Topology-based control design for congested areas in urban networks

Abstract

This paper addresses the problem of a boundary control design for traffic evolving in a large 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 a state with maximum possible throughput.

Boundary Control for Multi-Directional Traffic on Urban Networks

“…2b). It was found by first solving PDE for ρ (12) and then using (15), where we use α * = 0.51 obtained using (14). Further, we show the impact of boundary controller (18) on congested traffic after t = 5 min, t = 20 min and t = 50 min in Fig.…”

“…with α * given by (14). To get an expression for ρ d (x, y) at the boundary ∀(x, y) ∈ Γ out , we take ρ from step 1 and insert it into (15), which yields…”

“…Recently, [10] extended the LWR model to two dimensions with a space-dependent FD that incorporates network infrastructure parameters. A general method to calculate steady states in 2D LWR was presented in [13], while [14] elaborated a boundary controller for congested traffic that was further extended to traffic being in any (mixed) regime in [15]. L. Tumash and C. Canudas-de-Wit are with Univ.…”