Journal of Applied Mathematics and Stochastic Analysis
Volume 10 (1997), Issue 4, Pages 407-421
doi:10.1155/S1048953397000440
The MAP, M/G1,G2/1 queue with preemptive priority
Korea Advanced Institute of Science and Technology, Department of Mathematics and Center for Applied Mathematics, 373-1 Kusuong-Dong, Yusong-Gu, Taejon 305-701, Korea
Received 1 June 1996; Revised 1 December 1996
Copyright © 1997 Bong Dae Choi and Gang Uk Hwang. 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.
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.