A modified car-following model with variable safety distance and its feedback control research

Abstract

In this study, a modified car-following model is proposed to suppress the traffic jams. The optimal velocity (OV) function is extended by introducing variable safety headway distance. A comprehensive control scheme is constructed according to the feedback control theory. The stability condition for the modified model is obtained and the numerical simulation is carried out to illustrate the advantage of our model with the new control signal, and the results are consistent with the theoretical analysis. Introduction Over the last decades, traffic flow has gained more and more interests of many scholars and scientists, and traffic congestion has been a serious problem in the modern city traffic. In order to solve the increasingly serious traffic problems, research has been done on investigating the properties of traffic jams as much as possible, and obtained many significant results [1-7]. However, in expressway or highway with higher speed and larger headway, the models mentioned cannot be used to precisely reflect the real traffic phenomenon. In this case, the hyperbolic tangent part ( ) ( ) . tanh in OVM remains as a constant. That is to say, the following vehicle gets little or no influence despite the headway difference ( ) t xn ∆ is changing. So it is necessary to extend the typical safety headway distance parameter. Up to the present time, there has been a limited amount of research work concerning carfollowing model from the viewpoint of control methods [8-11]. And even fewer studies in the area have been conducted with considering variable safety headway distance(VSHD). In this paper, a new optimal velocity (OV) function with considering high speed following vehicle on expressway or highway is constructed by introducing variable safety headway distance. IMPROVED Car-following model To investigate the effect of high speed and large headway of vehicles in expressway or highway, a new car-following model is presented as follows: ( ) ( ) ( ) ( ) ( ) [ ] t v t v t x V a dt t x d n n n op new n − ∆ = , 2 2 (1) where ( ) ( ) ( ) t x t x t x n n n − = ∆ +1 is the headway difference between the th n considering vehicle and the preceding one; ( ) t xn is the th n vehicle's position; a is the sensitivity of driver and is the inverse of delay time; ( ) ( ) ( ) t v t x V n n op new , ∆ is the new optimal velocity function, which determines by the International Conference on Intelligent Systems Research and Mechatronics Engineering (ISRME 2015) © 2015. The authors Published by Atlantis Press 303 headway difference ( ) t xn ∆ and the variable safety headway distance. The new OV function can be expressed as: ( ) ( ) ( ) ( ) ( ) max tanh tanh 2 op new n n c c v V x t x t h h   = − +   � � (2) ( ) c s n v h T t dv h + = (3) where max v is the maximum speed of all the following vehicles, c h is the typical safety headway distance; s T is the time step unit and d is the reaction coefficient for ( ) t vn . In real traffic flow, the driver does not care about the specific value of the safety headway distance, unless the numerical value means traffic accident or danger. So the physical meaning of v h is the acceptable safety headway distance of a driver and it is variable and related with velocity of the considered vehicle. The dynamical equation is rewritten as follows: ( ) ( ) ( ) ( ) ( ) [ ] ( ) ( ) ( )    

Original document

The different versions of the original document can be found in:

• http://dx.doi.org/10.2991/isrme-15.2015.67 under the license https://creativecommons.org/licenses/by

• https://download.atlantis-press.com/article/18255.pdf

• https://www.atlantis-press.com/proceedings/isrme-15/18255,

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