QUEUE-LENGTH DISTRIBUTION FOR THE DISCRIMINATORY PROCESSOR-SHARING QUEUE

In this paper, we study a multiple class discriminatory processor-shar ing quene. The quene is assumed to have Poisson input an exponentially distributed service times. In this discipline there are K classes of customers. When there are n(i) customers present i the system of class i(i = 1, ..., K), each member of class j receives a fraction of the s erver's capacity given by alpha(j)/Sigma(i=1)(K) n(i) alpha(i). Thus, associated with class i customers is a weight alpha(i) which determine s the level of service discrimination. For this problem, we find the m oments of the quene-length distribution as a solution of linear simult aneous equations. We also prove a heavy traffic limit theorem for the joint quene-length distribution for this quene.