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

Bong Dae Choi and Gang Uk Hwang

 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

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.