Multi-gated perimeter flow control for monocentric cities: Efficiency and equity

Abstract

A control scheme for the multi-gated perimeter traffic flow control problem of monocentric cities is presented. The proposed scheme determines feasible and optimally distributed input flows for various gates located at the periphery of a protected network area. A parsimonious model is employed to describe the traffic dynamics of the protected network. To describe traffic dynamics outside of the protected area, the basic state-space model is augmented with additional state variables to account for vehicle queues at store-and-forward origin links at the periphery. The multi-gated perimeter flow control problem is formulated as a convex optimisation problem with finite horizon, and constrained control and state variables. This scheme aims to equalise the relative queues at origin links and to maintain the vehicle accumulation in the protected network around a desired set point, while the system’s throughput is maximised. For real-time control, the optimal control problem is embedded in a rolling-horizon scheme using the current state of the whole system as the initial state as well as predicted demand flows at origin/entrance links. Furthermore, practical flow allocation policies for single-region perimeter control strategies without explicitly considering entrance link dynamics are presented. These policies allocate a global perimeter-ordered flow to a number of candidate gates at the periphery of a protected network area by taking into account the different geometric characteristics of origin links. The proposed flow allocation policies are then benchmarked against the multi-gated perimeter flow control. A meticulous study is carried out for a 2.5 square mile protected network area of San Francisco, CA, including fifteen gates of different geometric characteristics. The results showed that the proposed approach is able to manage excessive queues outside of the protected network area and to optimally distribute the input flows, which confirms its efficiency and equity properties. Similar policies are expected to be utilised for dynamic routing and road pricing.