Busy period analysis of the state dependent M/M/1/K queue

Ahmad Al Hanbali; Onno Boxma

doi:10.1016/j.orl.2009.09.012

Busy period analysis of the state dependent M/M/1/K queue

Ahmad Al Hanbali^*, Onno Boxma

^*Corresponding author for this work

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

13 Scopus citations

Abstract

In this paper, we study the transient behavior of a state dependent M/M/1/K queue during the busy period. We derive in closed-form the joint transform of the length of the busy period, the number of customers served during the busy period, and the number of losses during the busy period. For two special cases called the threshold policy and the static policy we determine simple expressions for their joint transform.

Original language	English
Pages (from-to)	1-6
Number of pages	6
Journal	Operations Research Letters
Volume	38
Issue number	1
DOIs	https://doi.org/10.1016/j.orl.2009.09.012
State	Published - Jan 2010
Externally published	Yes

Keywords

Absorbing Markov chains
Busy period
Level dependent
M/M/1/K queue
Performance metrics

ASJC Scopus subject areas

Software
Management Science and Operations Research
Industrial and Manufacturing Engineering
Applied Mathematics

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10.1016/j.orl.2009.09.012

Cite this

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abstract = "In this paper, we study the transient behavior of a state dependent M/M/1/K queue during the busy period. We derive in closed-form the joint transform of the length of the busy period, the number of customers served during the busy period, and the number of losses during the busy period. For two special cases called the threshold policy and the static policy we determine simple expressions for their joint transform.",

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KW - Performance metrics

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Busy period analysis of the state dependent M/M/1/K queue

Abstract

Keywords

ASJC Scopus subject areas

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