Modeling gap acceptance behavior allowing for perceptual distortions and exogenous influences
Abstract
This work on gap acceptance is based on the premise that the decision to accept/reject a gap happens in a person's mind and therefore must be based on the perceived gap and not the measured gap. The critical gap must also exist in a person's mind and hence, together with the perceived gap, is a latent variable. Finally, it is also proposed that the critical gap is influenced by various exogenous variables such as subject and opposing vehicle types, and perceived waiting time. Mathematical models that (i) incorporate systematic and random distortions during the perception process and (ii) account for the effect of the various influencing variables are developed. The parameters of these models are estimated for two different gap acceptance data sets using the maximum likelihood technique. The data is collected as part of this study. The estimated parameters throw valuable insights into how these influencing variables affect the critical gap. The results corroborate the initial predictions on the nature of influence these variables must exert and give strength to the gap acceptance decision-making construct proposed here. This work also proposes a methodology to estimate a measurable/observable world emulator of the latent variable critical gap. The use of the emulator critical gap provides improved estimates of derived quantities like the average waiting time of subject vehicles. Finally, studies are also conducted to show that the number of rejected gaps can work as a reasonable surrogate for the influencing variable, waiting time.
Summary
This paper addresses the limitations of traditional gap acceptance models by acknowledging that drivers' decisions are based on *perceived* gaps and critical gaps, rather than measured ones. The authors argue that both perceived gap and critical gap are latent variables existing in the driver's mind, influenced by exogenous factors like vehicle types and waiting time. They develop mathematical models that incorporate both systematic and random distortions in the perception process and account for the influence of these exogenous variables on the critical gap. Model parameters are estimated using maximum likelihood estimation (MLE) on data collected from two intersections. The estimated parameters provide insights into how these variables affect the critical gap. The paper also introduces a method to estimate an "emulator critical gap" – a measurable proxy for the latent critical gap, which can be used to improve estimations of engineering quantities like average waiting time. Finally, the study explores using the number of rejected gaps as a surrogate for waiting time. The core innovation lies in explicitly modeling the perceptual processes involved in gap acceptance, moving beyond the assumption that drivers perfectly perceive gap sizes. This allows for a more nuanced understanding of how various factors influence the critical gap and ultimately the decision to accept or reject a gap. By introducing the concept of the "emulator critical gap," the researchers bridge the gap between the latent variables of the mind and the observable world, making the model practically applicable for traffic engineering and planning. The findings highlight the importance of considering perceptual distortions and exogenous influences when modeling gap acceptance behavior.
Key Insights
- •Perceptual distortions are significant: The paper explicitly models the systematic and random errors in gap perception, acknowledging that perceived gap size differs from measured gap size. This contrasts with most previous studies that assume drivers accurately evaluate gap sizes.
- •Critical gap is influenced by exogenous variables: The critical gap is not a fixed value but is influenced by factors like subject vehicle type, opposing vehicle type, and waiting time. For example, drivers are more risk-averse (longer critical gap) when the opposing vehicle is a truck.
- •Waiting time reduces critical gap: As waiting time increases, drivers become more willing to accept smaller gaps, indicating a trade-off between safety and urgency. There is a significant difference between zero and non-zero waiting times.
- •Emulator critical gap bridges the gap between latent and observable worlds: The paper proposes a method to estimate a measurable "emulator critical gap" that emulates the latent critical gap in the observable world. This allows practitioners to use the model for practical applications.
- •Number of rejected gaps as a waiting time surrogate: The study found that the number of rejected gaps can serve as a reasonable surrogate for waiting time, simplifying the model without significant loss of accuracy, especially when the mathematical model with waiting time is complex.
- •Model complexity increases with perceptual variables: The model for gap acceptance is more complex when influencing variables, such as waiting time, are also subject to perceptual distortion.
- •Beta is unidentifiable: The parameter beta in the gap perception model is unidentifiable, but this does not impede the determination of the emulator critical gap.
Practical Implications
- •Improved traffic simulation and modeling: Traffic simulation models can be enhanced by incorporating the findings on perceptual distortions and exogenous influences on gap acceptance behavior.
- •Better intersection design: Traffic engineers can use the emulator critical gap to design safer and more efficient intersections, considering the types of vehicles and the expected waiting times.
- •More accurate estimation of delays: The emulator critical gap can provide improved estimates of average waiting times of subject vehicles at intersections compared to traditional methods.
- •Targeted traffic management strategies: Understanding the influence of vehicle types and waiting times on gap acceptance can inform targeted traffic management strategies to improve traffic flow and reduce congestion.
- •Future research directions: Future research could focus on incorporating driver heterogeneity, examining the impact of other influencing variables (e.g., weather conditions), and validating the model in different traffic environments.