- Sojourn time asymptotics in Processor Sharing queues with varying service rate
- Queueing Systems
- Volume | Issue number
- 56 | 3-4
- Pages (from-to)
- Document type
- Faculty of Science (FNWI)
- Korteweg-de Vries Institute for Mathematics (KdVI)
Abstract 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.
Keywords Processor Sharing - Sojourn-time asymptotics - Large deviations - Change of measure - Varying capacity
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