The upper bound of queue length in generalized processor sharing system with FBM input traffic

Abstract

Since early 1990``s, it has been known that the Internet traffic is self-similar and long-range dependent, which differs from the traditional Poisson model used in telephone networks. Therefore, different approaches have been taken to model the Internet traffic more exactly. In this paper, we derive new upper bounds on queue length and delay of Generalized Processor Sharing (GPS) system for Fractional Brownian motion (FBM) input traffic. By using these results, the decay rate of queue length overflow probability and the maximum network delay time of the specific packet streams can be obtained and it is shown that the output behavior of every queue has long-range dependent (LRD) property.