The “backward-looking” effect in the continuum model considering a new backward equilibrium velocity function

Md Anowar Hossain,Jun Tanimoto

doi:10.1007/s11071-021-06894-2

Abstract

In this paper, a new continuum traffic model is developed considering the backward-looking effect through a new positive backward equilibrium speed function. As compared with the conventional full velocity difference model, the backward equilibrium velocity function, which is largely acceptably grounded from mathematical and physical perspectives, plays an important role in significantly enhancing the stability of the traffic flow field. A linear stability condition is derived to demonstrate the flow neutralization capacity of the model, whereas the Korteweg–de Vries–Burgers equation and the attendant analytical solution are deduced using nonlinear analysis to observe the traffic flow behavior near the neutral stability condition. A numerical simulation, used to determine the flow stability enhancement efficiency of the model, is also conducted to verify the theoretical results.

Highlights

In recent years, mass communication complexities have emerged within urban society
The model was fully consistent with the conventional full velocity difference (FVD) model when presuming p = 1.0, with the flow stabilization capacity of the proposed model significantly increased compared with the conventional FVD model, as shown in Fig. 1a and Fig
The backward equilibrium speed function was improved with the introduction of a positive function, much like with the forward equilibrium function, rather than the negative function used in previous studies

Summary

Introduction

Mass communication complexities have emerged within urban society. Scientists, transportation engineers, and local governments have put forward various ideas and projects to overcome the problem of traffic congestion. The BLOV car-following model is largely heralded from a real-life viewpoint, the model has several crucial drawbacks in terms of formulating the backward OV function, which is defined by a negative function that is regarded as unrealistic. To overcome this drawback, various robust car-following models have been proposed [37, 38] with the incorporation of a new backward OV function as a positive function, which inevitably increases the stability of the flow field.

Model formulation

Linear stability analysis

Nonlinear analysis

Numerical simulations

Findings

Conclusion