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The Theta-Model: achieving synchrony without clocks

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Abstract

We present a novel partially synchronous system model, which augments the asynchronous model by a (possibly unknown) bound Θ on the ratio of longest and shortest end-to-end delays of messages simultaneously in transit. An upper bound on those delays need not exist, however, and even Θ may hold only after some unknown global stabilization time. Θ-algorithms are fully message-driven and do not have access to bounded drift local clocks, which makes them particularly suitable for VLSI Systems-on-Chip, for example. In this model, we provide a simulation of (eventually achieved) lock-step rounds, which even works in the presence of Byzantine failures. It follows that most problems in distributed computing have a solution in our model: Using the basic consensus algorithm for partially synchronous systems by Dwork et al. (J ACM 35(2):288–323, 1988), for example, Byzantine consensus can be solved. We also introduce a timing transformation technique that facilitates simple correctness proofs and performance analyses of Θ-algorithms, and provide a detailed relation of the Θ-Model to other partially synchronous system models.

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References

  1. Aguilera, M.K., Delporte-Gallet, C., Fauconnier, H., Toueg, S.: Stable leader election. In: DISC ’01: Proceedings of the 15th International Conference on Distributed Computing, pp. 108–122. Springer, Berlin (2001)

  2. Aguilera, M.K., Delporte-Gallet, C., Fauconnier, H., Toueg, S.: On implementing Omega with weak reliability and synchrony assumptions. In: Proceeding of the 22nd Annual ACM Symposium on Principles of Distributed Computing (PODC’03), pp. 306–314. ACM Press, New York (2003)

  3. Aguilera, M.K., Delporte-Gallet, C., Fauconnier, H., Toueg, S.: Communication-efficient leader election and consensus with limited link synchrony. In: Proceedings of the 23th ACM Symposium on Principles of Distributed Computing (PODC’04), pp. 328–337. ACM Press, St. John’s (2004)

  4. Aguilera, M.K., Delporte-Gallet, C., Fauconnier, H., Toueg, S.: Consensus with byzantine failures and little system synchrony. In: Proceedings of the International Conference on Dependable Systems and Networks (DSN’06), pp. 147–155 (2006)

  5. Albeseder, D.: Evaluation of message delay correlation in distributed systems. In: Proceedings of the Third Workshop on Intelligent Solutions for Embedded Systems. Hamburg, Germany (2005)

  6. Ammar, Y., Buhrig, A., Marzencki, M., Charlot, B., Basrour, S., Matou, K., Renaudin, M.: Wireless sensor network node with asynchronous architecture and vibration harvesting micro power generator. In: sOc-EUSAI ’05: Proceedings of the 2005 joint conference on Smart objects and ambient intelligence, pp. 287–292. ACM, New York (2005)

  7. Anceaume E., Fernández A., Mostéfaoui A., Neiger G., Raynal M.: A necessary and sufficient condition for transforming limited accuracy failure detectors. J. Comput. Syst. Sci. 68(1), 123–133 (2004)

    Article  MATH  Google Scholar 

  8. Attiya H., Dwork C., Lynch N., Stockmeyer L.: Bounds on the time to reach agreement in the presence of timing uncertainty. J. ACM (JACM) 41(1), 122–152 (1994)

    Article  MATH  MathSciNet  Google Scholar 

  9. Beauquier J., Kekkonen-Moneta S.: Fault-tolerance and self-stabilization: impossibility results and solutions using self-stabilizing failure detectors. Int. J. Syst. Sci. 28(11), 1177–1187 (1997)

    Article  MATH  Google Scholar 

  10. Biely, M., Widder, J.: Optimal message-driven implementations of omega with mute processes. ACM Trans. Auton. Adaptive Syst. 4(1), Article 4, 22 pages (2009)

    Google Scholar 

  11. Chandra T.D., Toueg S.: Unreliable failure detectors for reliable distributed systems. J. ACM 43(2), 225–267 (1996)

    Article  MATH  MathSciNet  Google Scholar 

  12. Cristian F., Fetzer C.: The timed asynchronous distributed system model. IEEE Trans. Parallel Distrib. Syst. 10(6), 642–657 (1999)

    Article  Google Scholar 

  13. Dolev D., Dwork C., Stockmeyer L.: On the minimal synchronism needed for distributed consensus. J. ACM 34(1), 77–97 (1987)

    Article  MATH  MathSciNet  Google Scholar 

  14. Dolev S.: Self-stabilization. MIT Press, Cambridge (2000)

    MATH  Google Scholar 

  15. Dwork C., Lynch N., Stockmeyer L.: Consensus in the presence of partial synchrony. J. ACM 35(2), 288–323 (1988)

    Article  MathSciNet  Google Scholar 

  16. Ebergen J.C.: A formal approach to designing delay-insensitive circuits. Distrib. Comput. 5, 107–119 (1991)

    Article  MATH  Google Scholar 

  17. Ekanayake V., Clinton Kelly I., Manohar R.: An ultra low-power processor for sensor networks. SIGOPS Oper. Syst. Rev. 38(5), 27–36 (2004)

    Article  Google Scholar 

  18. Ferringer, M., Fuchs, G., Steininger, A., Kempf, G.: VLSI implementation of a fault-tolerant distributed clock generation. IEEE International Symposium on Defect and Fault-Tolerance in VLSI Systems (DFT2006), pp. 563–571 (2006)

  19. Fetzer, C., Schmid, U.: Brief announcement: On the possibility of consensus in asynchronous systems with finite average response times. In: Proceedings of the 23th ACM Symposium on Principles of Distributed Computing (PODC’04), p. 402. Boston, Massachusetts (2004)

  20. Fetzer, C., Schmid, U., Sü ßkraut, 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’05), pp. 271–280. IEEE Computer Society, Washington (2005)

  21. Fischer M.J., Lynch N.A., Paterson M.S.: Impossibility of distributed consensus with one faulty process. J. ACM 32(2), 374–382 (1985)

    Article  MATH  MathSciNet  Google Scholar 

  22. Fuegger, M., Schmid, U., Fuchs, G., Kempf, G.: Fault-tolerant distributed clock generation in VLSI systems-on-chip. In: Proceedings of the Sixth European Dependable Computing Conference (EDCC-6), pp. 87–96. IEEE Computer Society Press (2006)

  23. Gafni, E.: Round-by-round fault detectors (extended abstract): unifying synchrony and asynchrony. In: Proceedings of the Seventeenth Annual ACM Symposium on Principles of Distributed Computing, pp. 143–152. ACM Press, Puerto Vallarta (1998)

  24. Hermant J.F., Le Lann G.: Fast asynchronous uniform consensus in real-time distributed systems. IEEE Trans. Comput. 51(8), 931–944 (2002)

    Article  Google Scholar 

  25. Hermant, J.F., Widder, J.: Implementing reliable distributed real-time systems with the Θ-model. In: Proceedings of the 9th International Conference on Principles of Distributed Systems (OPODIS 2005). LNCS, vol. 3974, pp. 334–350. Springer, Pisa (2005)

  26. Hutle, M., Malkhi, D., Schmid, U., Zhou, L.: Brief announcement: Chasing the weakest system model for implementing omega and consensus. In: Proceedings Eighth International Symposium on Stabilization, Safety, and Security of Distributed Systems (formerly Symposium on Self-stabilizing Systems) (SSS 2006). LNCS, pp. 576–577. Springer, Dallas (2006)

  27. Hutle, M., Malkhi, D., Schmid, U., Zhou, L.: Chasing the weakest system model for implementing omega and consensus. IEEE Trans. Dependable Secure Comput. (2009, to appear)

  28. Hutle, M., Widder, J.: On the possibility and the impossibility of message-driven self-stabilizing failure detection. In: Proceedings of the Seventh International Symposium on Self Stabilizing Systems (SSS 2005), LNCS, vol. 3764, pp. 153–170. Springer, Barcelona (2005). Appeared also as brief announcement in Proceedings of the 24th ACM Symposium on Principles of Distributed Computing (PODC’05)

  29. Hutle, M., Widder, J.: Self-stabilizing failure detector algorithms. In: Proc. IASTED International Conference on Parallel and Distributed Computing and Networks (PDCN’05), pp. 485–490. IASTED/ACTA Press, Innsbruck (2005)

  30. Lamport L., Shostak R., Pease M.: The Byzantine generals problem. ACM Trans. Program. Lang. Syst. 4(3), 382–401 (1982)

    Article  MATH  Google Scholar 

  31. Le Lann, G., Schmid, U.: How to implement a timer-free perfect failure detector in partially synchronous systems. Tech. Rep. 183/1-127, Department of Automation, Technische Universität Wien (2003) (Replaced by Research Report 28/2005, Institut für Technische Informatik, TU Wien, 2005)

  32. Lundelius-Welch J., Lynch N.A.: A new fault-tolerant algorithm for clock synchronization. Inform. Comput. 77(1), 1–36 (1988)

    Article  Google Scholar 

  33. Lynch N.: Distributed Algorithms. Morgan Kaufman Publishers, Inc., San Francisco (1996)

    MATH  Google Scholar 

  34. Malkhi, D., Oprea, F., Zhou, L.: Ω meets paxos: Leader election and stability without eventual timely links. In: Proceedings of the 19th Symposium on Distributed Computing (DISC’05). LNCS, vol. 3724, pp. 199–213. Springer, Cracow (2005)

  35. Mostefaoui, A., Mourgaya, E., Raynal, M.: Asynchronous implementation of failure detectors. In: Proceedings of the International Conference on Dependable Systems and Networks (DSN’03). San Francisco, CA (2003)

  36. Mostefaoui, A., Powell, D., Raynal, M.: A hybrid approach for building eventually accurate failure detectors. In: Proceedings of the 10th International Pacific Rim Dependable Computing Symposium (PRDC’04), pp. 57–65. IEEE Computer Society (2004)

  37. Mostéfaoui, A., Raynal, M.: Solving consensus using chandra-toueg’s unreliable failure detectors: A general quorum-based approach. In: Jayanti, P. (ed.) Distributed Computing: 13th International Symposium (DISC’99). Lecture Notes in Computer Science, vol. 1693, pp. 49–63. Springer-Verlag GmbH, Bratislava (1999)

  38. Mostefaoui, A., Raynal, M., Travers, C.: Crash-resilient time-free eventual leadership. In: Proceedings of the 23rd IEEE Symposium on Reliable Distributed Systems (SRDS 2004), pp. 208–217. IEEE Computer Society (2004)

  39. Parkes, S., Armbruster, P.: SpaceWire: a spacecraft onboard network for real-time communications. In: Proceedings 14th IEEE-NPSS Real Time Conference, pp. 6–10 (2005)

  40. Ponzio, S.: The real-time cost of timing uncertainty: Consensus and failure detection. Master’s thesis, Massachusetts Institute of Technology (1991)

  41. Ponzio, S., Strong, R.: Semisynchrony and real time. In: Proceedings of the 6th International Workshop on Distributed Algorithms (WDAG’92), pp. 120–135. Haifa, Israel (1992)

  42. Schmid, U., Fetzer, C.: Randomized asynchronous consensus with imperfect communications. In: 22nd Symposium on Reliable Distributed Systems (SRDS’03), pp. 361–370. Florence, Italy (2003)

  43. Schmid, U., Steininger, A.: Dezentrale Fehlertolerante Taktgenerierung in VLSI Chips. Research Report 69/2004, Technische Universität Wien, Institut für Technische Informatik (2004). (Österr. Patentanmeldung A 1223/2004)

  44. Schmid, U., Weiss, B., Rushby, J.: Formally verified byzantine agreement in presence of link faults. In: 22nd International Conference on Distributed Computing Systems (ICDCS’02), pp. 608–616. Vienna, Austria (2002)

  45. Srikanth T.K., Toueg S.: Optimal clock synchronization. J. ACM 34(3), 626–645 (1987)

    Article  MathSciNet  Google Scholar 

  46. Sutherland I.E., Ebergen J.: Computers without clocks. Sci. Am. 287(2), 62–69 (2002)

    Article  Google Scholar 

  47. Veríssimo P., Casimiro A.: The timely computing base model and architecture. IEEE Trans. Comput. 51(8), 916–930 (2002)

    Article  Google Scholar 

  48. Vitányi, P.M.: Time-driven algorithms for distributed control. Report CS-R8510, C.W.I. (1985)

  49. Widder, J.: Booting clock synchronization in partially synchronous systems. In: Proceedings of the 17th International Symposium on Distributed Computing (DISC’03), LNCS, vol. 2848, pp. 121–135. Springer, Sorrento (2003)

  50. Widder, J.: Distributed computing in the presence of bounded asynchrony. Ph.D. thesis, Vienna University of Technology, Fakultät für Informatik (2004)

  51. Widder, J., Le Lann, G., Schmid, U.: Failure detection with booting in partially synchronous systems. In: Proceedings of the 5th European Dependable Computing Conference (EDCC-5). LNCS, vol. 3463, pp. 20–37. Springer, Budapest (2005)

  52. Widder J., Schmid U.: Booting clock synchronization in partially synchronous systems with hybrid process and link failures. Distrib. Comput. 20(2), 115–140 (2007)

    Article  Google Scholar 

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Authors and Affiliations

  1. Embedded Computing Systems Group (E182/2), Technische Universität Wien, Treitlstraße 3, 1040, Vienna, Austria

    Josef Widder & Ulrich Schmid

  2. Laboratoire d’Informatique LIX, École polytechnique, 91128, Palaiseau Cedex, France

    Josef Widder

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  1. Josef Widder
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  2. Ulrich Schmid
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Correspondence to Josef Widder.

Additional information

Supported by the FWF project Theta (proj. no. P17757-N04) and the BM:vit FIT-IT project DCBA (proj. no. 808198).

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Widder, J., Schmid, U. The Theta-Model: achieving synchrony without clocks. Distrib. Comput. 22, 29–47 (2009). https://doi.org/10.1007/s00446-009-0080-x

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