Macroscopic analysis of the fundamental diagram with inhomogeneous network and instable traffic

In this study, a region-based dynamic model is proposed to depict the traffic dynamics of an idealised grid-like unidirectional road network, and the impact of heterogeneity of the network on macroscopic traffic flow is investigated. The equilibrium solutions are obtained by solving the dynamic model, and the method of linear stability analysis is applied to test the stability of the solutions. Accordingly, the curves of macroscopic fundamental diagram (MFD) for various inhomogeneous networks are plotted and the effects of network heterogeneity on MFD are revealed. Two network heterogeneity parameters, road capacity and the attraction strength of a sub-region in the road network, are considered and the results show that both of them affect the shape of MFD significantly. Numerical simulations are performed and the result supports the theoretical analysis.