Eur. Phys. J. B (2013) 86: 92
https://doi.org/10.1140/epjb/e2012-30688-6

Regular Article

Safe distance car-following model including backward-looking and its stability analysis

¹ School of Transportation and Logistics, Southwest Jiaotong University, 111 Erhuanlubeiyiduan, Chengdu 610031, P.R. China
² Department of Civil and Environmental Engineering, University of Wisconsin-Madison, 53706 Madison, USA
³ Department of Civil and Environmental Engineering, University of Texas-Austin, 78701 Austin, USA

^a Apt. 303, 1309 Spring Street, Madison, 53715 Wisconsin, USA, e-mail: yangd8@gmail.com

Received: 26 July 2012
Received in final form: 19 September 2012
Published online: 13 March 2013

Abstract

The focus of this paper is the car-following behavior including backward-looking, simply called the bi-directional looking car-following behavior. This study is motivated by the potential changes of the physical properties of traffic flow caused by the fast developing intelligent transportation system (ITS), especially the new connected vehicle technology. Existing studies on this topic focused on general motors (GM) models and optimal velocity (OV) models. The safe distance car-following model, Gipps’ model, which is more widely used in practice have not drawn too much attention in the bi-directional looking context. This paper explores the property of the bi-directional looking extension of Gipps’ safe distance model. The stability condition of the proposed model is derived using the linear stability theory and is verified using numerical simulations. The impacts of the driver and vehicle characteristics appeared in the proposed model on the traffic flow stability are also investigated. It is found that taking into account the backward-looking effect in car-following has three types of effect on traffic flow: stabilizing, destabilizing and producing non-physical phenomenon. This conclusion is more sophisticated than the study results based on the OV bi-directional looking car-following models. Moreover, the drivers who have the smaller reaction time or the larger additional delay and think the other vehicles have larger maximum decelerations can stabilize traffic flow.