Hindawi Publishing Corporation Mathematical Problems in Engineering Volume 2013, Article ID 408756, 13 pages http://dx.doi.org/10.1155/2013/408756 Research Article A Car-Following Model Based on Quantified Homeostatic Risk Perception Guangquan Lu, 1 Bo Cheng, 2 Yunpeng Wang, 1 and Qingfeng Lin 1 1 Beijing Key Laboratory for Cooperative Vehicle Infrastructure Systems and Safety Control, Beihang University, Beijing 100191, China 2 State Key Laboratory of Automotive Safety and Energy, Tsinghua University, Beijing 100084, China Correspondence should be addressed to Guangquan Lu; lugq@buaa.edu.cn Received 16 April 2013; Revised 18 September 2013; Accepted 8 October 2013 Academic Editor: Cesar Cruz-Hernandez Copyright © 2013 Guangquan Lu et al. is is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. is study attempts to elucidate individual car-following behavior using risk homeostasis theory (RHT). On the basis of this theory and the stimulus-response concept, we develop a desired safety margin (DSM) model. Safety margin, defined as the level of perceived risk in car-following processes, is proposed and considered to be a stimulus parameter. Acceleration is assessed in accordance with the difference between the perceived safety margin (perceived level of risk) and desired safety margin (acceptable level of risk) of a driver in a car-following situation. Sixty-three cases selected from Next Generation Simulation (NGSIM) are used to calibrate the parameters of the proposed model for general car-following behavior. Other eight cases with two following cars taken from NGSIM are used to validate the model. A car-following case with stop-and-go processes is also used to demonstrate the performance of the proposed model. e simulation results are then compared with the calculations derived using the Gazis- Herman-Rothery (GHR) model. As a result, the DSM and GHR models yield similar results and the proposed model is effective for simulation of car following. By adjusting model parameters, the proposed model can simulate different driving behaviors. e proposed model gives a new way to explain car-following process by RHT. 1. Introduction Car-following models are used to determine individual driving behaviors under continuous traffic flow, in which vehicles do not make lane changes [1]. ese models are important for autonomous cruise control systems [2, 3] and are considered key evaluation tools for intelligent transporta- tion system strategies [4–6]. A number of researchers have proposed mathematical models for car-following simulation. Brackstone and McDonald provided an excellent review on the history of car-following models proposed in the 20th century [7]. Many studies have recently explored car- following behavior to improve existing models or construct new ones [1, 8–21]. Some researchers focus on the stability analysis of car following [16, 19]. Although most of the reviewed models effectively simu- late car-following behaviors and determine how car following occurs in actual scenarios, the reason why vehicles follow one another in a certain manner remains unclear. Hamdar et al. explained car-following behaviors based on the prospect the- ory of Kahnemann and Tversky and proposed a car following model by evaluating the gains and losses while driving [21]. Another risk-taking theory, Wilde’s risk homeostasis theory (RHT) is also helpful to explain car-following behaviors [22]. Wilde defines driving behavior as a homeostatic con- trolled self-regulation process, in which a driver alters his/her current behavior aſter comparing the instantaneously expe- rienced level of risk with the level of risk he/she is willing to take [22, 23]. According to RHT, people develop behav- ioral adaptation to compensate for the difference between perceived and acceptable risk [24]. is theory maintains that individuals submit to a certain level of subjectively estimated risk to their health or safety in exchange for the benefits they hope to receive from that activity [25]. Quantifying risk, especially perceived risk, is one of the key problems in RHT research. Some scholars quantify risk in RHT as “the accident