Mean approximate formulas for GI/G/1 processor-sharing system

Kentaro Hoshi*, Yoshiaki Shikata, Yoshitaka Takahashi, Naohisa Komatsu

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review


The processor-sharing (PS) rule arises as a natural paradigm in a variety of practical situations, including time-shared computer systems. Although there has been much work on Poisson-input queueing analysis for the PS rule, there have been few results for renewalinput GI/G/1 (PS) systems. We consider the GI/G/1 (PS) system to provide develop a two-moment approximation for the mean performance measures. We derive the relationship between the mean unfinished work and the conditional mean sojourn time for the GI/G/1 (PS) system. Using this relationship, we derive approximate formulas for the mean conditional sojourn time, mean sojourn time, and the mean number of customers in the GI/G/1 (PS) system. Numerical examples are presented to compare the approximation with exact and simulated results. We show that the proposed approximate formulas have good accuracy.

Original languageEnglish
Pages (from-to)2247-2253
Number of pages7
JournalIEICE Transactions on Communications
Issue number8
Publication statusPublished - 2011 Aug


  • Processor-sharing
  • Queues
  • Renewal input
  • Sojourn-time
  • Tele-traffic analysis
  • Unfinished-work

ASJC Scopus subject areas

  • Electrical and Electronic Engineering
  • Computer Networks and Communications
  • Software


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