Cost Models for Stochastic Clearing Systems

Stochastic clearing systems are characterized by a stochastic input process and an output mechanism that intermittently clears the system, i.e., instantaneously restores the net quantity in the system to zero. Asymptotic properties of such systems can be derived under weak probabilistic assumptions, the essential requirement being that limiting behavior can be determined by “averaging over a cycle,” as is the case, for example, with regenerative processes. In this paper we consider the problem of finding the optimal level, q, at which to clear when there are fixed clearing and variable holding costs. We also study a generalization of a clearing system in which the clearing operation restores the net quantity to a level m, which may be different from zero. Applications to bulk-service queues, demand-responsive public-service systems, and (s, S) inventory systems, among others, are discussed. The exact solutions that we obtain for the optimal clearing parameters are compared to those implied by deterministic approximations.