Determining the Moments of Queue-Length Distribution of Discriminatory Processor-Sharing Systems with Phase-Type Service Requirements

In this paper, we study discriminatory processor sharing systems in which different customer classes receive different rates of service according to class weights. DPS systems have many interesting applications in modelling of, e.g., computer or telecommunication systems. In prior work, assuming phase-type service requirement distribution, the moments of the number of customers have been found as a solution of a system of linear equations. In this paper, we present an alternative approach to the same problem allowing us to derive similar results. We use a method based on the theory of Markov decision processes and show that exact results are achieved. The moments of the queue length distribution may be solved from a system of linear equations. While not as efficient as the previous method, our approach also provides the value function of the system which may be used in policy optimization.