The Hamilton-Jacobi Partial Differential Equation and the Three Representations of Traffic Flow

119 citations recorded by the source corpus.

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

Stochastic Approximations for the Macroscopic Fundamental Diagram of Urban Networks (2015, methodology): “This gives the lattice X-model in Laval and Leclercq (2013): Xt̃,̃n = min { Xt̃−1,̃n + θΔx, Xt̃−1,̃n−1 − Δx } (C.1) To keep the solution exact, θ has to be an integer and Δn = κΔx,Δt = Δx/w.”
Traffic state estimation on highway: A comprehensive survey (2017, methodology): “A traffic state in a time–space region A was defined by Edie as follows: 3Technically, a set of two variables from among flow or headway, density or spacing, and speed or pace (Laval and Leclercq, 2013) is a sufficient definition for a traffic state, since q = ρv holds.”