International Journal of Stochastic Analysis

International Journal of Stochastic Analysis / 1997 / Article

Open Access

Volume 10 |Article ID 306101 | 15 pages | https://doi.org/10.1155/S1048953397000440

The MAP, M/G1,G2/1 queue with preemptive priority

Received01 Jun 1996
Revised01 Dec 1996

Abstract

We consider the MAP, M/G1,G2/1 queue with preemptive resume priority, where low priority customers arrive to the system according to a Markovian arrival process (MAP) and high priority customers according to a Poisson process. The service time density function of low (respectively: high) priority customers is g1(x) (respectively: g2(x)). We use the supplementary variable method with Extended Laplace Transforms to obtain the joint transform of the number of customers in each priority queue, as well as the remaining service time for the customer in service in the steady state. We also derive the probability generating function for the number of customers of low (respectively, high) priority in the system just after the service completion epochs for customers of low (respectively, high) priority.

Copyright © 1997 Hindawi Publishing Corporation. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


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