Exact waiting time and queue size distributions for equilibrium M/G/1 queues with Pareto service |
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| Authors: | Colin M. Ramsay |
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| Affiliation: | (1) Department of Finance, University of Nebraska-Lincoln, Lincoln, NE 68588-0426, USA |
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| Abstract: | This paper solves the problem of finding exact formulas for the waiting time cdf and queue length distribution of first-in-first-out M/G/1 queues in equilibrium with Pareto service. The formulas derived are new and are obtained by directly inverting the relevant Pollaczek-Khinchin formula and involve single integrals of non-oscillating real valued functions along the positive real line. Tables of waiting time and queue length probabilities are provided for certain parameter values under heavy traffic conditions. |
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| Keywords: | Laplace transform Kummer function Generalized exponential integral Steady-state queue Pollaczek-Khinchin formula Power-tail Heavy-tail Heavy traffic |
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