Approximation to the Transient Solution of the M/Ek/1 Queue

Griffiths, Jeffrey Deacon, Leonenko, Ganna M. ORCID: https://orcid.org/0000-0001-8025-661X and Williams, Janet Elizabeth 2008. Approximation to the Transient Solution of the M/Ek/1 Queue. INFORMS Journal on Computing 20 (4) , pp. 510-515. 10.1287/ijoc.1070.0262

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Abstract

This paper considers the Erlang queueing system M/Ek/1, where customers arrive at random at mean rate λ and the service times have an Erlang distribution with parameter k and mean service rate μ. It is difficult to obtain a transient solution in explicit form to the queue equations because of their complex structure. We propose a simple method of computing Wq(t)—the mean waiting time of a customer arriving in the queue at time t, based on an exponential function approximation.

Item Type:	Article
Date Type:	Publication
Status:	Published
Schools:	Mathematics Medicine MRC Centre for Neuropsychiatric Genetics and Genomics (CNGG)
Subjects:	Q Science > QA Mathematics
Uncontrolled Keywords:	queues; approximations; numerical methods
Publisher:	INFORMS
ISSN:	1091-9856
Last Modified:	07 Feb 2023 16:22
URI:	https://orca.cardiff.ac.uk/id/eprint/32974

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