This Is AuburnElectronic Theses and Dissertations

Time Dependent Queuing Systems




Flick, Allen

Type of Degree



Mathematics and Statistics


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.