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A discrete-time retrial queueing model with one server

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  • Nobel, Rein
  • Moreno, Pilar

Abstract

This paper presents a one-server queueing model with retrials in discrete-time. The number of primary jobs arriving in a time slot follows a general probability distribution and the different numbers of primary arrivals in consecutive time slots are mutually independent. Each job requires from the server a generally distributed number of slots for its service, and the service times of the different jobs are independent. Jobs arriving in a slot can start their service only at the beginning of the next slot. When upon arrival jobs find the server busy all incoming jobs are sent into orbit. When upon arrival in a slot jobs find the server idle, then one of the incoming jobs (randomly chosen) in that slot starts its service at the beginning of the next slot, whereas the other incoming jobs in that slot, if any, are sent into orbit. During each slot jobs in the orbit try to re-enter the system individually, independent of each other, with a given retrial probability. The ergodicity condition and the generating function of the joint equilibrium distribution of the number of jobs in orbit and the residual service time of the job in service are calculated. From the generating function several performance measures are deduced, like the average orbit size. Also the busy period and the number of jobs served during a busy period are discussed. To conclude, extensive numerical results are presented.

Suggested Citation

  • Nobel, Rein & Moreno, Pilar, 2008. "A discrete-time retrial queueing model with one server," European Journal of Operational Research, Elsevier, vol. 189(3), pages 1088-1103, September.
    • Handle: RePEc:eee:ejores:v:189:y:2008:i:3:p:1088-1103
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    References listed on IDEAS

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    1. I. Atencia & P. Moreno, 2006. "A Discrete-Time Geo/ G/1 retrial queue with the server subject to starting failures," Annals of Operations Research, Springer, vol. 141(1), pages 85-107, January.
    2. Li, Hui & Yang, Tao, 1998. "Geo/G/1 discrete time retrial queue with Bernoulli schedule," European Journal of Operational Research, Elsevier, vol. 111(3), pages 629-649, December.
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    Cited by:

    1. Rein Nobel, 2016. "Retrial queueing models in discrete time: a short survey of some late arrival models," Annals of Operations Research, Springer, vol. 247(1), pages 37-63, December.
    2. Atencia, I., 2017. "A Geo/G/1 retrial queueing system with priority services," European Journal of Operational Research, Elsevier, vol. 256(1), pages 178-186.

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