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Exact waiting time and queue size distributions for equilibrium M/G/1 queues with Pareto service

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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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  1. Department of Finance, University of Nebraska-Lincoln, Lincoln, NE, 68588-0426, USA

    Colin M. Ramsay

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  1. Colin M. Ramsay
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Correspondence to Colin M. Ramsay.

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Ramsay, C.M. Exact waiting time and queue size distributions for equilibrium M/G/1 queues with Pareto service. Queueing Syst 57, 147–155 (2007). https://doi.org/10.1007/s11134-007-9052-7

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  • DOI: https://doi.org/10.1007/s11134-007-9052-7

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