Queueing Systems

, Volume 39, Issue 4, pp 377–397 | Cite as

Analysis of the M/M/1 Queue with Processor Sharing via Spectral Theory

  • Fabrice Guillemin
  • Jacqueline Boyer


We show in this paper that the computation of the distribution of the sojourn time of an arbitrary customer in a M/M/1 with the processor sharing discipline (abbreviated to M/M/1 PS queue) can be formulated as a spectral problem for a self-adjoint operator. This approach allows us to improve the existing results for this queue in two directions. First, the orthogonal structure underlying the M/M/1 PS queue is revealed. Second, an integral representation of the distribution of the sojourn time of a customer entering the system while there are n customers in service is obtained.

M/M/1 queue processor sharing spectral theory orthogonal polynomials queue asymptotics 


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Copyright information

© Kluwer Academic Publishers 2001

Authors and Affiliations

  • Fabrice Guillemin
    • 1
  • Jacqueline Boyer
    • 1
  1. 1.France Telecom R&DLannionFrance

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