Effective bandwidths for multiclass Markov fluids and other ATM sources
IEEE/ACM Transactions on Networking (TON)
Large deviations and the generalized processor sharing scheduling for a two-queue system
Queueing Systems: Theory and Applications
Sojourn time asymptotics in the M/G/1 processor sharing queue
Queueing Systems: Theory and Applications
User-level performance of elastic traffic in a differentiated-services environment
Performance Evaluation
Large Deviation Analysis of Subexponential Waiting Times in a Processor-Sharing Queue
Mathematics of Operations Research
Performance of TCP-friendly streaming sessions in the presence of heavy-tailed elastic flows
Performance Evaluation - Long range dependence and heavy tail distributions
Tail asymptotics for discriminatory processor-sharing queues with heavy-tailed service requirements
Performance Evaluation - Long range dependence and heavy tail distributions
Large deviations of sojourn times in processor sharing queues
Queueing Systems: Theory and Applications
Sojourn time asymptotics in processor-sharing queues
Queueing Systems: Theory and Applications
A large-deviations analysis of the GI/GI/1 SRPT queue
Queueing Systems: Theory and Applications
Sojourn Time Tails In The M/D/1 Processor Sharing Queue
Probability in the Engineering and Informational Sciences
Traffic theory and the Internet
IEEE Communications Magazine
The equivalence between processor sharing and service in random order
Operations Research Letters
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This paper addresses the sojourn time asymptotics for a GI/GI/驴 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.