Analysis of the M/M/1 queue with processor sharing via spectral theory

Analysis of the M/M/1 queue with processor sharing via spectral theory

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Article ID: iaor20041292
Country: Netherlands
Volume: 39
Issue: 4
Start Page Number: 377
End Page Number: 397
Publication Date: Dec 2001
Journal: Queueing Systems
Authors: ,
Keywords: M/M/1 queues
Abstract:

We show in this paper that the computation of the distribution of the sojourn time of an arbitrary customer in an 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.

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