed storage for dynamic networks. Journal Parallel Distributed Computing 69(1), 100–116 (2009)CrossRefGoogle Scholar
  10. 10.
    Gilbert, S., Lynch, N., Shvartsman, A.: Rambo ii: Rapidly reconfigurable atomic memory for dynamic networks. In: International Conference on Dependable Systems and Networks, DSN 2003, p. 259. IEEE Computer Society, Los Alamitos (2003)Google Scholar
  11. 11.
    Gilbert, S., Lynch, N., Shvartsman, A.: Rambo: a robust, reconfigurable atomic memory service for dynamic networks. Distributed Computing 23, 225–272 (2010)MATHCrossRefGoogle Scholar
  12. 12.
    Gummadi, K., Dunn, R., Saroiu, S., Gribble, S., Levy, H., Zahorjan, J.: Measurement, modeling, and analysis of a peer-to-peer file-sharing workload. In: Proceedings of the Nineteenth ACM Symposium on Operating Systems Principles, SOSP 2003, pp. 314–329. ACM, New York (2003)CrossRefGoogle Scholar
  13. 13.
    Herlihy, M., Wing, J.: Linearizability: a correctness condition for concurrent objects. ACM Trans. Program. Lang. Syst. 12, 463–492 (1990)CrossRefGoogle Scholar
  14. 14.
    Klappenecker, A., Lee, H., Welch, J.L.: Dynamic Regular Registers in Systems with Churn. In: Défago, X., Petit, F., Villain, V. (eds.) SSS 2011. LNCS, vol. 6976, pp. 296–310. Springer, Heidelberg (2011)CrossRefGoogle Scholar
  15. 15.
    Ko, S., Hoque, I., Gupta, I.: Using tractable and realistic churn models to analyze quiescence behavior of distributed protocols. In: Proceedings of the 2008 Symposium on Reliable Distributed Systems, SRDS 2008, pp. 259–268. IEEE Computer Society, Washington, DC (2008)CrossRefGoogle Scholar
  16. 16.
    Krishnamurthy, S., El-Ansary, S., Aurell, E., Haridi, S.: A Statistical Theory of Chord Under Churn. In: van Renesse, R. (ed.) IPTPS 2005. LNCS, vol. 3640, pp. 93–103. Springer, Heidelberg (2005)CrossRefGoogle Scholar
  17. 17.
    Lamport, L.: On interprocess communication, Part I: Models, Part II: Algorithms. Distributed Computing 1(2), 77–101 (1986)MATHCrossRefGoogle Scholar
  18. 18.
    Leonard, D., Yao, Z., Rai, V., Loguinov, D.: On lifetime-based node failure and stochastic resilience of decentralized peer-to-peer networks. IEEE/ACM Transaction on Networking 15(3), 644–656 (2007)CrossRefGoogle Scholar
  19. 19.
    Liben-Nowell, D., Balakrishnan, H., Karger, D.: Analysis of the evolution of peer-to-peer systems. In: Proceedings of the Twenty-First Annual Symposium on Principles of Distributed Computing, PODC 2002, pp. 233–242. ACM, New York (2002)CrossRefGoogle Scholar
  20. 20.
    Lynch, N., Shvartsman, A.A.: RAMBO: A Reconfigurable Atomic Memory Service for Dynamic Networks. In: Malkhi, D. (ed.) DISC 2002. LNCS, vol. 2508, pp. 173–190. Springer, Heidelberg (2002)CrossRefGoogle Scholar
  21. 21.
    Merritt, M., Taubenfeld, G.: Computing with Infinitely Many Processes. In: Herlihy, M.P. (ed.) DISC 2000. LNCS, vol. 1914, pp. 164–178. Springer, Heidelberg (2000)CrossRefGoogle Scholar
  22. 22.
    Resnick, S.: Adventures in Stochastic Processes. Birkhäuser, Boston (1992)MATHGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2012

Authors and Affiliations

  • Silvia Bonomi
    • 1
  • Andreas Klappenecker
    • 2
  • Hyunyoung Lee
    • 2
  • Jennifer L. Welch
    • 2
  1. 1.Sapienza Università di RomaRomaItaly
  2. 2.Texas A&M UniversityCollege StationUSA

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