Analysis of a MAP/PH/1 Queue with Discretionary Priority Based on Service Stages

Ning Zhao (), Zhaotong Lian () and Kan Wu
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Ning Zhao: Faculty of Science, Kunming University of Science and Technology, Kunming, Yunnan, P. R. China
Zhaotong Lian: Faculty of Business Administration, University of Macau, Macau, P. R. China
Kan Wu: School of Mechanical and Aerospace Engineering, Nanyang Technological University, Singapore

Asia-Pacific Journal of Operational Research (APJOR), 2015, vol. 32, issue 06, 1-22

Abstract: In this paper, we study a MAP/PH/1 queue with two classes of customers and discretionary priority. There are two stages of service for the low-priority customer. The server adopts the preemptive priority discipline at the first stage and adopts the nonpreemptive priority discipline at the second stage. Such a queuing system can be modeled into a quasi-birth-and-death (QBD) process. But there is no general solution for this QBD process since the generator matrix has a block structure with an infinite number of blocks and each block has infinite dimensions. We present an approach to derive the bound for the high-priority queue length. It guarantees that the probabilities of ignored states are within a given error bound, so that the system can be modeled into a QBD process where the block elements of the generator matrix have finite dimensions. The sojourn time distributions of both high and low priority customers are obtained. Some managerial insights are given after comparing the discretionary priority rule with the preemptive and nonpreemptive disciplines numerically.

Keywords: Priority; discretionary; queuing system; sojourn time; matrix-geometric method (search for similar items in EconPapers)
Date: 2015
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DOI: 10.1142/S0217595915500426

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