Invariance of Stationary Distribution of States of Multimode Service Policy Networks

We consider open and closed preemptive-resume queueing systems with absolute priority of incoming customers. Single-server nodes have several service modes (regimes); the time of switching between the modes is exponential. Switching can be made to adjacent modes only. The amount of work required for servicing an incoming customer (workload) is a random variable with an arbitrary distribution function. For an open network, the input flow is Poissonian. We prove that the stationary distribution of the network states is invariant with respect to a functional form of workload distributions if the first moments are fixed.