Stochastic Comparisons in Vacations Models Tedijanto

Abstract

We consider single-server queueing systems, known as vacation models, where at every service completion the server either serves the next customer from the queue (if any) or takes a vacation (i.e., becomes unavailable to the customers for a random period of time), depending on the service policy employed. We identify some fairly general conditions under which the performance of two service policies can be stochastically compared. Under these conditions, we establish stochastic comparisons for the departure, queue size and waiting time processes. Using special cases of this result, we compare various well-known service policies. We also obtain stochastic monotonicity properties for some classes of parametrizable service policies.