Automation and Remote Control

, 69:1622

A note on application of the method of supplementary variables to the analysis of a processor sharing system

  • S. F. Yashkov
Information Processes

DOI: 10.1134/S0005117908090166

Cite this article as:
Yashkov, S.F. Autom Remote Control (2008) 69: 1622. doi:10.1134/S0005117908090166


We present a new proof of Theorem of 1989 about non-stationary (transient) distribution of the number of jobs in the M/G/1 queue with egalitarian processor sharing. To get this goal, we use the well-known method of supplementary variables. The complete proof of that non-trivial Theorem of 1989 (see Theorem 2.1) was first given in the author’s monograph [12, §2.8] (1989) by means of essentially novel analytic method. Before appearing author’s work, this problem had been considered from analytic viewpoint as insoluble one. In essence, Theorem 2.2 almost repeats Theorem 2.1, but with other proof. In Section 3, Theorem 2.2 is extended to the case of an M/G/1-EPS queue with catastrophes which appear according to a Poisson process.

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Copyright information

© MAIK Nauka 2008

Authors and Affiliations

  • S. F. Yashkov
    • 1
  1. 1.Institute for Information Transmission Problems (Kharkevich Institute)Russian Academy of SciencesMoscowRussia

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