On the ordering properties of GPS routers for multi-class QoS provision

This paper studies the ordering properties of quality of service (QoS) measures and their rendered values in multi-class QoS provision systems when generalized processor sharing (GPS)-based packet scheduling is employed at routers. GPS has been proposed as a building block for providing multiple service classes with differentiated services to applications with diverse QoS requirements. Previous works have concentrated on finding algorithms and implementations that faithfully approximate the fairness properties of GPS with some work done on deriving performance bounds when leaky-bucket traffic shaping is applied at traffic sources. In this paper, we study the problem of facilitating effective quality of service in multi-class systems with multidimensional QoS vectors containing both mean- and burstiness-related QoS indicators such as packet loss rate, delay, and jitter. We study the impact of traffic burstiness and network contention on the properties of rendered QoS in the service classes. We show that under bursty traffic conditions, it is intrinsically difficult for one service class to deliver quality of service superior in both mean- and burstiness-related QoS measures-delay and Jitter-over another when GPS scheduling is employed at routers. In particular, to achieve lower mean packet loss and packet loss variance, higher delay variance (i.e., Jitter) must be incurred. Conversely, the price for achieving lower mean delay and delay variance is higher packet loss variance. This result is applicable to both reserved and best-effort traffic classes and affects the "programming" of GPS routers for QoS provision by constraining what application QoS requirements can be effectively met. We show performance results in a specific GPS-based QoS provision platform-noncooperative multi-class QoS provision-which demonstrate the impact of the ordering results on providing effective quality of service to applications with diverse QoS requirements.