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Stability Conditions for Multidimensional Queueing Systems with Computer Applications

Author

Listed:
  • Wojciech Szpankowski

    (Purdue University, West Lafayette, Indiana)

Abstract

A fundamental question arising in the analysis of queueing systems is whether a system is stable or unstable. For systems modeled by infinite Markov chains, we may study the ergodicity and nonergodicity of the chains. Foster showed that sufficient conditions for ergodicity are linked with the average drift. However, complications arise when multidimensional Markov chains are analyzed. We present three methods that provide sufficient conditions for ergodicity and nonergodicity of a multidimensional Markov chain. These methods are next applied to two multidimensional queueing systems: buffered contention packet broadcast systems and coupled processor systems.

Suggested Citation

  • Wojciech Szpankowski, 1988. "Stability Conditions for Multidimensional Queueing Systems with Computer Applications," Operations Research, INFORMS, vol. 36(6), pages 944-957, December.
    • Handle: RePEc:inm:oropre:v:36:y:1988:i:6:p:944-957
    DOI: 10.1287/opre.36.6.944
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    Cited by:

    1. Adan, Ivo & Foss, Sergey & Shneer, Seva & Weiss, Gideon, 2020. "Local stability in a transient Markov chain," Statistics & Probability Letters, Elsevier, vol. 165(C).
    2. M. Saxena & I. Dimitriou & S. Kapodistria, 2020. "Analysis of the shortest relay queue policy in a cooperative random access network with collisions," Queueing Systems: Theory and Applications, Springer, vol. 94(1), pages 39-75, February.

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