Time Dependent Queuing Systems

Abstract

Using elementary probability theory, we establish limiting probabilities for the queue length of a queuing system whose arrivals follow a nonhomogeneous Poisson process and are served by a single server whose services also follow a nonhomogeneous Poisson process. We uniformly accelerate the process and conclude, under a special stability condition, that the queue length distribution is the same as a queue with constant rates. Extensions are provided for queues with multiple homogeneous servers and those with a nite capacity. Also included is a simulation of such a queuing system using the data from an Auburn University web server to model the arrival process.