Queueing analysis of high-speed multiplexers including long-range dependent arrival processes

With the advent of high-speed networks, a single link will carry hundreds or even thousands of applications. This results in a very natural application of the central limit theorem, to model the network traffic by a Gaussian stochastic processes. We study the tail probability P({Q>x}) of a queueing system when the input process is assumed to be a very general class of Gaussian processes which includes a large class of self similar or other types of long-range dependent Gaussian processes. For example, past work on fractional Brownian motion, and variations therein, are but a small subset of the work presented in this paper. This study is based on extreme value theory and we show that log P({Q>x})+m_x /2 grows at most on the order of logx, where m_x corresponds to the reciprocal of the maximum (normalized) variance of a Gaussian process directly related to the aggregate input process. The result is considerably stronger than the existing results in the literature based on large deviation theory, and we theoretically show that this improvement can be quite important in characterizing the asymptotic behavior of P({Q>x}). Through numerical examples, we also demonstrate that exp[-m_x/2] provides a very accurate estimate for a variety of long-range and short-range dependent input processes over the entire buffer range