Sojourn times in a processor sharing queue with service interruptions

Sojourn times in a processor sharing queue with service interruptions

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Article ID: iaor20013060
Country: Netherlands
Volume: 34
Issue: 1/4
Start Page Number: 351
End Page Number: 386
Publication Date: Jan 2000
Journal: Queueing Systems
Authors:
Keywords: M/M/1 queues
Abstract:

We study the sojourn times of customers in an M/M/1 queue with the processor sharing service discipline and a server that is subject to breakdowns. The lengths of the breakdowns have a general distribution, whereas the ‘on-periods’ are exponentially distributed. A branching process approach leads to a decomposition of the sojourn time, in which the components are independent of each other and can be investigated separately. We derive the Laplace–Stieltjes transform of the sojourn-time distribution in steady state, and show that the expected sojourn time is not proportional to the service requirement. In the heavy-traffic limit, the sojourn time conditioned on the service requirement and scaled by the traffic load is shown to be exponentially distributed. The results can be used for the performance analysis of elastic traffic in communication networks, in particular, the ABR service class in ATM networks, and best-effort services in IP networks.

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