A stochastic monotonicity result for cyclic service systems with limited service discipline

Motivated by the need to understand the behavior of polling schemes used in communication networks, an examination is made of the behavior of a limited service discipline in cyclic service systems with respect to the workload process of the system. The workload process represents the amount of work in the system at any given instant and is the basis for many important systemwide performance measures. It is shown that when there are positive walk times, the workload process is minimized by choosing the maximum allowable number of customers to be served per visit to be as large as possible. The result is proved using sample path comparison arguments and holds under general assumptions about the interval, service, and walk-time distributions