Boundary Control for Multi-Directional Traffic on Urban Networks

Abstract

This paper is devoted to boundary control design for urban traffic described on a macroscopic scale. The state corresponds to vehicle density that evolves on a continuum two-dimensional domain that represents a continuous approximation of a urban network. Its parameters are interpolated as a function of distance to physical roads. The dynamics are governed by a new macroscopic multi-directional traffic model that encompasses a system of four coupled partial differential equations (PDE) each describing density evolution in one direction layer: North, East, West and South (NEWS). We analyse the class of desired states that the density governed by NEWS model can achieve. Then a boundary control is designed to drive congested traffic to an equilibrium with the minimal congestion level. The result is validated numerically using the real structure of Grenoble downtown (a city in France).

Controller design for heterogeneous traffic with bottleneck and disturbances

“…It is natural to use the boundary control on the available control signals as the ramp metering or the variable speed limit to stabilize the highway traffic systems. Paper [21] contributes to the boundary control design for the multi-directional congested traffic evolving on the large-scale urban networks represented by a continuum two-dimensional plane. In [24], a reinforcement learning boundary controller is designed to mitigate the stop-and-go congested traffic for the 2 × 2 quasilinear Aw-Rascle-Zhang (ARZ) partial differential equations ⋆ Corresponding author Lina Guan.…”

Multi-directional continuous traffic model for large-scale urban networks

“…Also unlike [40], the NEWS model can be applied to any kind of sparse urban networks, since it treats densities in a 1D sense, and therefore does not rely on the assumption that a urban network is dense enough to be approximated as a continuum. A simple control for congested traffic with NEWS-governed dynamics has already been presented in [42].…”