Busy period distribution in state-dependent queues

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

doi:10.1007/BF01158903

Busy period distribution in state-dependent queues

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

^*Corresponding author for this work

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

6 Scopus citations

Abstract

We consider a state-dependent M/M/1 queue in which the arrival rate is a function of the instantaneous unfinished work (work backlog) in the system, and the customer's exponential service time distribution is allowed to depend on the unfinished work in the system at the instant that customer arrived. We obtain asymptotic approximations to both the busy period distributions as well as the residual busy period distribution. Our approximations are valid for systems with a rapid arrival rate and small mean service times.

Original language	English (US)
Pages (from-to)	285-305
Number of pages	21
Journal	Queueing Systems
Volume	2
Issue number	3
DOIs	https://doi.org/10.1007/BF01158903
State	Published - Sep 1987
Externally published	Yes

Keywords

State-dependent queues
busy period analysis
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/BF01158903

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title = "Busy period distribution in state-dependent queues",

abstract = "We consider a state-dependent M/M/1 queue in which the arrival rate is a function of the instantaneous unfinished work (work backlog) in the system, and the customer's exponential service time distribution is allowed to depend on the unfinished work in the system at the instant that customer arrived. We obtain asymptotic approximations to both the busy period distributions as well as the residual busy period distribution. Our approximations are valid for systems with a rapid arrival rate and small mean service times.",

keywords = "State-dependent queues, busy period analysis, singular perturbations",

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

year = "1987",

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AU - Knessl, C.

AU - Matkowsky, B. J.

AU - Schuss, Z.

AU - Tier, C.

PY - 1987/9

Y1 - 1987/9

N2 - We consider a state-dependent M/M/1 queue in which the arrival rate is a function of the instantaneous unfinished work (work backlog) in the system, and the customer's exponential service time distribution is allowed to depend on the unfinished work in the system at the instant that customer arrived. We obtain asymptotic approximations to both the busy period distributions as well as the residual busy period distribution. Our approximations are valid for systems with a rapid arrival rate and small mean service times.

AB - We consider a state-dependent M/M/1 queue in which the arrival rate is a function of the instantaneous unfinished work (work backlog) in the system, and the customer's exponential service time distribution is allowed to depend on the unfinished work in the system at the instant that customer arrived. We obtain asymptotic approximations to both the busy period distributions as well as the residual busy period distribution. Our approximations are valid for systems with a rapid arrival rate and small mean service times.

KW - State-dependent queues

KW - busy period analysis

KW - singular perturbations

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JF - Queueing Systems

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ER -

Busy period distribution in state-dependent queues

Abstract

Keywords

ASJC Scopus subject areas

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