Urban Traffic State Analysis Based on the Macroscopic Fundamental Diagrams of the Variability of Vehicle Densities

Macroscopic network traffic state analysis is the premise of relieving urban traffic congestion. Computer simulations contribute to settle the complexity of the urban network traffic flow dynamics in traffic states research. In this paper, we make a simulation of urban network gridlock formation process for the study of the variability of vehicle densities. Based on the simulation results, we get there important conclusions about network vehicle densities and put forward the concept of the standard deviation of the number of vehicles on all links (SDVL). We also use a mathematic matrix analysis method to verify the conclusions. Then we show that there exist macroscopic fundamental diagrams (MFD) based on SDVL. We describe and explain the shape of the SDVL-MFD using simulation data. And an effective macroscopic traffic state analysis method is proposed on the basis of macroscopic fundamental relations of SDVL, which could provide decision support for signal control scheme optimization and traffic state forecasting.