Sojourn time distribution in the M/M/1 queue with discriminatory processor-sharing

Jeongsim Kim; Bara Kim

doi:10.1016/j.peva.2004.05.005

Sojourn time distribution in the M/M/1 queue with discriminatory processor-sharing

Jeongsim Kim, Bara Kim

Department of Mathematics

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

20 Citations (Scopus)

Abstract

In this paper, we consider a queue with multiple K job classes, Poisson arrivals, exponentially distributed required service times in which a single processor serves according to the DPS discipline. More precisely, if there are n_i class i jobs in the system, i=1,...,K, each class j job receives a fraction α_j/∑_i=1^Kα _in_i of the processor capacity. For this queue, we obtain a system of equations for joint transforms of the sojourn time and the number of jobs. Using this system of equations we find the moments of the sojourn time as a solution of linear simultaneous equations, which solves an open problem.

Original language	English
Pages (from-to)	341-365
Number of pages	25
Journal	Performance Evaluation
Volume	58
Issue number	4
DOIs	https://doi.org/10.1016/j.peva.2004.05.005
Publication status	Published - 2004 Dec

Keywords

Discriminatory processor-sharing
Egalitarian processor-sharing
Joint transform
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.2004.05.005

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title = "Sojourn time distribution in the M/M/1 queue with discriminatory processor-sharing",

abstract = "In this paper, we consider a queue with multiple K job classes, Poisson arrivals, exponentially distributed required service times in which a single processor serves according to the DPS discipline. More precisely, if there are ni class i jobs in the system, i=1,...,K, each class j job receives a fraction αj/∑i=1Kα ini of the processor capacity. For this queue, we obtain a system of equations for joint transforms of the sojourn time and the number of jobs. Using this system of equations we find the moments of the sojourn time as a solution of linear simultaneous equations, which solves an open problem.",

keywords = "Discriminatory processor-sharing, Egalitarian processor-sharing, Joint transform, Sojourn time",

author = "Jeongsim Kim and Bara Kim",

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AU - Kim, Jeongsim

AU - Kim, Bara

N1 - Funding Information: This research was supported by University IT Research Center Project.

PY - 2004/12

Y1 - 2004/12

N2 - In this paper, we consider a queue with multiple K job classes, Poisson arrivals, exponentially distributed required service times in which a single processor serves according to the DPS discipline. More precisely, if there are ni class i jobs in the system, i=1,...,K, each class j job receives a fraction αj/∑i=1Kα ini of the processor capacity. For this queue, we obtain a system of equations for joint transforms of the sojourn time and the number of jobs. Using this system of equations we find the moments of the sojourn time as a solution of linear simultaneous equations, which solves an open problem.

AB - In this paper, we consider a queue with multiple K job classes, Poisson arrivals, exponentially distributed required service times in which a single processor serves according to the DPS discipline. More precisely, if there are ni class i jobs in the system, i=1,...,K, each class j job receives a fraction αj/∑i=1Kα ini of the processor capacity. For this queue, we obtain a system of equations for joint transforms of the sojourn time and the number of jobs. Using this system of equations we find the moments of the sojourn time as a solution of linear simultaneous equations, which solves an open problem.

KW - Discriminatory processor-sharing

KW - Egalitarian processor-sharing

KW - Joint transform

KW - Sojourn time

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DO - 10.1016/j.peva.2004.05.005

M3 - Article

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SN - 0166-5316

VL - 58

SP - 341

EP - 365

JO - Performance Evaluation

JF - Performance Evaluation

IS - 4

ER -

Sojourn time distribution in the M/M/1 queue with discriminatory processor-sharing

Abstract

Keywords

ASJC Scopus subject areas

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