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 serv...Show MoreMetadata
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 queueing system can be modelled 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 modelled into a QBD process where the block elements of the generator matrix have finite dimensions. Sojourn time distributions of both high and low priority customers are obtained.
Published in: 2015 Winter Simulation Conference (WSC)
Date of Conference: 06-09 December 2015
Date Added to IEEE Xplore: 18 February 2016
ISBN Information:
Electronic ISSN: 1558-4305