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 jobsize 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 samplepath 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.
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CWI. Probability, Networks and Algorithms [PNA]

Egorova, R.R, Mandjes, M.R.H, & Zwart, A.P. (2006). Sojourn time asymptotics in processor sharing queues. CWI. Probability, Networks and Algorithms [PNA]. CWI.