A queueing system with discrete autoregressive arrivals

Bara Kim; Yong Chang; Yeong Cheol Kim; Bong Dae Choi

doi:10.1016/j.peva.2006.05.008

A queueing system with discrete autoregressive arrivals

Bara Kim, Yong Chang, Yeong Cheol Kim, Bong Dae Choi

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

14 Citations (Scopus)

Abstract

We consider a discrete time single server queue with discrete autoregressive process of order 1 (DAR(1)) input. By extracting a Markov process from the queue size process and applying the BASTA property, we derive simple recursive formulae for the stationary distributions of the queue size and the waiting time. These formulae are simple, numerically stable and transform-free. A stochastic decomposition property is given for the stationary waiting time, and relations between the distributions of the stationary queue size and the stationary waiting time are discussed. Numerical examples are given for stationary distributions of the queue size and the waiting time for various DAR(1) inputs.

Original language	English
Pages (from-to)	148-161
Number of pages	14
Journal	Performance Evaluation
Volume	64
Issue number	2
DOIs	https://doi.org/10.1016/j.peva.2006.05.008
Publication status	Published - 2007 Feb

Bibliographical note

Funding Information:
This work was supported by grant No. R01-2001-00007 from the Korea Science & Engineering Foundation.

Keywords

DAR(1)
Discrete time queue
Queue size
Recursive formula
Stochastic decomposition
Waiting time

ASJC Scopus subject areas

Software
Modelling and Simulation
Hardware and Architecture
Computer Networks and Communications

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10.1016/j.peva.2006.05.008

Cite this

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title = "A queueing system with discrete autoregressive arrivals",

abstract = "We consider a discrete time single server queue with discrete autoregressive process of order 1 (DAR(1)) input. By extracting a Markov process from the queue size process and applying the BASTA property, we derive simple recursive formulae for the stationary distributions of the queue size and the waiting time. These formulae are simple, numerically stable and transform-free. A stochastic decomposition property is given for the stationary waiting time, and relations between the distributions of the stationary queue size and the stationary waiting time are discussed. Numerical examples are given for stationary distributions of the queue size and the waiting time for various DAR(1) inputs.",

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AU - Chang, Yong

AU - Kim, Yeong Cheol

AU - Choi, Bong Dae

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PY - 2007/2

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N2 - We consider a discrete time single server queue with discrete autoregressive process of order 1 (DAR(1)) input. By extracting a Markov process from the queue size process and applying the BASTA property, we derive simple recursive formulae for the stationary distributions of the queue size and the waiting time. These formulae are simple, numerically stable and transform-free. A stochastic decomposition property is given for the stationary waiting time, and relations between the distributions of the stationary queue size and the stationary waiting time are discussed. Numerical examples are given for stationary distributions of the queue size and the waiting time for various DAR(1) inputs.

AB - We consider a discrete time single server queue with discrete autoregressive process of order 1 (DAR(1)) input. By extracting a Markov process from the queue size process and applying the BASTA property, we derive simple recursive formulae for the stationary distributions of the queue size and the waiting time. These formulae are simple, numerically stable and transform-free. A stochastic decomposition property is given for the stationary waiting time, and relations between the distributions of the stationary queue size and the stationary waiting time are discussed. Numerical examples are given for stationary distributions of the queue size and the waiting time for various DAR(1) inputs.

KW - DAR(1)

KW - Discrete time queue

KW - Queue size

KW - Recursive formula

KW - Stochastic decomposition

KW - Waiting time

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EP - 161

JO - Performance Evaluation

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ER -

A queueing system with discrete autoregressive arrivals

Abstract

Bibliographical note

Keywords

ASJC Scopus subject areas

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