Exploratory Advanced Research Program

VASTO - Evolutionary Agent System for Transportation Outlook

Agent-Based Modeling and Simulation in The Dilemma Zone

2 Introduction

For decades, driving safety has been a major concern in the traffic management domain because car accidents not only affect the performance of the traffic system but also inflict huge damage in terms of deaths and major injuries to humans. According to the National Highway Traffic Safety Administration (NHTSA), 23 percent of the 29,757 fatal crashes in the United States in 2012 were crashes related to intersections. ⁽³⁾ This is because a driver at an intersection needs to consider multiple options (e.g., stop, proceed, turn right, and turn left) with respect to the traffic situation within a short amount of time. ⁽⁴⁾ Therefore, many studies related to driving safety have focused on drivers' behaviors at an intersection, aiming to reduce the risk of car crashes. One major concept is the dilemma zone (DZ), which is an area in which a driver cannot stop safely before the stop line or clear the intersection safely before the red phase. ⁽¹⁾ Whatever decision is made in the DZ, there could be a risk of a car crash, such as a rear end or right-angle collision.

To reduce the risk inherent to the DZ, ITE recommended a DZ model (or Type I DZ) based on the approaching speed and distance to the stop line of a vehicle. ⁽¹⁾ The Type I DZ is used to detect the DZ (x_dz) if the vehicle's approaching speed (V₀) to an intersection is already known. The goal of the Type I DZ is to minimize the DZ by controlling the length of the yellow phase so that a driver can choose either to proceed or stop at the onset of the yellow phase (i.e., option zone). In the Type I DZ, the DZ (x_dz) is detected by subtracting the minimum stopping distance (x_c) from the maximum yellow passing distance (x₀) at the onset of the yellow phase. To compute the minimum stopping distance (x_c) and the maximum yellow passing distance (x₀), the Type I DZ model includes the following factors: the approaching speed of the vehicle (V₀), the maximum deceleration rate when stopping (a₂), the maximum acceleration rate when proceeding (a₁), the perception-reaction time of the driver (PRT) for proceeding (δ₁) and stopping (δ₂), the length of the yellow phase (τ), the width of the intersection (w), and the average vehicle length (L).

Nonetheless, due to the uncertainty of the human reasoning process, car crashes still occur, even when a driver is in the option zone. To study the uncertainty in driver decisions, a Type II DZ has been proposed, which considers the stopping probability of drivers at the onset of the yellow phase. ⁽⁵⁾ This approach defines the DZ as being from the position at which 90 percent of drivers stop to the position at which 10 percent of drivers stop, so that the uncertainty aspect of driver decisions can be covered. Similar to the Type I DZ, the Type II DZ can be eliminated by controlling the length of the yellow phase. However, because the Type II DZ focuses only on the results of observations (i.e., stopping and proceeding) without considering the factors that impact driver decisions, controlling the length of the yellow phase is considered the only way to minimize the number of car crashes caused in the Type II DZ. This focus means that the Type II DZ model is difficult to handle in the case in which drivers are affected by other factors, such as traffic conditions.

Drivers' behaviors are affected by the surrounding environment, such as other vehicles' movements or intersection conditions.

In a DZ, the drivers' decisions are also influenced not only by their own condition (e.g., approaching speed and distance to the stop line of a vehicle) but also by the surrounding environment at an intersection. Gates et al. ⁽⁶⁾ claimed that the actions of vehicles in an adjacent lane affect drivers' decisions in the DZ. Huey and Ragland ⁽⁷⁾ similarly showed that the pedestrian countdown signal made drivers' behaviors more conservative (i.e., less likely to enter the intersection at the end of the yellow phase). A red-light photo enforcement camera is also known to be useful to mitigate red-light running by vehicles, thereby reducing the possibility of car crashes. ⁽⁸⁾

Therefore, in this study, we developed a new DZ model that includes the effects of three surrounding factors (i.e., presence of a pedestrian countdown signal, presence of a red-light photo enforcement camera, and behavior of an adjacent vehicle) in addition to factors such as the subject vehicle's approaching speed and distance to the stop line given by the Type I DZ model. The driver's decision model is then developed by ABMS under the E-BDI framework, which is able to represent the uncertain decisionmaking behavior of drivers via probabilistic inference algorithms such as the Bayesian belief network. ^{(9) (2)}