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Analytic and Computational Analysis of GI/M a , b / c Queueing System

Author

Listed:
  • Mohan Chaudhry

    (Department of Mathematics and Computer Science, Royal Military College of Canada, Kingston, ON K7K 7B4, Canada)

  • Jing Gai

    (Department of Mathematics and Computer Science, Royal Military College of Canada, Kingston, ON K7K 7B4, Canada)

Abstract

Bulk-service queueing systems have been widely applied in many areas in real life. While single-server queueing systems work in some cases, multi-servers can efficiently handle most complex applications. Bulk-service, multi-server queueing systems (compared to well-developed single-server queueing systems) are more complex and harder to deal with, especially when the inter-arrival time distributions are arbitrary. This paper deals with analytic and computational analyses of queue-length distributions for a complex bulk-service, multi-server queueing system GI/M a , b / c , wherein inter-arrival times follow an arbitrary distribution, a is the quorum, and b is the capacity of each server; service times follow exponential distributions. The introduction of quorum a further increases the complexity of the model. In view of this, a two-dimensional Markov chain has to be involved. Currently, it appears that this system has not been addressed so far. An elegant analytic closed-form solution and an efficient algorithm to obtain the queue-length distributions at three different epochs, i.e., pre-arrival epoch (p.a.e.), random epoch (r.e.), and post-departure epoch (p.d.e.) are presented, when the servers are in busy and idle states, respectively.

Suggested Citation

  • Mohan Chaudhry & Jing Gai, 2022. "Analytic and Computational Analysis of GI/M a , b / c Queueing System," Mathematics, MDPI, vol. 10(19), pages 1-22, September.
    • Handle: RePEc:gam:jmathe:v:10:y:2022:i:19:p:3445-:d:921880
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    References listed on IDEAS

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    1. Sim, S. H. & Templeton, J. G. C., 1985. "Steady state results for the M/M(a, b)/c batch-service system," European Journal of Operational Research, Elsevier, vol. 21(2), pages 260-267, August.
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