Topology-based control design for congested areas in urban networks

TL;DR

This paper proposes a topology-based boundary control method for large-scale urban traffic networks to maximize vehicle throughput in congested areas, using macroscopic vehicle density models and network topology information.

Contribution

It introduces a novel control design approach that simplifies 2D traffic dynamics into 1D equations using curvilinear coordinates, enabling effective congestion management.

Findings

Successfully maximized throughput in a numerical example

Controlled congestion from full to optimal flow state

Validated theoretical results with simulations

Abstract

This paper addresses the problem of a boundary control design for traffic evolving in a large-scale urban network. The traffic state is described on a macroscopic scale and corresponds to the vehicle density, whose dynamics are governed by a two-dimensional conservation law. We aim at designing a boundary control law such that the throughput of vehicles in a congested area is maximized. Thereby, the only knowledge we use is the network's topology, capacities of its roads and speed limits. In order to achieve this goal, we treat a 2D equation as a set of 1D equations by introducing curvilinear coordinates satisfying special properties. The theoretical results are verified on a numerical example, where an initially fully congested area is driven to the state with maximum possible througput.