Sojourn times in a processor sharing queue with service interruptions
type: Item
instance of: scholarly article
title: Sojourn times in a processor sharing queue with service interruptions
zbMATH Open document ID: 0942.90005
DOI: 10.1023/A:1019173523289
published in: Queueing Systems
publication date: 2000-07-05T00:00:00Z
review text: 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 sojurn 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.
Mathematics Subject Classification ID: 90B18
Mathematics Subject Classification ID: 90B22
Mathematics Subject Classification ID: 60K25
zbMATH DE Number: 1470596
zbMATH Keywords: processor sharing
zbMATH Keywords: service interruptions
zbMATH Keywords: sojourn time
zbMATH Keywords: elastic traffic
zbMATH Keywords: available bit rate services
zbMATH Keywords: best-effort traffic
author: Rudesindo Núñez-Queija
MaRDI profile type: Publication
full work available at URL: a:1019173523289
OpenAlex ID: W1583757272
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description: scientific article; zbMATH DE number 1470596