Derivation of Non-local Macroscopic Traffic Equations and Consistent Traffic Pressures from Microscopic Car-Following Models

Abstract

AbstractThis contribution compares several different approaches allowing one to derive macroscopic traffic equation directly from microscopic car-following models. While it is shown that some conventional approaches lead to theoretical problems, it is proposed to use an approach reminding of smoothed particle hydrodynamics to avoid gradient expansions. The derivation circumvents approximations and, therefore, demonstrates the large range of validity of macroscopic traffic equations, without the need of averaging over many vehicles. It also gives an expression for the “traffic pressure”, which generalizes previously used formulas. Furthermore, the method avoids theoretical inconsistencies of macroscopic traffic models, which have been criticized in the past by Daganzo and others.KeywordsTraffic PressureMacroscopic Traffic ModelsGradient ExpansionSmoothed Particle HydrodynamicsTheoretical InconsistenciesThese keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.