Multiclass first-order modelling of traffic networks using discontinuous flow-density relationships

Recently, the modelling of heterogeneous traffic flow has gained significant attention from traffic theorists. The influence of slow vehicles ( e. g. trucks) on traffic operations has been studied both from a micro and macroscopic level. Though multiclass traffic models have been successfully developed in literature, few of them are adequately used to describe traffic network operations. To this end, this article aims to propose a model to study the ( heterogeneous) traffic network operations based on the macroscopic modelling approach. More specifically, on the one hand, we introduce an extension of the classic Lighthill-Whitham-Richards model to describe multiclass traffic operations in the network. The proposed model is based on solving a system of hyperbolic partial differential equations describing multiclass traffic dynamics with discontinuous fluxes. On the other hand, a dynamic routing algorithm is applied to determine the turning flow at nodes based on the information provision of the current network situation. Numerical results have shown that the proposed model can capture some real traffic phenomena in multiclass traffic networks.