The processor-sharing queue with bulk arrivals and phase-type services

Jeongsim Kim; Bara Kim

doi:10.1016/j.peva.2006.05.006

The processor-sharing queue with bulk arrivals and phase-type services

Jeongsim Kim, Bara Kim

Department of Mathematics

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

9 Citations (Scopus)

Abstract

In this paper, we consider a queue with compound Poisson arrivals, phase type required service times in which a single processor serves according to the processor-sharing discipline. For this queue, we derive a system of equations for the transform of the queue-length and obtain the moments of the queue-length as a solution of linear equations. We also obtain a system of equations for the joint transforms of the sojourn time and the queue-length and find the moments of the sojourn time as a solution of linear equations. Numerical examples show that the smaller the variation of the required service times becomes, the larger the mean and variance of the sojourn times become.

Original language	English
Pages (from-to)	277-297
Number of pages	21
Journal	Performance Evaluation
Volume	64
Issue number	4
DOIs	https://doi.org/10.1016/j.peva.2006.05.006
Publication status	Published - 2007 May

Bibliographical note

Funding Information:
We thank the associate editor and the referees for their helpful comments. This work was supported by a Korea University Grant.

Keywords

Bulk arrivals
Joint transform
Processor-sharing
Queue-length
Sojourn time

ASJC Scopus subject areas

Software
Modelling and Simulation
Hardware and Architecture
Computer Networks and Communications

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10.1016/j.peva.2006.05.006

Cite this

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AU - Kim, Bara

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PY - 2007/5

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N2 - In this paper, we consider a queue with compound Poisson arrivals, phase type required service times in which a single processor serves according to the processor-sharing discipline. For this queue, we derive a system of equations for the transform of the queue-length and obtain the moments of the queue-length as a solution of linear equations. We also obtain a system of equations for the joint transforms of the sojourn time and the queue-length and find the moments of the sojourn time as a solution of linear equations. Numerical examples show that the smaller the variation of the required service times becomes, the larger the mean and variance of the sojourn times become.

AB - In this paper, we consider a queue with compound Poisson arrivals, phase type required service times in which a single processor serves according to the processor-sharing discipline. For this queue, we derive a system of equations for the transform of the queue-length and obtain the moments of the queue-length as a solution of linear equations. We also obtain a system of equations for the joint transforms of the sojourn time and the queue-length and find the moments of the sojourn time as a solution of linear equations. Numerical examples show that the smaller the variation of the required service times becomes, the larger the mean and variance of the sojourn times become.

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KW - Joint transform

KW - Processor-sharing

KW - Queue-length

KW - Sojourn time

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JO - Performance Evaluation

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ER -

The processor-sharing queue with bulk arrivals and phase-type services

Abstract

Bibliographical note

Keywords

ASJC Scopus subject areas

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