Queue-length distribution for the discriminatory processor-sharing queue

In this paper, we study a multiple class discriminatory processor-sharing queue. The queue is assumed to have Poisson input and exponentially distributed service times. In this discipline there are K classes of customers. When there are n(i) customers present in the system of class i(i = 1, . . . , K), each member of class j receives a fraction of the server's capacity given by α(j)/Σ^Ki=1 n(i)α(i). Thus, associated with class i customers is a weight α(i) which determines the level of service discrimination. For this problem, we find the moments of the queue-length distribution as a solution of linear simultaneous equations. We also prove a heavy traffic limit theorem for the joint queue-length distribution for this queue.