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

Jeongsim Kim, Bara Kim

Research output: Contribution to journalArticle

17 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 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.

Original languageEnglish
Pages (from-to)341-365
Number of pages25
JournalPerformance Evaluation
Volume58
Issue number4
DOIs
Publication statusPublished - 2004 Dec 1

Fingerprint

M/M/1 Queue
Processor Sharing
Sojourn Time
System of equations
Queue
Simultaneous equations
Linear equation
Open Problems
Siméon Denis Poisson
Transform
Moment
Class

Keywords

  • Discriminatory processor-sharing
  • Egalitarian processor-sharing
  • Joint transform
  • Sojourn time

ASJC Scopus subject areas

  • Computer Networks and Communications
  • Software
  • Modelling and Simulation
  • Statistics and Probability

Cite this

Sojourn time distribution in the M/M/1 queue with discriminatory processor-sharing. / Kim, Jeongsim; Kim, Bara.

In: Performance Evaluation, Vol. 58, No. 4, 01.12.2004, p. 341-365.

Research output: Contribution to journalArticle

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