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A maximum entropy priority approximation for a stableG/G/1 queue

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Summary

The principle of maximum entropy is used under two different sets of mean value constraints to analyse a stableG/G/1 queue withR priority classes under preemptive-resume (PR) and non-preemptive head-of-line (HOL) scheduling disciplines. New one-step recursions for the maximum entropy state probabilities are established and closed form approximations for the marginal queue length distribution per priority class are derived. To expedite the utility of the maximum entropy solutions exact analysis, based on the generalised exponential (GE) distribution, is used to approximate the marginal mean queue length and idle state probability class constraints for both the PR and HOLG/G/1 priority queues. Moreover, these results are used as building blocks in order to provide new approximate formulae for the mean and coefficient of variation of the effective priority service-time and suggest a maximum entropy algorithm for general open queueing networks with priorities in the context of the reduced occupancy approximation (ROA) method. Numerical examples illustrate the accuracy of the proposed maximum entropy approximations in relation to simulations involving different interarrival-time and service-time distributions per class. Comments on the extension of the work to more complex types of queueing systems are included.

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Author information

Correspondence to Demetres Kouvatsos.

Additional information

This work is sponsored in part by the Science and Engineering Research Council (SERC), UK, under grant GR/D/12422 and in part by the Ministry of Higher Education of the Algerian Government

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Kouvatsos, D., Tabet-Aouel, N. A maximum entropy priority approximation for a stableG/G/1 queue. Acta Informatica 27, 247–286 (1989). https://doi.org/10.1007/BF00572990

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Keywords

  • Maximum Entropy
  • Queue Length
  • Priority Queue
  • Entropy Solution
  • Priority Class