On differential equations arising in the theory of processor sharing queues

  • Authors:

  • S. F. Yashkov

  • Affiliations:

  • Institute for Information Transmission Problems (Kharkevich Institute), Russian Academy of Sciences, Moscow, Russia

  • Venue:
  • Automation and Remote Control
  • Year:
  • 2008

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Abstract

We give a probabilistic interpretation of some equations arising when the queueing system M/G/1 with egalitarian processor sharing is studied. To get this aim, we use, in addition to the new analytic method of the author, the well-known method of collective marks, in which two separate operations are involved: the "marking" of jobs, and the observation of "catastrophe" processes.