Routing and rate allocation to provide end-to-end delay guarantees under PGPS scheduling

This paper considers the problem of routing sessions with quality of service (QoS) requirements in a network under packet generalized processor sharing (PGPS) scheduling. PGPS is a non-preemptive scheduling policy that tracks GPS. The GPS policy operates by allocating a weight φ_n^m for a session n whose traffic uses link m. These weights determine the rate at which the traffic from session n is served at link m and the rate in turn determines the end-to end delay of packets belonging to session n. As a deterministic and easily computable end-to-end delay bound is available for locally stable sessions, we consider the locally stable regime in this paper. Two separate problems are considered in this paper. The first problem deals with the practically important inverse procedure of specifying appropriate weights for sessions at each link on their paths, that satisfy predetermined delay bounds, when the set of sessions to be routed is given. Here we show that the fixed routing case can be formulated as a linear program (LP) and the adaptive routing case can be formulated as a mixed integer linear program (MILP). The second problem examines the performance of PGPS scheduling policy when providing per-session QoS guarantees. We measure the performance in terms of weighted carried traffic. We derive an upper bound on the weighted carried traffic for any heuristic algorithm for admission control that operates within the locally stable domain. This upper bound can be obtained by computing a linear program (LP). By simulating a simple heuristic algorithm for admission control, we show that this upper bound is reasonably tight. Hence our upper bound can be used as a metric against which the performance of different algorithms can be compared