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A maximum entropy analysis of the M/G/1 and G/M/1 queueing systems at equilibrium

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Summary

The M/G/1 and G/M/1 queueing models are of great interest in the performance analysis of computer systems. For both models, the equilibrium solution for the number of jobs in the system varies with the probability distribution function representing the general (G-type) distribution. Even in the presence of empirical data, the characterisation of this function involves a degree of arbitrariness that may cause some variation in the performance metrics.

In this paper maximum entropy formalism is used to analyse the M/G/1- and G/M/1-queueing systems at equilibrium. A unique product form solution for the number of jobs in the M/G/1 system is derived and the corresponding service time distribution is determined. This solution is also presented as a limit of a sequence of maximum entropy solutions to two-stage M/G/1 systems. Furthermore, the maximum entropy solution to the G/M/1 queueing system is established and favourable comparisons with the method of stages and the diffusion approximation are made. It is also shown that the maximum entropy M/G/1- and G/M/1-systems satisfy local balance. Comments on the results so far obtained and their implications to the analysis of general queueing systems are included.

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Authors and Affiliations

  1. University of Bradford, BD 7 1DP, Bradford, West Yorkshire, UK

    M. A. El-Affendi & D. D. Kouvatsos

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  1. M. A. El-Affendi
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  2. D. D. Kouvatsos
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El-Affendi, M.A., Kouvatsos, D.D. A maximum entropy analysis of the M/G/1 and G/M/1 queueing systems at equilibrium. Acta Informatica 19, 339–355 (1983). https://doi.org/10.1007/BF00290731

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