Macroscopic fundamental diagram in simple model of urban traffic

Abstract

Macroscopic fundamental diagram (MFD) is a reproducible unimodal relation between average vehicle density and average flow rate in urban traffic. Although this idea is tested by a few observations and simulations, its mechanism is not well understood. In order to understand it, a simple graph-based model of urban traffic is proposed. MFDs in our model system are investigated numerically for grid networks. It is found that MFDs in our system are discontinuous, which is inconsistent with the observation of real urban traffic.