Numerical approximations of a traffic flow model on networks

Abstract

We consider a mathematical model for fluid-dynamic flows on networks which is based on conservation laws. Road networks are considered as graphs composed by arcs that meet at some junctions. The crucial point is represented by junctions, where interactions occurr and the problem is underdetermined. The approximation of scalar conservation laws along arcs is carried out by using conservative methods, such as the classical Godunov scheme and the more recent discrete velocities kinetic schemes with the use of suitable boundary conditions at junctions. Riemann problems are solved by means of a simulation algorithm which proceeds processing each junction. We present the algorithm and its application to some simple test cases and to portions of urban network.

Error bounds for Kalman filters on traffic networks

“…Consider a linear discrete system describing the evolution of a moving object. The state vector is constructed as ρ k = ρ 1 k , ρ 2 k , ρ 3 k , where ρ 1 k|k , ρ 2 k|k , and ρ 3 k|k are the location, speed, and acceleration of the moving object at time k ∈ N, respectively. The moving object travels with a constant acceleration.…”

“…The traffic states on the one-dimensional local sections evolve according to the SMM, and the SMM-J is used to describe the evolution of traffic states on local sections with junctions.As shown inFigure 4, consider a local section with n cells, three links and a junction. The number of cells on each link is n 1 , n 2 , and n 3 , respectively, with n 1 + n 2 + n 3 = n. The state variable at time k ∈ N is constructed asρ k = ρ 1 k , • • • , ρ n1 k , ρ n1+1 k , • • • , ρ n1+n2 k , ρ n1+n2+1 k , • • • , ρ n k .As a common treatment[28,30,35,38,39], the boundary flows, denoted by φ 1 k , φ 2 k , and φ 3 k , are considered to be deterministic system inputs (please refer to[3] for the concept of using ghost cells to compute boundary flows using boundary state measurements). The SMM-J describes the evolution of ρ k using a switched linear dynamics, and is derived under the following assumptions:…”

Fluidsim: A Car Traffic Simulation Prototype Based on FluidDynamic

“…The choice of ∆s turns out to be a fundamental parameter in this sense. Let us now describe in more details the Godunov scheme, while we refer the reader to [25] for the other schemes.…”

Car path tracking in traffic flow networks with bounded buffers at junctions

“…More precisely, in the case of road networks, the macroscopic dynamics is typically given by hyperbolic conservation laws such that the traffic flow at junctions is distributed according to coupling conditions. Within this framework, also on‐ramps or roundabouts can be modeled, cf . In Goatin and Garavello and Herty et al, a novel type of intersection was introduced considering that junctions may have a storage capacity as buffers.…”

“…Within this framework, also on-ramps or roundabouts can be modeled, cf. 4 In Goatin and Garavello 5 and Herty et al, 6 a novel type of intersection was introduced considering that junctions may have a storage capacity as buffers. The approach is closely related to supply chains or production networks, where goods must wait in a buffer to be processed, see D'Apice et al 7 Recent publications couple microscopic and macroscopic models to analyze the path of a single vehicle that travels along a road, see previous studies.…”