Upper bounds for individual queue length distribution in GPS with LRD traffic input

We analyze the arrival process of Long range dependent (LRD) traffic and demonstrate that it is a Weibull Bounded Burstiness (WBB) process. By decomposing a generalized processor sharing (GPS) system into isolated queues and servers, we then obtain two upper bounds on the individual session queue length, which are useful for Quality of Service (QoS) control. We also demonstrate that some parameters in determining the upper bound on an individual session queue, such as the index, the asymptotic constant and the decay rate may be affected by other flows existing in the GPS system. However, under certain conditions, by carefully choosing the GPS weight parameters, an individual session with LRD traffic input can be well isolated from other flows.