The Asynchronous Bounded-Cycle Model

  • Peter Robinson
  • Ulrich Schmid
Part of the Lecture Notes in Computer Science book series (LNCS, volume 5340)

Abstract

This paper shows how synchrony conditions can be added to the purely asynchronous model in a way that avoids any reference to message delays and computing step times, as well as any global constraints on communication patterns and network topology. Our Asynchronous Bounded-Cycle (ABC) model just bounds the ratio of the number of forward- and backward-oriented messages in certain (“relevant”) cycles in the space-time diagram of an asynchronous execution. We show that clock synchronization and lock-step rounds can easily be implemented and proved correct in the ABC model, even in the presence of Byzantine failures. We also prove that any algorithm working correctly in the partially synchronous Θ-Model also works correctly in the ABC model. Finally, we relate our model to the classic partially synchronous model, and discuss aspects of its applicability in real systems.

Keywords

Fault-tolerant distributed algorithms partially synchronous models clock synchronization 

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 1.
    Aguilera, M.K., Delporte-Gallet, C., Fauconnier, H., Toueg, S.: Communication-efficient leader election and consensus with limited link synchrony. In: Proceedings of the 23rd ACM symposium on Principles of Distributed Computing (PODC 2004), St. John’s, Newfoundland, Canada, pp. 328–337. ACM Press, New York (2004)Google Scholar
  2. 2.
    Alpern, B., Schneider, F.B.: Defining liveness, Tech. report, Ithaca, NY, USA (1984)Google Scholar
  3. 3.
    Attiya, H., Dwork, C., Lynch, N., Stockmeyer, L.: Bounds on the time to reach agreement in the presence of timing uncertainty. Journal of the ACM (JACM) 41(1), 122–152 (1994)MathSciNetCrossRefMATHGoogle Scholar
  4. 4.
    Biely, M., Widder, J.: Optimal message-driven implementation of omega with mute processes. In: Datta, A.K., Gradinariu, M. (eds.) SSS 2006. LNCS, vol. 4280, pp. 110–121. Springer, Heidelberg (2006)CrossRefGoogle Scholar
  5. 5.
    Chandra, T.D., Toueg, S.: Unreliable failure detectors for reliable distributed systems. Journal of the ACM 43(2), 225–267 (1996)MathSciNetCrossRefMATHGoogle Scholar
  6. 6.
    Dolev, D., Dwork, C., Stockmeyer, L.: On the minimal synchronism needed for distributed consensus. Journal of the ACM 34(1), 77–97 (1987)MathSciNetCrossRefMATHGoogle Scholar
  7. 7.
    Dwork, C., Lynch, N., Stockmeyer, L.: Consensus in the presence of partial synchrony. Journal of the ACM 35(2), 288–323 (1988)MathSciNetCrossRefGoogle Scholar
  8. 8.
    Fetzer, C., Schmid, U., Süßkraut, M.: On the possibility of consensus in asynchronous systems with finite average response times. In: Proceedings of the 25th International Conference on Distributed Computing Systems (ICDCS 2005), Washington, DC, USA, pp. 271–280. IEEE Computer Society, Los Alamitos (2005)Google Scholar
  9. 9.
    Fischer, M.J., Lynch, N.A., Paterson, M.S.: Impossibility of distributed consensus with one faulty process. Journal of the ACM 32(2), 374–382 (1985)MathSciNetCrossRefMATHGoogle Scholar
  10. 10.
    Hadzilacos, V., Toueg, S.: Fault-tolerant broadcasts and related problems. In: Mullender, S. (ed.) Distributed Systems, 2nd edn., pp. 97–145. Addison-Wesley, Reading (1993)Google Scholar
  11. 11.
    Hutle, M., Malkhi, D., Schmid, U., Zhou, L.: Brief announcement: Chasing the weakest system model for implementing omega and consensus. In: Datta, A.K., Gradinariu, M. (eds.) SSS 2006. LNCS, vol. 4280, pp. 576–577. Springer, Heidelberg (2006)CrossRefGoogle Scholar
  12. 12.
    Lamport, L.: Time, clocks, and the ordering of events in a distributed system. Commun. ACM 21(7), 558–565 (1978)CrossRefMATHGoogle Scholar
  13. 13.
    Malkhi, D., Oprea, F., Zhou, L.: Ω meets paxos: Leader election and stability without eventual timely links. In: Fraigniaud, P. (ed.) DISC 2005, vol. 3724, pp. 199–213. Springer, Heidelberg (2005)CrossRefGoogle Scholar
  14. 14.
    Mattern, F.: Virtual time and global states of distributed systems. In: Proceedings of the International Workshop on Parallel and Distributed Algorithms, pp. 215–226. Elsevier Science Publishers B.V, Amsterdam (1989)Google Scholar
  15. 15.
    Mattern, F.: On the relativistic structure of logical time in distributed systems. In: Parallel and Distributed Algorithms, pp. 215–226. Elsevier Science Publishers B.V, Amsterdam (1992)Google Scholar
  16. 16.
    Moser, H., Schmid, U.: Optimal clock synchronization revisited: Upper and lower bounds in real-time systems. In: Shvartsman, M.M.A.A. (ed.) OPODIS 2006. LNCS, vol. 4305, pp. 95–109. Springer, Heidelberg (2006)CrossRefGoogle Scholar
  17. 17.
    Mostefaoui, A., Mourgaya, E., Raynal, M., Travers, C.: A time-free assumption to implement eventual leadership. Parallel Processing Letters 16, 189–208 (2006)MathSciNetCrossRefGoogle Scholar
  18. 18.
    Ponzio, S., Strong, R.: Semisynchrony and real time. In: Segall, A., Zaks, S. (eds.) WDAG 1992. LNCS, vol. 647, pp. 120–135. Springer, Heidelberg (1992)CrossRefGoogle Scholar
  19. 19.
    Robinson, P., Schmid, U.: The Asynchronous Bounded-Cycle Model, Research Report 24/2008, Technische Universität Wien, Institut für Technische Informatik, Treitlstr. 1-3/182-1, 1040 Vienna, Austria (2008)Google Scholar
  20. 20.
    Vitányi, P.M.B.: Distributed elections in an archimedean ring of processors. In: Proceedings of the sixteenth annual ACM symposium on Theory of computing, pp. 542–547. ACM Press, New York (1984)CrossRefGoogle Scholar
  21. 21.
    Widder, J., Le Lann, G., Schmid, U.: Failure detection with booting in partially synchronous systems. In: Dal Cin, M., Kaâniche, M., Pataricza, A. (eds.) EDCC 2005. LNCS, vol. 3463, pp. 20–37. Springer, Heidelberg (2005)Google Scholar
  22. 22.
    Widder, J., Schmid, U.: Achieving synchrony without clocks, Research Report 49/2005, Technische Universität Wien, Institut f. Technische Informatik (submitted)Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2008

Authors and Affiliations

  • Peter Robinson
    • 1
  • Ulrich Schmid
    • 1
  1. 1.Embedded Computing Systems Group (E182/2)Technische Universität WienViennaAustria

Personalised recommendations