Preemptive Resume Priority Queue

The queue length probability generating function for a preemptive resume priority queue characterized by Poisson arrivals and general service time distributions has been obtained by using the “supplemetary vanable method”. The preempted item follows the “resume” rule so that upon re-entry the service on the nonpriority unit is started at the point where it was interrupted when preemption occurred. Apart from the steady-state solution, the Laplace transform of the time dependent probability generating function and the length of busy periods has also been obtained.