A macroscopic model for multiple user-class traffic operations: Derivation, analysis and numerical results

Abstract

In this report we derive a macroscopic Multiple User-Class traffic model from mesoscopic principles. These principles yield equilibrium relationships between traffic density and equilibrium velocities as a function of the current traffic conditions, the traffic composition, and the distribution of user-class dependent desired velocities, rather than these relations need to be defined exogenously. These relations encompass contributions of drivers accelerating towards their user-class specific desired velocity on the one hand, and contributions resulting from interaction between vehicles of the same or different classes on the other hand. Additionally, the velocity variance variable is introduced describing deviations from the average speed within the user-classes. We discuss several mathematical properties of the MUC equations. One of the results is an alternative model formulation, namely using the so-called conservative variables desity, momentum and energy, rather than the primitive variables density, velocity and velocity variance. Using this formulation, several new approaches are derived to numerically approximate solutions of the flow model. We discuss first results from macroscopic simulation using the developed multiple user-class traffic flow model. The simulation results are employed to investigate whether fundamental traffic flow model-equations hold. It is concluded that the MUC-model satisfies the anisotropy condition, the 'invariant personality condition', and the 'unaffected slow vehicles' condition. A test case illustrates the self-formation of congestion.

Original document

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