Sojourn time asymptotics in processor sharing queues

Abstract

This paper addresses the sojourn time asymptotics for a GI/GI/\xe2\x80\xa2 queue operating under the \nProcessor Sharing (PS) discipline with stochastically varying service rate. Our focus is on the \nlogarithmic estimates of the tail of sojourn-time distribution, under the assumption that the jobsize \ndistribution has a light tail. Whereas upper bounds on the decay rate can be derived under \nfairly general conditions, the establishment of the corresponding lower bounds requires that the \nservice process satisfies a samplepath large-deviation principle. We show that the class of \nallowed service processes includes the case where the service rate is modulated by a Markov \nprocess. Finally, we extend our results to a similar system operation under the Discriminatory \nProcessor Sharing (DPS) discipline. Our analysis relies predominantly on large-deviations \ntechniques