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Ergodicity of one-dimensional resource sharing systems

Author

Listed:
  • Andjel, Enrique
  • López, F. Javier
  • Sanz, Gerardo

Abstract

We study one-dimensional resource sharing systems which can be seen as interacting particle systems taking values in . We first get, by coupling techniques, an estimate of their invariant measures. Then, for processes having a reversible measure, we show the uniqueness of the invariant measure and conclude that they are ergodic. As a consequence, we prove that every loss network on with calls of bounded length is ergodic.

Suggested Citation

  • Andjel, Enrique & López, F. Javier & Sanz, Gerardo, 2002. "Ergodicity of one-dimensional resource sharing systems," Stochastic Processes and their Applications, Elsevier, vol. 98(1), pages 1-22, March.
    • Handle: RePEc:eee:spapps:v:98:y:2002:i:1:p:1-22
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    References listed on IDEAS

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    1. Graham, Carl & Méléard, Sylvie, 1994. "Fluctuations for a fully connected loss network with alternate routing," Stochastic Processes and their Applications, Elsevier, vol. 53(1), pages 97-115, September.
    2. Satoru Fujishige & Naoki Katoh & Tetsuo Ichimori, 1988. "The Fair Resource Allocation Problem with Submodular Constraints," Mathematics of Operations Research, INFORMS, vol. 13(1), pages 164-173, February.
    3. Hunt, P. J. & Kurtz, T. G., 1994. "Large loss networks," Stochastic Processes and their Applications, Elsevier, vol. 53(2), pages 363-378, October.
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