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A modified vacation model M[x]/G/1 system

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  • Jau‐Chuan Ke
  • Yunn‐Kuang Chu

Abstract

This paper studies the operating characteristics of an M[x]/G/1 queueing system under a modified vacation policy, where the server leaves for a vacation as soon as the system is empty. The server takes at most J vacations repeatedly until at least one customer is found waiting in the queue when the server returns from a vacation. We derive the system size distribution at different points in time, as well as the waiting time distribution in the queue. Further, we derive some important characteristics including the expected length of the busy period and idle period. This shows that the results generalize those of the multiple vacation policy and the single vacation policy M[x]/G/1 queueing system. Finally, a cost model is developed to determine the optimum of J at a minimum cost. Copyright © 2006 John Wiley & Sons, Ltd.

Suggested Citation

  • Jau‐Chuan Ke & Yunn‐Kuang Chu, 2006. "A modified vacation model M[x]/G/1 system," Applied Stochastic Models in Business and Industry, John Wiley & Sons, vol. 22(1), pages 1-16, January.
    • Handle: RePEc:wly:apsmbi:v:22:y:2006:i:1:p:1-16
    DOI: 10.1002/asmb.607
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