STATISTICAL-ANALYSIS OF THE GENERALIZED PROCESSOR SHARING SCHEDULING DISCIPLINE

In this paper, we develop bounds on the individual session backlog and delay distribution under the generalized processor sharing (GPS) sche duling discipline. This work is motivated by, and is an extension of, Parekh and Gallager's deterministic study of the GPS scheduling discip line with leaky-bucket token controlled sessions [15], [16]. Using the exponentially bounded burstiness (E.B.B.) process model introduced in [18] as a source traffic characterization, we establish results that extend the deterministic study of GPS: For a single GPS server in isol ation, we present statistical bounds on the distributions of backlog a nd delay for each session. In the network setting, we show that networ ks belonging to a broad class of GPS assignments, the so-called consis tent relative session treatment (CRST) GPS assignments, are stable in a stochastic sense. In particular, we establish simple bounds on the d istribution of backlog and delay for each session in a rate proportion al processor sharing (RPPS) GPS network with arbitrary topology.