A Simple Queue with Several Preemptive Priority Classes

Customers of a single server negative exponential queue are divided into R preemptive priority classes. The difference equations for the steady state probabilities are solved by the method of generating functions. The similarity between these and the equations for the Laplace transforms of the temporal probabilities is noted. This enables the Laplace transform of the temporal generating function to be derived in a simple way from the steady state solution. Inverse transformations are carried out in a few particular cases. Explicit results are given only for the special case when all service rates are equal. The general case requires only additional calculation, the method being the same.