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Stochastic analysis of a single server retrial queue with general retrial times

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  • A. Gómez‐Corral

Abstract

Retrial queueing systems are widely used in teletraffic theory and computer and communication networks. Although there has been a rapid growth in the literature on retrial queueing systems, the research on retrial queues with nonexponential retrial times is very limited. This paper is concerned with the analytical treatment of an M/G/1 retrial queue with general retrial times. Our queueing model is different from most single server retrial queueing models in several respectives. First, customers who find the server busy are queued in the orbit in accordance with an FCFS (first‐come‐first‐served) discipline and only the customer at the head of the queue is allowed for access to the server. Besides, a retrial time begins (if applicable) only when the server completes a service rather upon a service attempt failure. We carry out an extensive analysis of the queue, including a necessary and sufficient condition for the system to be stable, the steady state distribution of the server state and the orbit length, the waiting time distribution, the busy period, and other related quantities. Finally, we study the joint distribution of the server state and the orbit length in non‐stationary regime. © 1999 John Wiley & Sons, Inc. Naval Research Logistics 46: 561–581, 1999

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  • A. Gómez‐Corral, 1999. "Stochastic analysis of a single server retrial queue with general retrial times," Naval Research Logistics (NRL), John Wiley & Sons, vol. 46(5), pages 561-581, August.
    • Handle: RePEc:wly:navres:v:46:y:1999:i:5:p:561-581
    DOI: 10.1002/(SICI)1520-6750(199908)46:53.0.CO;2-G
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    References listed on IDEAS

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    1. J. R. Artalejo & G. I. Falin, 1996. "On the orbit characteristics of the M/G/ 1 retrial queue," Naval Research Logistics (NRL), John Wiley & Sons, vol. 43(8), pages 1147-1161, December.
    2. 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.
    3. S. W. Fuhrmann & Robert B. Cooper, 1985. "Stochastic Decompositions in the M / G /1 Queue with Generalized Vacations," Operations Research, INFORMS, vol. 33(5), pages 1117-1129, October.
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