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Some Theorems on Instability with Applications to Multiaccess Protocols

Author

Listed:
  • Wojciech Szpankowski

    (Purdue University, West Lafayette, Indiana)

  • Vernon Rego

    (Purdue University, West Lafayette, Indiana)

Abstract

An important question in stochastic modeling is whether a denumerable state Markov chain describing a system is stable or not. Adopting a general definition of stability, we discuss some conditions for instability. We extend slightly previous results on nonergodicity, and we present new criteria for moments of a chain to be infinite. Finally, we apply these instability conditions to study some multidimensional Markov chains that describe multiaccess protocols in a broadcast environment. In particular, we prove that the exponential backoff algorithm is unstable for λ > 0.461, and the decentralized dynamic control algorithm is unstable for λ > e −1 = 0.368.

Suggested Citation

  • Wojciech Szpankowski & Vernon Rego, 1988. "Some Theorems on Instability with Applications to Multiaccess Protocols," Operations Research, INFORMS, vol. 36(6), pages 958-966, December.
    • Handle: RePEc:inm:oropre:v:36:y:1988:i:6:p:958-966
    DOI: 10.1287/opre.36.6.958
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