Time-Varying Queues

Service systems abound with queues, but the most natural direct models are often timevarying queues, which require nonstandard analysis methods beyond stochastic textbooks. This paper surveys the literature on time-varying queues. Most of the literature concerns manyserver queues, which arise in large-scale service systems, such as in customer contact centers and hospital emergency departments, but there also has been some work on single-server queues with time-varying arrivals, which arise in some settings, such as airplanes coming to land at an airport 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 recently been extended to time-varying models as well as stationary models.