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Binary Exponential Backoff Is Stable for High Arrival Rates

  • Hesham Al-Ammal
  • Leslie Ann Goldberg
  • Phil MacKenzie
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 1770)

Abstract

Goodman, Greenberg, Madras and March gave a lower bound of n Ω(log n) for the maximum arrival rate for which the n-user binary exponential backoff protocol is stable. Thus, they showed that the protocol is stable as long as the arrival rate is at most n Ω(log n). We improve the lower bound, showing that the protocol is stable for arrival rates up to O(n −.9).

Keywords

Arrival Rate Bernoulli Trial Multiple Access Channel Average Message Binary Exponential Backoff 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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References

  1. 1.
    D. Aldous, Ultimate instability of exponential back-off protocol for acknowledgement-based transmission control of random access communication channels, IEEE Trans. Inf. Theory IT-33(2) (1987) 219–233.CrossRefMathSciNetGoogle Scholar
  2. 2.
    G. Fayolle, V.A. Malyshev and M.V. Menshikov, Topics in the Constructive Theory of Countable Markov Chains, (Cambridge Univ. Press, 1995)Google Scholar
  3. 3.
    L.A. Goldberg and P.D. MacKenzie, Analysis of practical backoff protocols for contention resolution with multiple servers, Journal of Computer and Systems Sciences, 58 (1999) 232–258.zbMATHCrossRefMathSciNetGoogle Scholar
  4. 4.
    L.A. Goldberg, P.D. MacKenzie, M. Paterson and A. Srinivasan, Contention resolution with constant expected delay, Pre-print (1999) available at http://www.dcs.warwick.ac.uk/~leslie/pub.html. (Extends a paper by the first two authors in Proc. of the Symposium on Foundations of Computer Science (IEEE) 1997 and a paper by the second two authors in Proc. of the Symposium on Foundations of Computer Science (IEEE) 1995.)
  5. 5.
    J. Goodman, A.G. Greenberg, N. Madras and P. March, Stability of binary exponential backoff, J. of the ACM, 35(3) (1988) 579–602.CrossRefMathSciNetGoogle Scholar
  6. 6.
    J. Håstad, T. Leighton and B. Rogoff, Analysis of backoff protocols for multiple access channels, SIAM Journal on Computing 25(4) (1996) 740–774.zbMATHCrossRefMathSciNetGoogle Scholar
  7. 7.
    F.P. Kelly, Stochastic models of computer communication systems, J.R. Statist. Soc. B 47(3) (1985) 379–395.zbMATHGoogle Scholar
  8. 8.
    F.P. Kelly and I.M. MacPhee, The number of packets transmitted by collision detect random access schemes, The Annals of Probability, 15(4) (1987) 1557–1568.zbMATHCrossRefMathSciNetGoogle Scholar
  9. 9.
    R.M. Metcalfe and D.R. Boggs, Ethernet: Distributed packet switching for local computer networks. Commun. ACM, 19 (1976) 395–404.CrossRefGoogle Scholar
  10. 10.
    P. Raghavan and E. Upfal, Contention resolution with bounded delay, Proc. of the ACM Symposium on the Theory of Computing 24 (1995) 229–237.Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2000

Authors and Affiliations

  • Hesham Al-Ammal
    • 1
  • Leslie Ann Goldberg
    • 2
  • Phil MacKenzie
    • 2
  1. 1.Department of Computer ScienceUniversity of WarwickCoventryUK
  2. 2.Information Sciences Center, Bell LaboratoriesLucent TechnologiesMurray Hill

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