Boundary Control for Multi-Directional Traffic on Urban Networks

Liudmila Tumash (1) , Carlos Canudas de Wit (1) , Maria Laura Delle Monache (1)

1 DANCE - Dynamics and Control of Networks

This paper is devoted to the boundary control design for traffic evolving on large-scale urban networks. The state corresponds to the vehicle density that evolves on a continuum two-dimensional plane. This plane represents an urban network, whose parameters are interpolated as a function of distance to the physical roads. The dynamics of the vehicle density are governed by a newly developed multi-direction traffic flow model called the NSWE-model that encompasses a system of four coupled partial differential equations (PDEs). Each of these PDEs describes the density evolution in one of the four cardinal directions: North, South, West and East. For this model we design a control applied at the network's upstream boundary to drive a multi-directional congested traffic state to a desired equilibrium state. We analyse the class of desired states the system can be driven to. Finally, the result is validated numerically using the real network of Grenoble downtown.

Domaines: Equations aux dérivées partielles [math.AP]

Liudmila Tumash, Carlos Canudas de Wit, Maria Laura Delle Monache. Boundary Control for Multi-Directional Traffic on Urban Networks. 2021. ⟨hal-03182546v1⟩