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Probabilistic Decomposition Method on the ServerIndices of an /G/1 Vacation Queue

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  • Renbin Liu

Abstract

This paper develops a probabilistic decomposition method for an /G/1 repairable queueing system with multiple vacations, in which the customers who arrive during server vacations enter the system with probability p . Such a novel method is used to analyze the main performance indices of the server, such as the unavailability and the mean failure number during . It is derived that the structures of server indices are two convolution equations. Further, comparisons with existing methods indicate that our method is effective and applicable for studying server performances in single-server /G/1 vacation queues and their complex variants. Finally, a stochastic order and production system with a multipurpose production facility is numerically presented for illustrative purpose.

Suggested Citation

  • Renbin Liu, 2014. "Probabilistic Decomposition Method on the ServerIndices of an /G/1 Vacation Queue," Journal of Applied Mathematics, Hindawi, vol. 2014, pages 1-9, January.
    • Handle: RePEc:hin:jnljam:241636
    DOI: 10.1155/2014/241636
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    Cited by:

    1. Tom van Woensel & Frederico R B Cruz, 2014. "Optimal Routing in General Finite Multi-Server Queueing Networks," PLOS ONE, Public Library of Science, vol. 9(7), pages 1-15, July.

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