A Markov-modulated M/G/1 queue I: Stationary distribution

C. Knessl; B. J. Matkowsky; Z. Schuss; C. Tier

doi:10.1007/BF01150670

A Markov-modulated M/G/1 queue I: Stationary distribution

C. Knessl^*, B. J. Matkowsky, Z. Schuss, C. Tier

^*Corresponding author for this work

School of Mathematical Sciences

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

17 Scopus citations

Abstract

We consider an M/G/1 queueing system in which the arrival rate and service time density are functions of a two-state stochastic process. We describe the system by the total unfinished work present and allow the arrival and service rate processes to depend on the current value of the unfinished work. We employ singular perturbation methods to compute asymptotic approximations to the stationary distribution of unfinished work and in particular, compute the stationary probability of an empty queue.

Original language	English
Pages (from-to)	355-374
Number of pages	20
Journal	Queueing Systems
Volume	1
Issue number	4
DOIs	https://doi.org/10.1007/BF01150670
State	Published - May 1987

Keywords

Markov modulated queues
State dependent M/G/1 queue
singular perturbations

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10.1007/BF01150670

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abstract = "We consider an M/G/1 queueing system in which the arrival rate and service time density are functions of a two-state stochastic process. We describe the system by the total unfinished work present and allow the arrival and service rate processes to depend on the current value of the unfinished work. We employ singular perturbation methods to compute asymptotic approximations to the stationary distribution of unfinished work and in particular, compute the stationary probability of an empty queue.",

keywords = "Markov modulated queues, State dependent M/G/1 queue, singular perturbations",

author = "C. Knessl and Matkowsky, {B. J.} and Z. Schuss and C. Tier",

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AU - Tier, C.

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N2 - We consider an M/G/1 queueing system in which the arrival rate and service time density are functions of a two-state stochastic process. We describe the system by the total unfinished work present and allow the arrival and service rate processes to depend on the current value of the unfinished work. We employ singular perturbation methods to compute asymptotic approximations to the stationary distribution of unfinished work and in particular, compute the stationary probability of an empty queue.

AB - We consider an M/G/1 queueing system in which the arrival rate and service time density are functions of a two-state stochastic process. We describe the system by the total unfinished work present and allow the arrival and service rate processes to depend on the current value of the unfinished work. We employ singular perturbation methods to compute asymptotic approximations to the stationary distribution of unfinished work and in particular, compute the stationary probability of an empty queue.

KW - Markov modulated queues

KW - State dependent M/G/1 queue

KW - singular perturbations

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A Markov-modulated M/G/1 queue I: Stationary distribution

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Keywords

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