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Conditions for stability and instability of retrial queueing systems with general retrial times

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  • Kernane, Tewfik

Abstract

We study the stability of single server retrial queues under general distribution for retrial times and stationary ergodic service times, for three main retrial policies studied in the literature: classical, constant and control policies. The approach used is the renovating events approach to obtain sufficient stability conditions by strong coupling convergence of the process modeling the dynamics of the system to a unique stationary ergodic regime. We also obtain instability conditions by convergence in distribution to improper limiting sequences.

Suggested Citation

  • Kernane, Tewfik, 2008. "Conditions for stability and instability of retrial queueing systems with general retrial times," Statistics & Probability Letters, Elsevier, vol. 78(18), pages 3244-3248, December.
    • Handle: RePEc:eee:stapro:v:78:y:2008:i:18:p:3244-3248
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    1. Yang, T. & Posner, M. J. M. & Templeton, J. G. C. & Li, H., 1994. "An approximation method for the M/G/1 retrial queue with general retrial times," European Journal of Operational Research, Elsevier, vol. 76(3), pages 552-562, August.
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    Cited by:

    1. Dieter Fiems, 2022. "Retrial queues with generally distributed retrial times," Queueing Systems: Theory and Applications, Springer, vol. 100(3), pages 189-191, April.
    2. Dieter Fiems, 2023. "Retrial queues with constant retrial times," Queueing Systems: Theory and Applications, Springer, vol. 103(3), pages 347-365, April.

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