Generalized processor sharing with long-range dependent traffic input

We develop an upper bound on the individual session queue length of long range dependent (LRD) traffic under the generalized processor sharing (GPS) scheduling discipline. This work is based on the analysis of the arrival process of LRD traffic, which is demonstrated to be a Weibull bounded burstiness (WBB) process. Decomposing the GPS system into isolated queues and servers, we are able to obtain the bound on the individual session queue length from their arrival processes. Our work proves that, in different scenarios, different parameters of the upper bound of an individual session queue, such as the index, the asymptotic constant and the decay rate can be affected by other flows existing in the GPS system. Under certain conditions, by carefully choosing the weight parameters, an individual session with LRD traffic input can be well isolated from other flows in a GPS system.