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

TL;DR

This paper characterizes when stationary probabilities in Markovian discriminatory processor sharing systems have a product geometric form, showing it only occurs in egalitarian systems, and provides asymptotic analysis for large numbers of flows.

Contribution

It proves that only egalitarian systems have a closed product geometric form for stationary probabilities and derives their exact asymptotic behavior for large system sizes.

Findings

Stationary probabilities have a product geometric form only in egalitarian systems.

Derived the exact asymptotic form of stationary probabilities for large numbers of flows.

Provided a detailed tail asymptotic analysis of the system.

Abstract

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