On the work load process in a general preemptive resume priority queue

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Abstract
Consider the following queuing system: A sequence of customers arrive at a service unit in a recurrent stream. A customer is of priority k with probability πk , k = 1, …, n. A class i customer preempts service of class k, k > i. Interrupted service is resumed without loss or gain in service time. Service is FIFO within classes. Service times for class k are drawn from a general distribution function Bk (t). Using the method of phases and a resolution technique from the theory of Markov processes we obtain Laplace transforms of various distributions.

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