Perimeter flow control in heterogeneous networks

In this paper, we macroscopically describe the traffic dynamics in heterogeneous transportation networks by utilizing the Macroscopic Fundamental Diagram (MFD) for urban networks a widely observed relation between mean flow and density of vehicles. A generic mathematical model for multi-reservoir networks with well-defined MFDs for each reservoir is presented first. Two alternative optimal control methodologies are employed for the design of perimeter flow control strategies that aim at distributing the accumulation in each reservoir as homogeneously as possible, and maintaining the rate of vehicles that are allowed to enter each reservoir around a desired point, while the system’s throughput is maximized. Based on the two control methodologies, perimeter control actions may be computed in real-time through a linear multivariable feedback regulator (LQ) and a linear multivariable integral feedback regulator (LQI). To this end, the heterogeneous network of the Downtown of San Francisco is partitioned into three homogeneous reservoirs that exhibit well-defined MFDs. These MFDs are then used to design and compare the proposed multivariable regulators with a pre-timed signal control plan and a single-reservoir perimeter control strategy. The impact of the perimeter control actions to the three reservoirs and the whole network is demonstrated via simulation by the use of the corresponding MFDs.