In this paper, the authors study a discriminatory processor sharing queue with Poisson arrivals, K classes and general service times. For this queue, they 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. The authors show that this conditional sojourn time can be decomposed into n+1 components if there are n customers present when the tagged customer arrives. Further, they show that these n+1 components can be obtained as a solution of a system of non-linear integral equations. These results generalize known results about the M/G/1 egalitarian processor sharing queue.
