Mean sojourn times for phase-type discriminatory processor sharing systems

In a discriminatory processor sharing (DPS) queueing model, each job (or customer) belongs to one out of finitely many classes. The arrival processes are Poisson. Classes differ with respect to arrival rates and service time distributions. Moreover, classes have different priority levels. All jobs present are served simultaneously but the fraction of the server’s capacity allocated to each one of them is proportional to their class priority parameter (while the total capacity is of course fixed).