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Geo/G/1 retrial queue with 2nd optional service

Author

Listed:
  • Ivan Atencia
  • Pilar Moreno

Abstract

We consider a discrete-time Geo/G/1 retrial queue in which all the arriving customers demand a first essential service whereas only some of them ask for a second optional service. We study the Markov chain underlying the considered queueing system and derive a stochastic decomposition law. We also develop a recursive procedure for computing the distributions of the orbit and system size as well as the marginal distributions of the orbit size when the server is idle and busy with an essential or optional service. Finally, we prove the convergence to the continuous-time counterpart and show some numerical results.

Suggested Citation

  • Ivan Atencia & Pilar Moreno, 2006. "Geo/G/1 retrial queue with 2nd optional service," International Journal of Operational Research, Inderscience Enterprises Ltd, vol. 1(4), pages 340-362.
    • Handle: RePEc:ids:ijores:v:1:y:2006:i:4:p:340-362
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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.

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