Time-Varying Queues

Abstract

Service systems abound with queues, but the most natural direct models are often time-varying queues, which may require nonstandard analysis methods beyond stochastic textbooks. This paper provides an overview of time-varying queues. Most of the recent literature concerns many-server queues, which arise in large-scale service systems, such as in customer contact centers and hospital emergency departments, but there also has been some new work on single-server queues with time-varying arrivals, which arise in some settings, such as airplanes coming to land at an airport, cars coming to a traffic intersection and medical staff waiting for the availability of special operating rooms in a hospital. The understanding of many-server queues and single-server queues is enhanced by heavy-traffic limits, which have been extended to time-varying models as well as stationary models.