A multi-class multi-server accumulating priority queue with application to health care

We consider the accumulating priority queue (APQ), a priority queue where customer priorities are a function of their waiting time. This time-dependent priority model was first proposed by Kleinrock (1964), and, more recently, Stanford et al. (2013) derived the waiting time distributions for the various priority classes when the queue has a single server. The present work derives expressions for the waiting time distributions for a multi-server APQ with Poisson arrivals for each class, and a common exponential service time distribution. It also comments on how to choose feasible accumulation rates to satisfy specified performance objectives for each class.