A decomposition theorem and related results for the discriminatory processor sharing queue

In this paper, we study a discriminatory processor sharing queue with Poisson arrivals,K classes and general service times. For this queue, we prove a decomposition theorem for the conditional sojourn time of a tagged customer given the service times and class affiliations of the customers present in the system when the tagged customer arrives. We show that this conditional sojourn time can be decomposed inton+1 components if there aren customers present when the tagged customer arrives. Further, we show that thesen+1 components can be obtained as a solution of a system of non-linear integral equations. These results generalize known results about theM/G/1 egalitarian processor sharing queue.