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The queueing system MX/G/1 and its ramifications

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  • M. L. Chaudhry

Abstract

This paper deals with the bulk arrival queueing system MX/G/1 and its ramifications. In the system MX/G/1, customers arrive in groups of size X (a random variable) by a Poisson process, the service times distribution is general, and there is a single server. Although some results for this queueing system have appeared in various books, no unified account of these, as is being presented here, appears to have been reported so far. The chief objectives of the paper are (i) to unify by an elegant procedure the relationships between the p.g.f.'s where Pn and Pn+ are the limiting probabilities of queue lengths being n at random and departure epochs respectively, (ii) to correct an error in the paper by Krakowski and generalize his results and (iii) to discuss some other interesting cases of the system MX/G/1 and its special cases.

Suggested Citation

  • M. L. Chaudhry, 1979. "The queueing system MX/G/1 and its ramifications," Naval Research Logistics Quarterly, John Wiley & Sons, vol. 26(4), pages 667-674, December.
    • Handle: RePEc:wly:navlog:v:26:y:1979:i:4:p:667-674
    DOI: 10.1002/nav.3800260411
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