Statistical multiplexing is very important in high-speed ATM type of networks, since it allows applications to efficiently share valuable network resources. However, statistical multiplexing can also lead to congestion which must be effectively controlled in order to provide users satisfactory quality of service. In this report we study a fundamental measure of network congestion, the tail of the steady state queue length distribution at an ATM multiplexer. In particular, we focus on the case when the aggregate traffic to the multiplexer can be characterized by a Gaussian process. In our approach, an ATM multiplexer is modeled by a fluid queue serving a large number of input processes. We derive asymptotic upper bounds to P({Q > x)) the tail of the queue length distribution, and provide several numerical examples to illustrate the tightness of the bounds. Our study is based on Extreme Vulue Theory, and therefore different from the popular Markovian and Large Deviation techniques.

Date of this Version

September 1997