Consider a single server queue serving a multiclass population. Some popular scheduling policies for such a system (and of interest in this paper) are the discriminatory processor sharing (DPS), discriminatory random order service (DROS), generalized processor sharing (GPS) and weighted fair queueing (WFQ). The aim of this paperis to show a certain equivalence between these scheduling policiesfor the special case when the multiclass population have identical and exponential service requirements. In fact , we show  the equivalence between two broader classes of policies that generalize the above mentioned four policies. We specifically show that the sojourn time distribution for a customer of a particular class in a system with the  DPS (GPS) scheduling policy is a constant multiple of the  waiting time distribution of a customer of the same class in a system with the DROS (respectively WFQ) policy.
Consider 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 processor sharing (GPS) and weighted fair queueing (WFQ). In this paper, we propose two classes of policies, namely MPS (multiclass processor sharing) and MROS (multiclass random order service), that generalize the four policies mentioned above. For the special case when the multiclass population arrive according to Poisson processes and have independent and exponential service requirement with parameter \mu , we show that the tail of the sojourn time distribution for a class i customer in a system with the MPS policy is a constant multiple of the tail of the waiting time distribution 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.
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of a customer of the same class