The KdV—Burgers equation in a modified speed gradient continuum model

Abstract

In this paper, the Taylor expansion is adopted to modify the model. The backward travel problem is overcome by our model, which exists in many higher-order continuum models. The neutral stability condition of the model is obtained through the linear stability analysis. Nonlinear analysis shows clearly that the density fluctuation in traffic flow leads to a variety of density waves. Moreover, the Korteweg-de Vries-Burgers (KdV-Burgers) equation is derived to describe the traffic flow near the neutral stability line and the corresponding solution for traffic density wave is derived. The numerical simulation is carried out to investigate the local cluster effects. The results are consistent with the realistic traffic flow and also further verify the results of nonlinear analysis.

Bifurcation analysis of a speed gradient continuum traffic flow model

“…The critical density values of the model corresponding to the parameters above were 0.042 veh/m and 0.07 veh/m, which can easily be found out by the stability condition [21]. The traffic flow will be unstable between these critical densities.…”

“…L.L. Lai et al [21] studied the model with a periodic boundary condition. In fact, the traffic phenomena induced by the bifurcation critical points on an open road are much more obvious than those on a closed road, so we here assume that the main road is an open road, i.e., ρ (1, t) = ρ (2, t) , ρ (L, t) = ρ (L − 1, t) , v (1, t) = v (2, t) , v (L, t) = v (L − 1, t) .…”

Stability analysis of a viscous continuous traffic flow model

“…In 2000, Aw [6] first proposed the anisotropic speed gradient model. After that, some similar macro anisotropic models had been proposed [7][8][9][10] .…”

“…At present, the research on macro traffic flow mainly focus on analyzing the stability by using characteristic analysis method, deriving the solution equations of different regions [8,9,10] . There are few studies on the equilibrium point and its stability.…”