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

Mohan Chaudhry and Jing Gai ()
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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

Mathematics, 2022, vol. 10, issue 19, 1-22

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.

Keywords: queues; bulk service; multi-server; Markov chain; quorum (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2022
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