On the equivalence between multiclass processor sharing and random order scheduling policies

International audienceConsider a single server system serving a multiclass population. Some popular scheduling policies for such system are the discriminatory processor sharing (DPS), discriminatory random order service (DROS), generalized processorsharing (GPS) and weighted fair queueing (WFQ). In this paper, we propose two classes of policies, namely MPS (Multi-class Processor Sharing) and MROS (Multi-class Random Order Service), that generalize the four policiesmentioned above. For the special case when the multi-class population arrive according to Poisson processes and have independent and exponential service requirement with parameter µ, we show that the tail of the sojourn timedistribution for a class i customer in a system with the MPS policy is a constant multiple of the tail of the waiting timedistribution of a class i customer in a system with the MROS policy. This result implies that for a class i customer, the tail of the sojourn time distribution in a system with the DPS (GPS) scheduling policy is a constant multiple of the tail of the waiting time distribution in a system with the DROS (respectively WFQ) policy