An Eigenvalue Approach to Analyzing a Finite Source Priority Queueing Model |
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Authors: | Steve Drekic Winfried K Grassmann |
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Institution: | (1) Department of Statistics and Actuarial Science, University of Waterloo, Waterloo, Ontario, Canada, N2L 3G1;(2) Department of Computer Science, University of Saskatchewan, Saskatoon, Saskatchewan, Canada, S7N 5A9 |
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Abstract: | In this paper, we present a novel approach to determining the steady-state distribution for the number of jobs present in a 2-class, single server preemptive priority queueing model where the low priority source population is finite. Arrivals are assumed to be Poisson with exponential service times. The system investigated is a quasi birth and death process, and the joint distribution is derived via the method of generalized eigenvalues. Using this approach, we are able to obtain all eigenvalues and corresponding eigenvectors explicitly. Furthermore, we link this method to the matrix analytic approach by obtaining an explicit solution for the rate matrix R. Two numerical examples are given to illustrate the procedure and highlight some important computational features. |
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Keywords: | priority queues generalized eigenvalues quasi-birth-and-death process matrix analytic methods |
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