Analytical queue length distributions of GPS systems with long range dependent service capacity

Generalized Processor Sharing (GPS) is an idealized scheduling mechanism with given weights assigned to individual traffic flows for service differentiation. Based on the principle of GPS, a number of variants have been proposed and deployed in real-world communication systems where the service capacity of network channels is usually variable. This paper proposes an analytical performance model for GPS systems with the variable service capacity characterized by Long Range Dependent (LRD) processes. The model is able to accommodate heterogeneous fractional Brownian motion (fBm) and Poisson traffic in multi-service networks. We derive the expressions of the queue length distributions of the GPS system and individual traffic flows. The accuracy of the analytical model is validated through comparison between analytical and simulation results.