A Markov-modulated M/G/1 queue II: Busy period and time for buffer overflow

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

doi:10.1007/BF01150671

A Markov-modulated M/G/1 queue II: Busy period and time for buffer overflow

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

^*Corresponding author for this work

Engineering Sciences and Applied Mathematics

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

6 Scopus citations

Abstract

We consider an M/G/1 queue where the arrival and service processes are modulated by a two state Markov chain. We assume that the arrival rate, service time density and the rates at which the Markov chain switches its state, are functions of the total unfinished work (buffer content) in the queue. We compute asymptotic approximations to performance measures such as the mean residual busy period, mean length of a busy period, and the mean time to reach capacity.

Original language	English (US)
Pages (from-to)	375-399
Number of pages	25
Journal	Queueing Systems
Volume	1
Issue number	4
DOIs	https://doi.org/10.1007/BF01150671
State	Published - May 1 1987

Keywords

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

ASJC Scopus subject areas

Statistics and Probability
Computer Science Applications
Management Science and Operations Research
Computational Theory and Mathematics

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10.1007/BF01150671

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abstract = "We consider an M/G/1 queue where the arrival and service processes are modulated by a two state Markov chain. We assume that the arrival rate, service time density and the rates at which the Markov chain switches its state, are functions of the total unfinished work (buffer content) in the queue. We compute asymptotic approximations to performance measures such as the mean residual busy period, mean length of a busy period, and the mean time to reach capacity.",

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

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

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AU - Knessl, C.

AU - Matkowsky, Bernard J

AU - Schuss, Z.

AU - Tier, C.

PY - 1987/5/1

Y1 - 1987/5/1

N2 - We consider an M/G/1 queue where the arrival and service processes are modulated by a two state Markov chain. We assume that the arrival rate, service time density and the rates at which the Markov chain switches its state, are functions of the total unfinished work (buffer content) in the queue. We compute asymptotic approximations to performance measures such as the mean residual busy period, mean length of a busy period, and the mean time to reach capacity.

AB - We consider an M/G/1 queue where the arrival and service processes are modulated by a two state Markov chain. We assume that the arrival rate, service time density and the rates at which the Markov chain switches its state, are functions of the total unfinished work (buffer content) in the queue. We compute asymptotic approximations to performance measures such as the mean residual busy period, mean length of a busy period, and the mean time to reach capacity.

KW - Markov modulated queues

KW - State dependent M/G/1 queue

KW - busy period

KW - singular perturbations

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A Markov-modulated M/G/1 queue II: Busy period and time for buffer overflow

Abstract

Keywords

ASJC Scopus subject areas

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