Article

Queueing Systems

, Volume 19, Issue 3, pp 331-344

First online:

Waiting time distributions for closed M/M/N processor sharing queues

  • Jens BrabandAffiliated withSiemens AG, Bereich Verkehrstechnik

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Abstract

We consider a multiple server processor sharing model with a finite number of terminals (customers). Each terminal can submit at most one job for service at any time. The think times of the terminals and the service time demands are independently exponentially distributed. We focus our attention on the exact detailed analysis of the waiting time distribution of a tagged job. We give the Laplace-Stieltjes transform of the waiting time distribution conditioned on the job's service time demand and the state of the other terminals and show that these transforms can be efficiently evaluated and inverted. Further results include the representation of conditioned waiting times as mixtures of a constant and several exponentially distributed components. The numerical precision of our results is being compared with results from a discrete approximation of the waiting time distributions.

Keywords

Processor sharing multiple server queues central server model waiting time distributions Laplace transforms numerical inversion