Macroscopic traffic dynamics with heterogeneous route patterns

Abstract

This paper investigates at an aggregated (macroscopic) scale the effects of route patterns on a road network. Four main variables are considered: the production, the mean speed, the outflow and the mean travel distance. First, a simple network with heterogeneous travel distances between origins and destinations is studied by simulation. It appears that the mean travel distance is not only very sensitive to the changes in the origin–destination (OD) matrix but also to the internal traffic conditions within the network. When this distance is assumed constant as usual in the literature, significant errors may appear when estimating the outflow at the network perimeter. The OD matrix also modifies the shape of the macroscopic fundamental diagram (MFD) to a lesser extend. Second, a new modeling framework is proposed to account for multiple macroscopic routes within reservoirs (spatial aggregates of road network) in the context of MFD simulation. In contrast to existing works, partial accumulations are defined per route and traffic waves are tracked at this level. This leads to a better representation of wave propagation between the reservoir frontiers. A Godunov scheme is combined to a HLL Riemann approximate solver in order to derive the model numerical solutions. The accuracy of the resulting scheme is assessed for several simple cases. The new framework is similar to some multiclass models that have been elaborated in the context of link traffic dynamics.