Family of macroscopic node models

Abstract

The complete family of theoretically sound macroscopic node models is presented and analysed. Based on the behaviour of drivers approaching and passing through intersections, an analytical model family is presented. Properties like the invariance principle and the conservation of turning fractions are satisfied. The model family is analysed using max-plus algebra and the complete set of feasible solutions is determined. The node models proposed by Tampère et al. (2011), Gibb (2011), and Flötteröd & Rohde (2011) are members of the family. Furthermore, efficient methods to determine solutions of the node model are presented. Such methods are very useful in dynamic network loading which is in turn key for dynamic traffic assignment.