Technical Report CS0536

Title: Ergodicity of Queueing Networks With Several Customer Classes and Arbitrary Work-Conserving Scheduling
Authors: Zvi Rosberg
Abstract: We consider a network of service stations with different classes of customers where interarrival times and service requirments have phase-type distributions, and the service discipline is an arbitrary work-conserving policy. We show that the underlying Markov process is ergodic, if and only if the utilization at each service station is less than one. We also show, that all the moments of the queue lengths under-the stationary distribution, are finite.
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