This article has been accepted for inclusion in a future issue of this journal. Content is final as presented, with the exception of pagination. IEEE TRANSACTIONS ON INTELLIGENT TRANSPORTATION SYSTEMS 1 A Formal Approach for Modeling and Simulation of Human Car-Following Behavior Jin Woo Ro , Partha S. Roop, Avinash Malik, and Prakash Ranjitkar Abstract—Car-following is the activity of safely driving behind a leading vehicle. Traditional mathematical car-following models capture vehicle dynamics without considering human factors, such as driver distraction and the reaction delay. Consequently, the resultant model produces overly safe driving traces during simulation, which are unrealistic. Some recent work incorporate simplistic human factors, though model validation using experi- mental data is lacking. In this paper, we incorporate three distinct human factors in new compositional car-following model called modal car-following model, which is based on hybrid input output automata (HIOA). HIOA have been widely used for the specifica- tion and verification of cyber-physical systems. HIOA incorporate the modeling of the physical system combined with discrete mode switches, which is ideal for describing piece-wise continuous phenomena. Thus, HIOA models offer a succinct framework for the specification of car-following behavior. The human factors considered in our approach are estimation error (due to imperfect distance perception), reaction delay, and temporal anticipation. Two widely used car-following models called Intelligent Driver Model (IDM) and Full Velocity Difference Model (FVDM) are used for extension and comparison purpose. We evaluate the root mean square (rms) error of the following vehicle position using the traces obtained from human drives through different driving scenarios. The result shows that our model reduces the rms error in IDM and FVDM by up to 48.8% and 7.41%, respectively. Index Terms— Cyber-physical systems, vehicle dynamics, human factors. I. I NTRODUCTION I NTELLIGENT Transportation Systems (ITS) [1] seek to combine advances in computer and transportation engineer- ing to improve the overall safety and efficiency of the road net- work. An example of Intelligent Transportation Systems (ITS) is the vehicle platooning system [2] which aims is to improve the traffic flow by minimizing the distance between vehicles while ensuring safety. Since human drivers can be involved in the system, human driving behaviour needs to be considered during the simulation. For this purpose, Car-following (CF) model [3], [4] have been widely used to simulate the human driving behaviours, and the model accuracy in terms of the generated vehicle trajectory is of the most important aspect for the simulation. Manuscript received February 4, 2017; revised April 11, 2017 and September 11, 2017; accepted September 21, 2017. The Associate Editor for this paper was P. Zingaretti (Guest Editor MESA). (Corresponding author: Jin Woo Ro.) The authors are with the Electrical and Computer System Engineering Department, The University of Auckland, Auckland 1141, New Zealand (e-mail: jinwooro@gmail.com). Color versions of one or more of the figures in this paper are available online at http://ieeexplore.ieee.org. Digital Object Identifier 10.1109/TITS.2017.2759273 The car-following behaviour consists of mechanical (i.e., one dimensional vehicle kinematics) and psychologi- cal (i.e., random human factors such as delay, imperfect distance perception) aspects [5], [6]. The conventional CF models largely ignore the psychological aspect by oversim- plifying the human factors [6]. Such models are particularly appreciated in the city-level traffic simulation [5], however, for the safety-critical ITS simulation, it is more desirable to examine the influence of the random human behaviours on the system. For example, observing systems with nondeterministic human responses can be useful for detecting the system failure (e.g., crash). Thus, the need for modelling human factors in car-following movement has been addressed in [5]. The car-following behaviour in a platoon can be modelled as a cyber-physical system [7], where a network of distrib- uted controllers (i.e., human drivers) are used for controlling physical processes (i.e., one dimensional vehicle kinematics). In formally modelling such a system, Hybrid Input Output Automata (HIOA) [8], [9] is widely used as the framework to capture the discrete control operation (e.g., human reaction) and the continuous evolution of variables (e.g., velocity). A formal model of the system can used for correct imple- mentation of the model and also can be used for the formal verification. Particularly, it is known that the state-of-the- art traffic microsimulators, VISSIM [10] and AIMSUN [11], can produce undesirable behaviour such as vehicle passing through another vehicle and vehicle disappearance [12]. Such ambiguous and incorrect behaviour should be avoided in the design of safety critical ITS. In order to avoid such problems, we propose the use of HIOA as a formal model of the human car-following behaviour. To the best of our knowledge, it is the first time that the random human reaction delay is designed using HIOA. In this paper, we formulate three well-known human factors: estimation error, reaction delay, and temporal anticipation. Since human factors are based on random “mode changes”, we explicitly bound the possible random behaviour within the realistic range as reported in [13] and [14]. For mod- elling human factors and car-following dynamics, we use for the first time, a formal model called Hybrid Input Output Automata (HIOA) [8], [9]. HIOA effectively captures both the discrete and continuous evolution of car-following behaviour not feasible in earlier models. Since our model operates based on “modes”, we call our work as Modal Car-following Model (MCFM). Results include comparison of the proposed model with experimental data collected from human drivers. 1524-9050 © 2017 IEEE. Personal use is permitted, but republication/redistribution requires IEEE permission. See http://www.ieee.org/publications_standards/publications/rights/index.html for more information.