In this paper, a new high-order continuum model for a freeway with merging and diverging geometries is presented. Three formulations describing traffic friction at freeway merging or diverging areas are reviewed. A new formulation for traffic friction is proposed and compared with the existing formulations based on tests against field data. In addition, a numerical modification for avoiding unjustified upstream flow propagation that has been observed in high-order models is developed. For this purpose, a Riemann problem-based method, namely the Harten-Lax-van Leer (HLLE) flux-difference splitting method, is employed. Intuitive tests demonstrate that such an approach can be very successful in preventing the flow from moving at negative speed. Field data tests for merging and diverging freeway geometries show that implementation of the proposed high-order model with the HLLE method yields low error levels and is more accurate than the simple continuum model at congested flows. Furthermore the proposed formulation for traffic friction seems to yield a smaller error in volume than the existing formulations. In addition the proposed high-order model is less sensitive to the choice of the speed-density relationship.
Liu, G., Lyrintzis, A. S., & Michalopoulos, P. G. (1996). Modelling of freeway merging and diverging flow dynamics. Applied Mathematical Modelling, 20(6), 459–469. https://doi.org/10.1016/0307-904X(95)00165-G