Statistical analysis of generalized processor sharing scheduling discipline

In this paper, we consider the problem of providing statistical guarantees (for example, on the tail distribution of delay) 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 GPS scheduling discipline with leaky-bucket token controlled sessions [PG93a,b, Parekh92]. Using the exponentially bounded burstiness (E.B.B.) process model introduced in [YaSi93a] 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 tail 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 tail distribution of backlog and delay for each session in a Rate Proportional Processor Sharing (RPPS) GPS network with arbitrary topology.