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In this paper, we establish two different results. The first result is acharacterization theorem saying that if the stationary state probabilities fororiginally described Markovian discriminatory processor sharing (DPS) systemhave a closed product geometric form (the exact definition is given in thepaper), then the system must only be Egalitarian, i.e. all flows in this systemmust have equal priorities. The second result is the tail asymptotics for thestationary probabilities. We provide a detailed asymptotic analysis of thesystem, and obtain the exact asymptotic form of the stationary probabilities inDPS systems when the number of flows in the system is large.

Characterization and asymptotic analysis of the stationary probabilities in Discriminatory Processor Sharing Systems