The MAP,M/G1,G2/1 Queue with Preemptive Priority

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 gl(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.