Sojourn time asymptotics in processor sharing queues with varying service rate

R.R. Egorova, M.R.H. Mandjes, B. Zwart

Research output: Contribution to journalArticleAcademicpeer-review

3 Citations (Scopus)
3 Downloads (Pure)


This paper addresses the sojourn time asymptotics for a GI/GI/· queue operating under the Processor Sharing (PS) discipline with stochastically varying service rate. Our focus is on the logarithmic estimates of the tail of sojourn-time distribution, under the assumption that the job-size distribution has a light tail. Whereas upper bounds on the decay rate can be derived under fairly general conditions, the establishment of the corresponding lower bounds requires that the service process satisfies a sample-path large-deviation principle. We show that the class of allowed service processes includes the case where the service rate is modulated by a Markov process. Finally, we extend our results to a similar system operation under the Discriminatory Processor Sharing (DPS) discipline. Our analysis relies predominantly on large-deviations techniques.
Original languageEnglish
Pages (from-to)169-181
JournalQueueing Systems
Issue number3-4
Publication statusPublished - 2007


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