Traffic Flow Theory and Chaotic Behavior

摘要

Many commonly occurring natural systems are modeled with mathematical experessions and exhibit a certain stability. The inherent stability of these equations allows them to serve as the basis for engineering predictions. More complex models, such as those for modeling traffic flow, lack stability and thus require considerable care when used as a basis for predictions. In 1960, Gazis, Herman, and Rothery introduced their generalized car-follow (or GHR) equation for modeling traffic flow. Experience has shown that this equation may not be continuous for the entire range of input parameters. The discontinuous behavior and nonlinearity of the equations suggest chaotic solutions for certain ranges of input parameters. Understanding the chaotic tendencies of this equation allows engineers to improve the reliability of models and predictions based on those models. The paper describes chaotic behavior and briefly discusses the methodology of the algorithm used to detect its presence in the GHR equation. It also discusses two systems modeled with the GHR equation and their associated chaotic properties.