Closed-Form Deterministic End-to-End Performance Bounds for the Generalized Processor Sharing Scheduling Discipline

The Generalized Processor Sharing (GPS) scheduling discipline is an important scheduling mechanism that can support both class isolation and bandwidth sharing among different service classes, thus making it an appealing choice for networks providing multiple services with Quality-of-Service guarantees. In this paper, we study a broad class of GPS networks known as Consistent Relative Session Treatment (CRST) GPS networks and establish closed-form end-to-end performance bounds for CRST GPS networks. This result generalizes the results of Parekh and Gallager (1994) where simple, closed-form end-to-end performance bounds are derived for a special sub-class of CRST GPS networks, the so-called Rate Proportional Processor Sharing (RPPS) GPS networks, but performance bounds for the general CRST GPS networks do not have closed-form. Our result is obtained through the notion of CRST partition, which in fact yields a broader class of CRST GPS networks than the one originally defined in (Parekh and Gallager, 1993). Moreover, our approach is quite general. It not only applies to the deterministic analysis of GPS networks, but can also be employed in the study of GPS networks in a stochastic setting.