Population effects in Multiclass Processor Sharing Queues

Abstract

Consider a single server queueing system with several classes of customers, each having its own renewal input process and its own general service times distribution. Upon completing service, customers may leave, or reenter the queue, possibly as customers of a different class. The server is operating under the egalitarian or the discriminatory processor sharing discipline.In this paper, we consider the fluid approximation of this multiclass processor sharing queue. We first provide the results allowing to compute the trajectories for this model, under the egalitarian PS discipline. Asymptotic results for overloaded queues are also stated. Next, we show that a simple transformation allows to compute the solution for the discriminatory PS queue as well. Finally, we illustrate the different results through numerical experiments. We compare transient trajectories with simulations, and we discuss the fairness issue that may arise in overloaded PS queues.