A time-dependent busy period queue length formula for the M / E k / 1 queue

Jung Woo Baek; Seung Ki Moon; Ho Woo Lee

doi:10.1016/j.spl.2014.01.004

A time-dependent busy period queue length formula for the M / _{E k} / 1 queue

Jung Woo Baek, Seung Ki Moon, Ho Woo Lee

Department of Industrial and Systems Engineering

Research output: Contribution to journal › Article › peer-review

6 Scopus citations

Abstract

In this paper, a closed-form time-dependent busy period queue length probability is obtained for the M / _{E k} / 1 queue. This probability is frequently needed when we compare the length of the busy period and the maximum amount of service that can be rendered to the existing customers. The transient probability is given in terms of the generalized modified Bessel function of the second type of Griffiths et al. (2006a). The queue length probability for the M / M / 1 queue is also presented as a special case.

Original language	English
Pages (from-to)	98-104
Number of pages	7
Journal	Statistics and Probability Letters
Volume	87
Issue number	1
DOIs	https://doi.org/10.1016/j.spl.2014.01.004
State	Published - Apr 2014

Keywords

Erlang distribution
Markovian queue
Transient analysis

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abstract = "In this paper, a closed-form time-dependent busy period queue length probability is obtained for the M / E k / 1 queue. This probability is frequently needed when we compare the length of the busy period and the maximum amount of service that can be rendered to the existing customers. The transient probability is given in terms of the generalized modified Bessel function of the second type of Griffiths et al. (2006a). The queue length probability for the M / M / 1 queue is also presented as a special case.",

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AB - In this paper, a closed-form time-dependent busy period queue length probability is obtained for the M / E k / 1 queue. This probability is frequently needed when we compare the length of the busy period and the maximum amount of service that can be rendered to the existing customers. The transient probability is given in terms of the generalized modified Bessel function of the second type of Griffiths et al. (2006a). The queue length probability for the M / M / 1 queue is also presented as a special case.

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KW - Markovian queue

KW - Transient analysis

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ER -

A time-dependent busy period queue length formula for the M / _{E k} / 1 queue

Abstract

Keywords

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