Optimal perimeter control for Three Urban Regions

Homogenous network regions have been given a relationship between network vehicle density and network space-mean flow by a macroscopic fundamental diagram (MFD) which is used on the urban traffic. This point has been achieved from empirical data analysis of cities. We formulate the optimal perimeter control for three-region urban cities by using MFDs. Then each of these regions is modeled as a simple system. Model predictive control (MPC) is a method to find a solution for the optimal perimeter control problem. It is obvious that there are low interactions between regions, but in this paper, for simplifying the system models and equations these interactions are eliminated. Besides the MPC form, we used a PID controller for these systems to show differences between the two methods. PID controller cannot track systems carefully but it can get us an average of the flow of each system but in the MPC form tracking is more accurate and comparison results illustrate which the performances of the model predictive control (MPC) are finer than the PID controller. The results which are discussed in this paper can be expanded to improve the efficiency of the hierarchical control strategies for heterogeneously crowded cities.