Stochastic comparisons in vacation models

The paper considers 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. Some fairly general conditions are considered, under which the performance of two service policies can be stochastically compared. Under these conditions, stochastic comparisons are established for the departure, queue size and waiting time processes. Using special cases of this result, various well-known service policies are compared. Stochastic monotonicity properties for some classes of parametrizable service policies are also obtained.