Asymptotic regimes and approximations for discriminatory processor sharing

Abstract

We study the joint queue length distribution of the Discriminatory Processor Sharing model, assuming all classes have phase-type service requirement distributions. We show that the moments of the joint queue length distribution can be obtained by solving linear equations. We use this to study the system in two asymptotic regimes. In the first regime, the different user classes operate on strictly separated time scales. Then we study the system in heavy traffic.