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Queueing Systems

, Volume 14, Issue 3–4, pp 239–273 | Cite as

The M/G/1 processor-sharing model: transient behavior

  • M. Yu. Kitaev
Invited Paper

Abstract

This paper deals with the M/G/1 model with processor-sharing service discipline. LetL*(t, x) denote the number of jobs present at timet whose attained service time is not greater thanx,x⩾0, andV0(t,z) the sojourn time of a tagged job placed in the system at timet and requiringz units of service. Explicit analytical expressions are obtained for the joint distribution ofL*(t, ·) andV0(t, ·) under various initial conditions in terms of the Laplace transform with respect tot. It is shown that for initial conditions of special kind (there is one job or none) the results can be expressed in a closed form.

Keywords

Processor-sharing time-sharing transient behavior virtual sojourn time distribution branching process marked point process random measure predictable projection random time change 

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Copyright information

© J.C. Baltzer AG, Science Publishers 1993

Authors and Affiliations

  • M. Yu. Kitaev
    • 1
  1. 1.MoscowRussia

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