Queueing processes in GPS and PGPS with LRD traffic inputs

Long range dependent (LRD) traffic whose single server queue process is Weibull Bounded (WB) is first analyzed. Two upper bounds on the individual session's queue length of LRD traffic under the generalized processor sharing (GPS) scheduling discipline are then contributed. It is shown that the index parameter in the upper bound of one LRD flow, (in addition to the decay rate and the asymptotic constant), may be affected by other LRD flows. A new concept, called LRD isolation, is subsequently contributed and accompanying it, a new technique is contributed to check whether a flow, with a given GPS weight assignment, can be guaranteed to be LRD isolated. This technique is also amenable for use in an online call admission control (CAC) scenario. When existing flows have already been assigned contract weights that cannot be changed, our technique can be used to determine minimum contract weights to be assigned to a new flow in order to guarantee the flow to be LRD isolated. The results are also extended to a PGPS (packet-based GPS) scheduler and relevant numerical results are provided to show the usefulness of our bounds and LRD isolation technique.