Title: The randomized vacation policy for a batch arrival queue
Authors: Ke, Jau-Chuan
Huang, Kai-Bin
Pearn, Wen Lea
Department of Industrial Engineering and Management
Keywords: Cost;Randomized control;Supplementary variable technique;Batch arrival vacation queue
Issue Date: 1-Jun-2010
Abstract: This paper examines an M([x])/G/1 queueing system with a randomized vacation policy and at most J vacations. Whenever the system is empty, the server immediately takes a vacation. If there is at least one customer found waiting in the queue upon returning from a vacation, the server will be immediately activated for service. Otherwise, if no customers are waiting for service at the end of a vacation, the server either remains idle with probability p or leaves for another vacation with probability 1 - p. This pattern continues until the number of vacations taken reaches J. If the system is empty by the end of the Jth vacation, the server is dormant idly in the system. If there is one or more customers arrive at server idle state, the server immediately starts his services for the arrivals. For such a system, we derive the distributions of important characteristics, such as system size distribution at a random epoch and at a departure epoch, system size distribution at busy period initiation epoch, idle period and busy period, etc. Finally, a cost model is developed to determine the joint suitable parameters (p*, J*) at a minimum cost, and some numerical examples are presented for illustrative purpose. (C) 2009 Elsevier Inc. All rights reserved.
URI: http://dx.doi.org/10.1016/j.apm.2009.09.007
ISSN: 0307-904X
DOI: 10.1016/j.apm.2009.09.007
Volume: 34
Issue: 6
Begin Page: 1524
End Page: 1538
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