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

Authors:
Fabrice Guillemin;Jacqueline Boyer
Affiliations:
France Telecom R&D, 2, Avenue Pierre Marzin, 22300 Lannion, France Fabrice.Guillemin@rd.francetelecom.fr;France Telecom R&D, 2, Avenue Pierre Marzin, 22300 Lannion, France Jacqueline.Boyer@rd.francetelecom.fr
Venue:
Queueing Systems: Theory and Applications
Year:
2001

Citing 3
Cited 5

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Large deviations of sojourn times in processor sharing queues

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Fluid and diffusion limits for transient sojourn times of processor sharing queues with time varying rates

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Processor sharing: A survey of the mathematical theory

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Abstract

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.