Statistical multiplexing is very important in high-speed networks, since it allows network applications to efficiently share network resources. However, statistical multiplexing can also lead to congestion which must be properly controlled in order to provide users with a satisfactory level of quality of service. In this report we study P({Q > x)), the tail of the steady state queue length distribution at a highspeed multiplexer. The tail distribution P({Q > x)) is a fundamental measure of network congestion and thus i.mportant for the efficient design and control of these networks. In partic:ular, we focus on the case when the aggregate traffic to the multiplexer can be characterized by a stationary Gaussian process. In our approach, a multiplexer is modeled by a fluid queue serving a large number of input processes. We propose a lower bound and two asymptotic upper bounds for P({Q > x)), and provide several numerical examples to illustrate the tightness of these bounds. We also us: these bounds to study important properties of the tail probability. Further, we apply these bounds for a large number of non-Gaussian input sources, and validate their performance via simulations. Wherever possible, we have condilcted our simulation study using Importance Sampling in order to improve its reliability and to effectively capture rare events. Our analytical study is based on Extreme Value Theory, and therefore different from the approaches using traditional Markovian and Large Deviations techniques.

Date of this Version

February 1998