Sojourn time distribution in the M/M/1 queue with discriminatory processor-sharing

In this paper, we consider a queue with multiple K job classes, Poisson arrivals, exponentially distributed required service times in which a single processor serves according to the DPS discipline. More precisely, if there are ni class i jobs in the system, i=1,…,K, each class j job receives a fraction αj/∑i=1Kαini of the processor capacity. For this queue, we obtain a system of equations for joint transforms of the sojourn time and the number of jobs. Using this system of equations we find the moments of the sojourn time as a solution of linear simultaneous equations, which solves an open problem.