۱- Introduction and motivation

۲- Literature review

۳- Methodology

۴- Data and calibration

۵- Simulation analysis

۶- Conclusions

References

Abstract

The objective of this paper is to develop a micro-economic modeling approach for car-following behaviors that may capture different risk-taking tendencies when dealing with different traffic conditions. The proposed framework allows for the consideration of perception subjectivity and judgement errors that may lead to unsafe acceleration driving maneuvers with the possibility of real-end collisions. The modeling approach relies on a generalized utilitybased formulation with three specific types of subjective utility functions (SUFs): Prospect Utility (PT) subjective utility function, Constant Relative Risk Aversion (CRRA) subjective utility function, and an Exponential Constant Relative Risk Aversion (ECRA) subjective utility function. The formulation is assessed in terms of its homogeneous macroscopic properties (thus leading to a triangular fundamental diagram) and its non-homogeneous microscopic properties (thus leading to realistic following behavior facing different traffic scenarios). Once tested in terms of feasibility, the modeling approach is calibrated against real-life trajectory data. A Genetic Algorithm (GA) method is adopted to minimize a spacing-mixed-error term while considering inter-driving heterogeneity. The three models (i.e. PT, CRRA and ECRA) produce acceptable error values with the PT model showing the best fit, followed by the ECRA model, followed by the CRRA model. Even though the CRRA and the PT models show similar intensity in the acceleration response to the behavior of a lead vehicle with more disturbance (stochasticity/randomness) seen with the CRRA SUF, the PT and the ECRA models show more realistic wave formation despite their difference in terms of individual acceleration distribution functions. The ECRA model results in an amplified sensitivity to the behavior of the lead vehicle with the acceleration probability distribution function skewed to the left (i.e. towards decelerating rather than accelerating). The calibration exercise is followed by a simulation exercise. The three suggested models produce a homogeneous congestion phase, but a clear transient single/multiple wave formation is seen with the PT and the ECRA models. These latter models are able to reproduce all the congestion regimes observed on real-world surface transportation networks. The ECRA is characterized by a decreased capacity and increased traffic disturbances with additional shockwave formation. Finally, the different models allow the possibility of perception or judgement errors with the explicit incorporation of a collision probability and a collision weight in the suggested formulation approach.

Motivation

The ultimate goal of this paper is to provide a comprehensive numerically verifiable theory for subjective utilitybased car-following models. Car-following is still considered the basic driving maneuver that explains different congestion dynamics and collision formations (NHTSA, 2016; FHWA, 2004). However, in the era of autonomous vehicles, aren’t we removing the subjective utility and the human component from the driving process? Why do we need to understand driving behavior in a micro-economic context given that one of the reasons behind the introduction of driver-less cars is the elimination of the human error and thus the reduction of traffic incidents? Interestingly enough, traffic simulation models including microscopic acceleration models have been built naturally to account for vehicle automation rather than human driving decision making processes (Van Lint and Calvert, 2018). Except for the earlier efforts seen in the psychophysical models (Wiedemann and Reiter, 1992 – utilized in the VISSIM traffic simulation tool) and the utility-based models (Ahmed, 1999 – utilized in the MITSIM traffic simulation tool), traffic scientists did not account for terms like emergency behavior, perception indifference, stochasticity and randomness in execution when capturing driving behavior. Most of the driver behavior models including the one-dimensional acceleration models remain deterministic and collision-free (Hamdar, 2015). Some additional efforts have been dedicated to incorporating human decision-making processes into existing traffic models (Treiber et al., 2006). However, very few psychology-based or economics-based constructs have been introduced in order to capture the cognitive dimensions behind some observed maneuvers. These dimensions include fatigue, mental load, risk, sensitivity, stress, and uncertainty. Recently, Human Factor (HF) researchers and traffic flow researchers have been focusing on such terms while trying to account for them in new or existing driving behavior modeling frameworks (Hoogendoorn et al., 2014; Saifuzzaman and Zheng, 2014; Saifuzzaman et al., 2017). This research falls under this category of work where the authors would like to establish a family of car-following models accounting for sensitivity, stochasticity and randomness, risk and uncertainty. These models should be calibrated and validated while reproducing different congestion dynamics and incident-prone behaviours.