Abstract

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 Gallager '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 traffic 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 socalled 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 Sharin...

Citations