2021/03/16 by Liudmila Tumash, Tumash, Liudmila, Carlos Canudas de Wit +3
Engineering · Social Sciences · #Analysis of PDEs (math.AP) #Evacuation and Crowd Dynamics #FOS: Mathematics #Optimization and Control (math.OC) #Traffic control and management #Transportation Planning and Optimization
paper · pdf · doi:10.48550/arxiv.2103.08998
openalex publication_date 2021/03/16 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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.