Asymptotic behavior of generalized processor sharing queues under subexponential assumptions

Abstract

We analyze the behavior of Generalized Processor Sharing (GPS) queues with heavy-tailed service times. We compute the exact tail asymptotics of the stationary workload of an individual class and give new conditions for reduced-load equivalence and induced burstiness to hold. We also show that both phenomena can occur simultaneously. Our proofs rely on the single big event theorem and new fluid limits obtained for the GPS system that can be of interest by themselves.