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Stationary analysis of a single server retrial queue with priority and vacation

Author

Listed:
  • D. Arivudainambi
  • I. Averbakh
  • O. Berman

Abstract

We study a single server retrial queue with Bernoulli vacations and a priority queue. A customer who finds the server busy upon arrival, either joins the priority queue with probability α, or leaves the service area and enters a retrial group (orbit) with probability α-bar (= 1 − α). Using the supplementary variable technique, we find the joint probability generating function of the number of customers in the priority queue and of the number of customers in the retrial group in a closed form. Also, we find explicit expressions for the mean queue length and the mean waiting time for both queues, and derive steady-state performance measures for the system. We show that the general stochastic decomposition law for M/G/1 vacation models holds for our system too. Some special cases and numerical results are also discussed.

Suggested Citation

  • D. Arivudainambi & I. Averbakh & O. Berman, 2009. "Stationary analysis of a single server retrial queue with priority and vacation," International Journal of Operational Research, Inderscience Enterprises Ltd, vol. 5(1), pages 26-47.
  • Handle: RePEc:ids:ijores:v:5:y:2009:i:1:p:26-47
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    Cited by:

    1. Seyed Khodadadi & Fariborz Jolai, 2012. "A fuzzy based threshold policy for a single server retrial queue with vacations," Central European Journal of Operations Research, Springer;Slovak Society for Operations Research;Hungarian Operational Research Society;Czech Society for Operations Research;Österr. Gesellschaft für Operations Research (ÖGOR);Slovenian Society Informatika - Section for Operational Research;Croatian Operational Research Society, vol. 20(2), pages 281-297, June.

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