Skip to main content

Stability of Distributed Algorithms in the Face of Incessant Faults

  • Conference paper
Stabilization, Safety, and Security of Distributed Systems (SSS 2009)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 5873))

Included in the following conference series:

Abstract

For large distributed systems built from inexpensive components, one expects to see incessant failures. This paper proposes two models for such faults and analyzes two well-known self-stabilizing algorithms under these fault models. For a small number of processes, the properties of interest are verified automatically using probabilistic model-checking tools. For a large number of processes, these properties are characterized using asymptotic bounds from a direct Markov chain analysis and approximated by numerical simulations.

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 84.99
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 109.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

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

    MATH  Google Scholar 

  2. Schneider, M.: Self-stabilization. ACM Comput. Surv. 25, 45–67 (1993)

    Article  Google Scholar 

  3. Herman, T.: A comprehensive bibliography on self-stabilization. A Working Paper in the Chicago Journal of Theoretical Computer Science (2002), http://www.cs.uiowa.edu/ftp/selfstab/bibliography/

  4. Steiner, C.: Bot in the delivery:KIVA systems. Forbes Magazine (2009), http://www.forbes.com/forbes/2009/0316/040_bot_time_saves_nine.html

  5. of Energy, U. (Smart Grid), http://www.oe.energy.gov/smartgrid.htm

  6. Akyildiz, L.F., Su, W., Sankarasubramaniam, Y., Cayirci, E.: A survey on sensor networks. IEEE Communications Magazine 40, 102–114 (2002)

    Article  Google Scholar 

  7. Pelc, A., Peleg, D.: Feasibility and complexity of broadcasting with random transmission failures. Theoretical Computer Science 370, 279–292 (2007)

    Article  MATH  MathSciNet  Google Scholar 

  8. Kar, S., Moura, J.: Distributed average consensus in sensor networks with random link failures. In: Acoustics, Speech and Signal Processing, vol. 2, pp. II–1013–II–1016. IEEE, Los Alamitos (2007)

    Google Scholar 

  9. Nesterenko, M., Arora, A.: Local tolerance to unbounded byzantine faults. In: IEEE SRDS, pp. 22–31 (2002)

    Google Scholar 

  10. Dijkstra, E.W.: Self-stabilizing systems in spite of distributed control. Commun. ACM 17, 643–644 (1974)

    Article  MATH  Google Scholar 

  11. Ghosh, S., Karaata, M.H.: A self-stabilizing algorithm for coloring planar graphs. Distrib. Comput. 7, 55–59 (1993)

    Article  MATH  MathSciNet  Google Scholar 

  12. Hinton, A., Kwiatkowska, M., Norman, G., Parker, D.: PRISM: A tool for automatic verification of probabilistic systems. In: Hermanns, H., Palsberg, J. (eds.) TACAS 2006. LNCS, vol. 3920, pp. 441–444. Springer, Heidelberg (2006)

    Chapter  Google Scholar 

  13. Katoen, J.P., Kemna, T., Zapreev, I., Jansen, D.N.: Bisimulation minimisation mostly speeds up probabilistic model checking. In: Grumberg, O., Huth, M. (eds.) TACAS 2007. LNCS, vol. 4424, pp. 87–101. Springer, Heidelberg (2007)

    Chapter  Google Scholar 

  14. Agha, G., Meseguer, J., Sen, K.: PMaude: Rewrite-based specification language for probabilistic object systems. In: 3rd Workshop on Quantitative Aspects of Programming Languages, QALP 2005 (2005)

    Google Scholar 

  15. Younes, H.: Ymer: A statistical model checker. In: Etessami, K., Rajamani, S.K. (eds.) CAV 2005. LNCS, vol. 3576, pp. 429–433. Springer, Heidelberg (2005)

    Google Scholar 

  16. Hermanns, H.: Interactive Markov Chains: The Quest for Quantified Quality. Springer, Heidelberg (2002)

    Book  MATH  Google Scholar 

  17. Segala, R.: A compositional trace-based semantics for probabilistic automata. In: Lee, I., Smolka, S.A. (eds.) CONCUR 1995. LNCS, vol. 962, pp. 234–248. Springer, Heidelberg (1995)

    Google Scholar 

  18. Wu, S.H., Smolka, S., Stark, E.: Composition and behaviors of probabilistic I/O automata. Theoretical Computer Science 176, 1–38 (1997)

    Article  MATH  MathSciNet  Google Scholar 

  19. de Alfaro, L.: Formal Verification of Probabilistic Systems. PhD thesis, Stanford University, CA, Technical Report STAN-CS-TR-98-1601 (1997)

    Google Scholar 

  20. Canetti, R., Cheung, L., Kaynar, D., Liskov, M., Lynch, N., Pereira, O., Segala, R.: Task-structured Probabilistic I/O Automata. In: Proc. of the 8th Intl. Workshop on Discrete Event Systems – WODES 2006. IEEE catalog number 06EX1259 (2006)

    Google Scholar 

  21. Aziz, A., Sanwal, K., Singhal, V., Brayton, R.: Model-checking continuous-time markov chains. ACM Trans. Comput. Logic 1, 162–170 (2000)

    Article  MathSciNet  Google Scholar 

  22. Young, P.: The evolution of conventions. Econometrica 61, 57–84 (1993)

    Article  MATH  MathSciNet  Google Scholar 

  23. Billingsley, P.: Probability and Measure. John Wiley & Sons, New York (1995)

    MATH  Google Scholar 

  24. Shwartz, A., Weiss, A.: Large deviations for performance analysis. Chapman & Hall, London (1995)

    MATH  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Editor information

Editors and Affiliations

Rights and permissions

Reprints and permissions

Copyright information

© 2009 Springer-Verlag Berlin Heidelberg

About this paper

Cite this paper

Lee DeVille, R.E., Mitra, S. (2009). Stability of Distributed Algorithms in the Face of Incessant Faults. In: Guerraoui, R., Petit, F. (eds) Stabilization, Safety, and Security of Distributed Systems. SSS 2009. Lecture Notes in Computer Science, vol 5873. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-05118-0_16

Download citation

  • DOI: https://doi.org/10.1007/978-3-642-05118-0_16

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-05117-3

  • Online ISBN: 978-3-642-05118-0

  • eBook Packages: Computer ScienceComputer Science (R0)

Publish with us

Policies and ethics