An extended traffic flow model on a gradient highway with the consideration of the relative velocity

Abstract

In this paper, an extended traffic flow model on a single-lane gradient highway is proposed with the consideration of the relative velocity. The stability condition is obtained by the use of linear stability analysis. It is shown that the stability of traffic flow on the gradient varies with the slope and the coefficient of the relative velocity: when the slope is constant, the stable regions increase with the increase of the coefficient of the relative velocity; when the coefficient of the relative velocity is constant, the stable regions increase with the decrease of the slope in downhill and increase with the increase of the slope in uphill. The Burgers, Korteweg-de Vries, and modified Korteweg-de Vries equations are derived to describe the triangular shock waves, soliton waves, and kink-antikink waves in the stable, metastable, and unstable region, respectively. The numerical simulation shows a good agreement with the analytical result, which shows that the traffic congestion can be suppressed by introducing the relative velocity.

A New Continuum Model considering Driving Behaviors and Electronic Throttle Effect on a Gradient Highway

“…In recent years, in the theory of carfollowing, the slope factor has also been considered by researchers. For example, Yang et al [52] gave a car-following model on the slope to study the effects of the road's slope on the electricity consumption, Zhou et al [53] came up with a generalized car-following model of relative speed on slope, and considering the influence of gravity, Chen et al [54] proposed a generalized model with consideration of the gravitational force. However, the above models do not consider the driver's driving characteristics and the influence of electronic throttle effect on the stability of traffic flow.…”

“…e following is an extended model of the relative velocity of traffic flow on a gradient road proposed by Zhou et al [53] in 2014,…”

Introducing the Effects of Road Geometry Into Microscopic Traffic Models for Automated Vehicles

“…To account for the influences of road slope, different approaches have been used so far in the literature to extend the OVM ( [9], [10]), the FVDM ( [11], [12]), and the IDM [13] car following models.…”

Robust Stabilization and H∞ Control of Cooperative Driving System with Time Delay in Variable Speed‐Limited Area from Cyber‐Physical Perspective

“…These were presented in [17][18][19][20][21]. In addition, some modified coupled map OV models were proposed to direct at different conditions and factors, such as road structures [22,23] and multiple vehicles systems [24,25]. Time delays lead to poor driving behavior, weak robustness, and instability [26][27][28].…”