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Computational analysis of single-server bulk-arrival queues: GIX/M/1

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Abstract

This paper deals with numerical computations for the bulk-arrival queueing modelGI X/M/1. First an algorithm is developed to find the roots inside the unit circle of the characteristic equation for this model. These roots are then used to calculate both the moments and the steady-state distribution of the number of customers in the system at a pre-arrival epoch. These results are used to compute the distribution of the same random variable at post-departure and random epochs. Unifying the method used by Easton [7], we have extended its application to the special cases where the interarrival time distribution is deterministic or uniform, and to cases whereX has a given arbitrary distribution. We also improved on the various root-finding methods used by several previous authors so that high values of the parameters, in particular large batch sizes, can be investigated as well.

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References

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Authors and Affiliations

  1. Department of Mathematics and Computer Science, Royal Military College of Canada, K7K 5L0, Kingston, Ontario, Canada

    G. Brière & M. L. Chaudhry

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  1. G. Brière
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  2. M. L. Chaudhry
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Brière, G., Chaudhry, M.L. Computational analysis of single-server bulk-arrival queues: GIX/M/1. Queueing Syst 2, 173–185 (1987). https://doi.org/10.1007/BF01158398

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  • DOI: https://doi.org/10.1007/BF01158398

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