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 cities is presented. The proposed scheme determines feasible and optimally distributed input flows for the various gates located at the periphery of a protected network. A parsimonious model is employed to describe the traffic dynamics of the protected network. To describe traffic dynamics outside of the protected area, the state-space model is augmented with additional state variables to account for vehicle queues at store-and-forward origin links at the periphery. The perimeter flow control problem is formulated as a convex optimisation problem with finite horizon, and constrained control and state variables. It 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 system as the initial state as well as predicted demand flows at entrance links. Furthermore, practical flow allocation policies for single-region perimeter control without explicitly considering entrance link dynamics are presented. These policies allocate a global perimeter-ordered flow to candidate gates at the periphery of a protected network 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 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 have showed that the proposed scheme is able to manage excessive queues outside of the protected network and to optimally distribute the input flows, which confirms its efficiency and equity properties.

Figures (6)

• Figure 1: Protected network with entrance link dynamics.
• Figure 2: Description of downtown San Francisco: (a) Protected network area (boundary in red colour) and fifteen controlled gates of entrance (illustrated by the blue arrows); (b) Network fundamental diagram of downtown San Francisco, adopted by KA_NG_PartB:2013. R1-R10 denote ten different replications in AIMSUN microscopic simulator to reproduce the NFD.
• Figure 3: (a) Demand/disturbances within the protected network area; (b) and (c) Sensitivity analysis and performance of multi-gated perimeter flow control for different optimisation horizon $N_o$ and different demand scenarios: (b) TTS within the protected network and outside network area; (c) RQB within the protected network and outside network area; Each line in the legend of the figures indicates a different initial state $n(0)$ veh for a different demand scenario (-d: no demand, md: medium demand, hd: high demand).
• Figure 4: (a, b) State and control trajectories without link dynamics; (c) State trajectories of the protected network for different initial points with and without disturbance; (d--o) State and control trajectories of six selected origin links (gates) for different initial points with and without disturbance. For the initial value of vehicle accumulation $n(0)$, see the legend in each subfigure; initial queues at origin links $\ell_o(0) = 0.7 \ell_{o,\max}, \, \forall\, o \in \cal O$.
• Figure 5: Total time spent within the protected network and gated links under MGC, CAP, and OAP for four initial states in a scenario without external demand.