Statistical Analysis of the Generalized ProcessorSharing Scheduling

|In this paper, we develop bounds on the individual session backlog and delay distribution under the Generalized Processor Sharing (GPS) scheduling discipline. This work is motivated by, and is an extension of, Parekh and Gal-lager's deterministic study of the GPS scheduling discipline with leaky-bucket token controlled sessions 15], 16]. Using the exponentially bounded burstiness (E.B.B.) process model introduced in 18] as a source traac characterization, we establish results that extend the deterministic study of GPS: for a single GPS server in isolation, we present statistical bounds on the distributions of backlog and delay for each session. In the network setting, we show that networks belonging to a broad class of GPS assignments, the so-called Consistent Relative Session Treatment (CRST) GPS assignments, are stable in a stochastic sense. In particular, we establish simple bounds on the distribution of backlog and delay for each session in a Rate Proportional Processor Sharing (RPPS) GPS network with arbitrary topology.