Title: Multi-threshold policy for a multi-server queue with synchronous single vacation
Authors: Wu, Chia-Huang
Ke, Jau-Chuan
Department of Industrial Engineering and Management
Keywords: M/M/c queue;Multiple-threshold;Synchronous single vacation
Issue Date: 1-Mar-2013
Abstract: This paper considers an infinite buffer M/M/c queueing system in which servers follow a multi-threshold vacation policy. With such a policy, at a service completion instant, if the number of customers in the system is less than a prefixed threshold value, part of servers together take a single vacation (or leave for a random amount of time doing other secondary job). At the vacation completion instant, they return to the system for serving the customers. Some practical production and inventory systems or call centers could be modeled as this Markovian queue with a multi-threshold vacation policy. Using the Markovian process model, we obtain the exact closed-form expression of rate matrix and the stationary distribution of the number of customers in the system. A cost model is developed to search the joint optimal values of the thresholds of vacation policy and service rate of each server, which minimizes the long-term average cost. Some numerical results are presented to illustrate the optimization procedures. (C) 2012 Elsevier Ltd. All rights reserved.
URI: http://dx.doi.org/10.1016/j.mcm.2012.10.012
ISSN: 0895-7177
DOI: 10.1016/j.mcm.2012.10.012
Volume: 57
Issue: 5-6
Begin Page: 1122
End Page: 1130
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