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Queueing Systems

, Volume 17, Issue 1–2, pp 129–136 | Cite as

On the transient behavior of the processor sharing queue

  • Alain Jean-Marie
  • Philippe Robert
Article

Abstract

We analyze the transient behavior of the single server queue under the processor sharing discipline. Under fairly general assumptions, we give the rate of growth of the number of customers in the queue as well as the asymptotic behavior of the residual service times described in terms of a renormalized point process.

Keywords

Point processes transience of single server queues ergodic theorems 

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References

  1. [1]
    S. Yashkov, On a heavy traffic limit theorem for theM/G/1 processor sharing queue, Commun. Statist.-Stoch. Models 9 (1993) 467–471.Google Scholar
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    J. Neveu,Processus Ponctuels, Lecture Notes in Mathematics, vol. 598 (Springer, Berlin, 1976).Google Scholar
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    P. Franken, D. König, U. Arndt and V. Schmidt,Queues and Point Processes (Wiley, Chichester, 1981).Google Scholar
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    F. Baccelli and P. Brémaud,Palm Probabilities and Stationary Queues, Lecture Notes in Statistics, vol. 41 (Springer, Berlin, 1987).Google Scholar

Copyright information

© J.C. Baltzer AG, Science Publishers 1994

Authors and Affiliations

  • Alain Jean-Marie
    • 1
  • Philippe Robert
    • 2
  1. 1.INRIAValbonne CedexFrance
  2. 2.INRIA, Domaine de VoluceauLe Chesnay CedexFrance

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