Perimeter and boundary flow control for heterogeneous transportation 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 network-wide mean flow and density of vehicles. A generic mathematical model for multi-reservoir networks with well-defined MFDs for each reservoir is presented first. Then, an optimal control methodology is employed for the design of perimeter and boundary 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. Perimeter control occurs at the periphery of the network while boundary control occurs at the inter-transfers between neighborhood reservoirs. Based on this control methodology, control actions may be computed in real-time through a linear multivariable integral feedback regulator (LQI). To this end, the heterogeneous network of Downtown San Francisco is partitioned into three homogeneous reservoirs that exhibit well-defined MFDs. These MFDs are then used to design and compare the proposed LQI regulator with a pre-timed signal control plan and a bang-bang controller. Finally, the impact of the control actions to the network is demonstrated via simulation by the use of the corresponding MFDs and other performance measures.