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

Jeongsim Kim, Bara Kim

Research output: Contribution to journalArticle

18 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

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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