Time Dependent Queuing Systems
Type of DegreeThesis
DepartmentMathematics and Statistics
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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.