  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.

Performance;Probability