Harmonic Analysis and Optimization of Traffic Signal Systems

Abstract

This paper develops applications of harmonic analysis for traffic signal performance evaluation and optimization. Link Performance Functions in synchronized signal networks measure delay or travel time as a function of offsets.They depend on a variety of factors, including: traffic flow characteristics, link physical characteristics, and traffic signal controls. Being periodic with the cycle time they can be modeled as a Fourier Serieswhich is an expansion of a periodic function f(x)in terms of a sum of sines and cosines. Just a few harmonics can provide good approximations to the original functions. The paper shows how to derive the principal harmonics in terms of the underlying traffic, link and signal data. This enables one to construct a simple and very effective model for analysis, optimization and control. The paper proceeds to apply this model in two cases. The first case involves performance estimation of signal controlled intersections for planning and design purposes. The second case develops a novel Dynamic Programming optimization model which provides a rigorous procedure for signal coordination and synchronization.