The motivation behind this research is the need for a real-time implementable, yet accurate, procedure for estimating an origin-destination (O-D) trip-table based on entering and exiting traffic volume data for a given freeway section. These tables help in on-line control of traffic facilities, and consequently, are of significant use in alleviating traffic congestion. The dynamism of the approach captures the variations in the traffic counts with time which are in tum used to predict user travel patterns. Two models have been developed for this problem, one based on a least squares estimation and the other based on an <i>1</i>₁ norm approach. Two projected conjugate gradient schemes are investigated for solving the constrained least squares problem, and an interior point affine scaling algorithm that is applied to the dual problem is explored for solving the <i>1</i>₁ estimation linear programming problem. Computational results are presented on a set of test problems involving the determination of O-D trip tables for both intersection and freeway scenarios in order to demonstrate the viability of the proposed methods. These results exhibit that, unlike as reported in the literature based on previous efforts, properly designed parameter optimization methods can indeed provide accurate estimates in a realtime implementation. Hence, this research presents a competitive alternative to the iterative statistical techniques that have been heretofore used because of their real-time processing capabilities, despite their inherent inaccuracies. We hope that the proposed technology enhances existing methods for constructing O-D trip-tables from traffic counts. / Master of Science