Delay performance in stochastic processing networks with priority service

We evaluate the delay performance of an open multi-class stochastic processing network of multiserver resources with preemptive-resume priority service. We show that the stationary distribution of aggregate queue lengths has product form. For each service class we derive explicit expressions for the following stationary perfomance measures: The mean and, under feedforwarding routing, the Laplace transform of the delay distribution at each resource. We show that these measures are the same as if the resources were operating in isolation.