Invariance in resource sharing problems

Several processes or users share a common resource. Each process is described by a two state Markov chain with a "thinking" state and a service "request" state. The problem is to select a preemptive priority scheme to assign the resource among simultaneously requesting processes so as to maximize resource utilization. When the average thinking times of the processes are the same, the utilization is invariant under the assignment schemes. The invariance result extends to certain hitting time distributions for a broader class of Markov chains.