A behavioral microeconomic foundation for car-following models. (April 2020) - Hamdar, Samer H.; Dixit, Vinayak V.; Talebpour, Alireza; Treiber, Martin
Highlights: A generalized utility-based formulation of a car-following is offered. This includes Prospect Utility and two variants of Constant Relative Risk Aversion. The macroscopic and microscopic properties of the different functions are derived. The model was calibrated and validated using 1000 individual trajectory sets. The model's characteristics are analyzed via simulation and sensitivity analysis. 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 utility-based 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.