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.