Queueing analysis of high-speed networks with Gaussian traffic models

Jinwoo Choe, Purdue University

Abstract

In this thesis, we study an important measure of network congestion: the queue length (buffer occupancy) distribution at a (statistical) multiplexer. In our approach, by appealing to the Central Limit Theorem, we model a multiplexer as a fluid queue serving a Gaussian input process at a constant service rate. We first consider the case when the input process is short-range dependent, and derive two asymptotic upper bounds for [special characters omitted], the tail of the queue length distribution. One of our bounds is in a single-exponential form and provides an upper bound to the asymptotic constant (i.e., the leading constant of the exponential asymptote of the tail probability). However, we show that this bound, being of a single-exponential form, may not accurately capture the tail probability. Our numerical studies on a known lower bound motivate the development of our second asymptotic upper bound. This bound, which we call the maximum-variance asymptotic upper bound, is expressed in terms of the maximum variance of a Gaussian process, and enables the accurate estimation of the tail probability over a wide range of queue lengths. We also consider the cases when the input process is long-range dependent, and derive stronger asymptotic results than currently available in the literature. These results suggest that the same expression as the maximum-variance asymptotic upper bound should provide an accurate estimate of the tail probability, even when the input process is long-range dependent. We apply our results to Gaussian as well as multiplexed non-Gaussian traffic sources (such as voice and video traffic sources), and validate the performance of the Gaussian traffic modeling via simulations. Our analytical study is based on Extreme Value Theory, and therefore different from the approaches using traditional Markovian and large deviation techniques.

Degree

Ph.D.

Advisors

Shroff, Purdue University.

Subject Area

Electrical engineering

COinS