Highly Influenced. View 6 excerpts, cites background. Analyzing dilemma driver behavior at signalized intersection under mixed traffic conditions. Innovative countermeasures for red light running prevention at signalized intersections: A driving simulator study.
View 8 excerpts, cites methods and background. The adaptive algorithm of a four way intersection regulated by traffic lights with four phases within a cycle. Driving rules adopt permissive or restrictive policies concerning yellow light running YLR. In a restrictive policy, vehicles behind the stop line are not allowed to enter the intersection on … Expand. View 2 excerpts, cites methods and background. Yellow phase dilemma zone is dynamically distributed at high-speed signalized intersections because of varying driving behaviors in response to yellow indications.
This article presents an … Expand. Dilemma zone DZ , also called decision zone in other literature, is an area where drivers face an indecisiveness of stopping or crossing at the yellow onset. The DZ issue is a major reason for the … Expand. A review of the yellow interval dilemma.
This paper deals with the evolution of rules concerning the setting of the yellow interval duration of a traffic light and the associated "amber yellow light dilemma". Driver decisions in dilemma zones could result in crash-prone situations at signalized intersections, as an improper decision to stop by the leading driver, combined with the following driver deciding to go, can result in a rear-end collision.
Sahar and Montasir [ 10 ] proposed a novel safety surrogate measure to capture the degree and frequency of dilemma zone-related conflicts at each approaching intersection. Papaioannou [ 11 ] analyzed the relationship between the dilemma zone and the safety level of signalized intersections. This research indicated that a large percentage of drivers facing the yellow signal are caught in the dilemma zone due to high approaching speeds and exercise aggressive behavior.
More than half of the drivers choose to cross the STOP line instead of stopping, showing that drivers are neither afraid of the law nor believe that an accident may be caused as a consequence of their choice. Gates [ 12 ] and Kim [ 13 ] evaluated the stopping characteristics of vehicles in the dilemma zone using video cameras.
The field study showed that the different types of drivers and vehicles had different responses in the dilemma zone. Long [ 14 ] used the fuzzy decision tree model to analyze the driver decision to go or stop in the dilemma zone at a signalized intersection, considering the vehicle location, velocity and remaining time of the yellow signal. Qi [ 15 ] converted the traffic signal light and drivers into a double game model, and through quantification of their earnings under different choice conditions, determined the optimum the driver decision-making via the Nash equilibrium solution concept.
The research results showed that the driver aggressiveness parameter can be estimated by monitoring the driver historical response to yellow indications. Savolainen, Sharma and Gates [ 17 , 18 ] investigated how signal timing strategies such as yellow signal duration, all-red clearance interval, advance warning flasher, and automated camera enforcement impact driver decision-making.
Lu [ 19 ] used high-resolution event-based data to analyze the yellow-light running behavior of drivers. The research showed that snowing weather conditions cause more yellow-light running events. Bar-Gera and Musicant [ 20 ] used naturalistic data from digital enforcement cameras to quantify yellow signal driver behavior. The results showed that the frequencies of entrance time after yellow onset are relatively stable during the beginning of the yellow phase.
Different drivers exhibit their respective traffic behavior, which is affected by internal factors and external factors. The internal factors are the driver self-attributes, including driver gender, age, driving experiences, cultural background, etc. The external factors are the driving environment, including traffic conditions, road surface conditions, and weather conditions.
It is difficult to use kinetic equations to model traffic behavior in controlling vehicles when the drivers approach signalized intersections [ 25 ]. However, driver behavior can be partly reflected by the changes in vehicle motion before, during, and after decision-making and after vehicle operation.
The driver perceives surrounding information, estimates the driving situation, makes decisions to control the vehicle, and then changes the vehicle motion status by adjusting the steering wheel or changing the vehicle speed by stepping on the gas or brake pedal. These processes can be indicated by high-fidelity vehicle dynamics models that consider the driver to have the internal abilities of driving considering perception, traffic condition estimation, and driving experimental learning and the external abilities of operating vehicles under various driving scenarios.
Compared with the normal vehicle kinetic model, the vehicle dynamics model must be more adaptive, stochastic, and time-invariant. These kinds of models can represent driver behavior [ 26 , 27 ]. Yang [ 28 ], Cairano [ 29 ] and Dominic [ 30 ] pointed out that driver behavior has stochastic characteristics. Driver behavior can be modeled and explained with stochastic variables or stochastic processes.
Therefore, when a driver drives to a signalized intersection at the onset of a yellow signal indication, the driver behavior can be described as [ 31 ]: 1 The driver perceives the traffic environment to generate the expected driving state. Throughout the driving processes, driver behavior is affected by the road surface conditions, traffic flow conditions, weather conditions and driver physiology.
In the whole process, driver behavior is consistent with the characteristics and principle of model predictive control MPC [ 32 — 34 ]. However, although MPC can deal with disturbances and uncertainties, it is based on the min-max method and cannot efficiently model driver behavior in the dilemma zone, which needs to consider the disturbance and uncertainty of a person-vehicle-road system in real time at a signalized intersection.
Stochastic model predictive control SMPC has the advantage of analyzing and modeling the system, which is stochastic and uncertain [ 29 ]. In this paper, we attempt to use SMPC to model driver behavior in the dilemma zone. The aims of this paper are as follows. A mathematical modeling method is used to study driver behavior in the dilemma zone based on stochastic model predictive control, along with considering the dynamic characteristics of human cognition and execution.
Providing a feasible solution for modeling driver behavior more accurately and then potentially improving the understanding of the driver-vehicle-environment system in the dilemma zone, exploring the modeling framework of driver behavior in the dilemma zone, including the perception module, decision-making module, and operation module.
We propose an SMPC-based high-fidelity vehicle dynamics and motion model to describe the processes of driver behavior at the onset of yellow signal indication when approaching the signalized intersection and use the CarSim simulator to verify the validity of the proposed model. The rest of the paper is structured as follows: Section 2 presents the model of driver behavior in the dilemma zone.
The simulation and model verification are presented in Section 3. Section 4 concludes this article with a summary of contributions and limitations, as well as perspectives on future work.
When a driver approaches the signalized intersection, he or she will perceive the traffic environment, including the traffic light, the distance from the stop-line and the traffic flow in the approaching direction. Then, he or she will estimate the traffic environment and driving state vehicle motion status to decide whether to stop before the stop-line or to pass through the signalized intersection.
After the decision is made, he or she optimizes the driving operation and operates the vehicle based on his or her driving experience, reaction time, age, ability to handle vehicle, etc. Therefore, the whole process can be divided into three modules: the perception module, the decision-making module, and the operation module.
The framework of the driving behavior is shown in Fig 1. When driving to the signalized intersection at the onset of a yellow signal indication, the driver perceives traffic conditions by sensory organs such as vision, auditory, and tactile. All traffic condition information is processed, conducted, and interpreted by the driver brain. Then, the brain generates the expected driving state, which is the ability to predict the vehicle motion status based on the driver experience and current vehicle motion status [ 35 ].
Therefore, the perception module model is composed of a traffic condition perception model and an expectation driving state model. The driver perceives road surface conditions, traffic conditions, and vehicle interior motion status by sensory organs. However, not all the information obtained from sensory organs is processed by the brain. The information is selected, processed and comprehended by the cognitive neural system of the driver [ 36 , 37 ].
In different driving environments, the objects concerning the drivers are different. The driver pays more attention to the objects that impact the driving status most. Regarding selective attention, Broadbent [ 38 ] considered that there is a large amount of information stimulation from the surroundings, but the ability of the sensory channel to receive information and the ability of the cognitive system to process information are limited. Therefore, it is necessary to filter and adjust the large amount of information input from the outside world.
There is only one channel that passes through a filter into the advanced analysis phase, and this filter demonstrates the selectivity of attention. Then, Deutsch proposed the response selection model RSM in [ 39 ]. Compared to the filter model FM proposed by Broadbent in , Deutsch considered that there are several channels that pass through the filter and enter the advanced analysis phase. Kahneman [ 40 ] proposed the capacity division model CDM in Kahneman considered that selective attention is essentially a resource allocation mechanism that allocates the limited information processing capacity of human beings according to the resource allocation scheme under the constraints of various factors.
Based on the theory proposed by Broadbent, Deutsch and Kahneman, researchers have proposed many hypotheses such as the maximum stimulus hypothesis, minimal stimulus hypothesis, and capability of the maximum stimulus number hypothesis to analyze the critical threshold of the filter [ 41 ]. However, the selective attention models mentioned above are based on the theory of psychology.
In driver behavior modeling, we do not focus on quantizing the complex psychological characteristics of drivers and use only the research results of selective attention that consider the complex psychological characteristics of humans and affect drivers in different driving scenes. In this paper, we use the theory of RSM and the maximum stimulus hypothesis to describe driver selective attention in the dilemma zone as follows: When a driver approaches the signalized intersection at the onset of the yellow signal indication, the objects in the driving environment will stimulate the driver sensory organ [ 42 ].
This phenomenon is expressed by the following mathematical formula:. ST i t is the i th object stimulus to the driver at time t in the driving environment. ST c is the threshold of stimulus to the driver to receive attention in the driving environment. When a driver is caught in the dilemma zone, he or she will pay more attention to the traffic light, current vehicle distance from the stop-line, and current vehicle speed, which are the key factors for the driver to make decisions in the proceeding driving operation in the dilemma zone [ 45 ].
In the driver behavior modeling, we consider only the ability of driving surrounding perception affecting drivers to make decisions in dilemma zones. After perceiving the driving surroundings in the dilemma zone, the driver will generate an expected driving state in mind before deciding whether to pass through the signalized intersection or not.
The expected driving state relies on the vehicle current speed, the distance from the forward vehicle or from the stop-line, and the rest time of the yellow signal.
In this process, the driver focuses on the vehicle location and vehicle speed. Therefore, we can describe that the expected driving state as the change in location when the vehicle approaches the signalized intersection.
N E relates to the degree of driver expectation. A greater value of N E means more concentration in the driving environment and a better traffic condition for the approaching entrance lane of the signalized intersection.
As the vehicle location and the yellow signal status change, the expectation driving state of the driver will change in every reaction period. The diagram of the expected driving state in the dilemma zone is shown in Fig 2.
When the driver realizes that he or she is caught in the dilemma zone with real-time selective attention to the driving environment, he or she must decide whether to decelerate to stop before the stop-line or to accelerate to pass through the signalized intersection. In this situation, the driver evaluates the driving conditions, makes a decision, and optimizes the driving state to cope with the decision and to drive safely and comfortably.
Therefore, we divide the decision-making module into two models: 1 the driving condition estimation model, and 2 the decision-making and optimization model. In the process of decision making in the dilemma zone, the driver will estimate the forward traffic state of the road and the driving state of the vehicle. To describe these characteristics, we try to model the driver cognitive characteristics in this situation [ 48 , 49 ].
We rewrite F y and F x as:. Putting formula 4 into formula 3 , formula 3 can be rewritten as:. With the kinematic equation of vehicle motion, the vehicle movement can be described as:. In the dilemma zone, the foremost reaction of the driver is to consider decelerating to stop before the stop-line or accelerating to go through the intersection. The yaw angle in this paper is considered close to zero. The formula 6 can be rewritten as follows:.
Combining formula 5 and formula 7 , the state of driving condition estimation can be formed as a fourth-order status variable:. Formula 5 and formula 7 can be combined as a matrix:. In every perception-expectation-response period T, the dynamic driving condition estimation can be described as a discretization equation.
After estimating the traffic condition and vehicle state while making decisions in the dilemma zone, the driver will evaluate the vehicle motion and optimize the vehicle status in the next reaction period. We try to use the dynamic discretization equation to describe the estimated state based on stochastic model prediction control theory [ 33 , 34 , 50 ].
As a driver obtains the vehicle motion status by estimation in mind, he or she tries to optimize the vehicle status to make the driving comfortable and safe. Due to the restrictions of driver driving experiences, response ability, and cognitive characteristics, the action of optimization and the expected vehicle state will be delayed.
Delays may occur in the process of traffic perception, decision-making, driving expectation and optimization. We use the delay transfer function to describe this phenomenon as [ 25 ]:. Based on the stochastic model prediction control theory, we can obtain the driver reaction and operation in every step in the dilemma zone and model the rolling horizon driver behavior model in the dilemma zone by using the sequence formulas in the perception module, decision-making module and operation module.
In this paper, we use the CarSim 8. CarSim is universally the preferred tool for analyzing vehicle dynamics, developing active controllers, calculating the performance characteristics of a car, and engineering next-generation active safety systems. CarSim includes configurable high-fidelity and real-time vehicle dynamics models, which can accurately reflect vehicle dynamics and motion under various driving conditions, and includes models of complex road and road structures, high-fidelity traffic, weather and lighting conditions, and vehicle models for cars, SUVs, trucks, and buses [ 51 ].
In China, cars and SUVs make up the bulk of traffic flow in urban city. The vehicle model parameter settings in CarSim are shown in Table 1.
The driver behavior and vehicle dynamics model in the dilemma zone proposed in this paper are defined by formulas and variables added with VS commands and VS configurable functions, handled by built-in controllers and solvers. Traffic light is defined as a target object and combined with ranging sensors in CarSim.
Roads and reference paths are created with Scene Builder and defined with configurable functions to build dilemma zone scenarios and traffic event sequences. A snapshot of the traffic scene in the simulator is shown in Fig 3.
In traffic event sequences, we use kinetic equations to define the range of the dilemma zone and assume that:. When the driver realizes the yellow signal indication, the initial vehicle speed is V 0. If the driver decides to stop before the stop-line, the minimum distance to stop safely is [ 6 ]:. If the driver decides to pass through the signalized intersection, the maximum distance to pass through safety is [ 6 ]:.
To analyze the degree of attention affecting driver behavior, we set N E as 5, 10, 15 to examine the relationship by comparing the expectation path to the simulation path under different driving conditions. The simulation experiments are divided into two groups: 1 the driver decides to stop before the stop-line; or 2 the driver decides to pass through the signalized intersection.
The range and location of dilemma zone for different driver is different. To make the trajectory data compareable, the observation range is setting as meter along the driving approaching. The starting observation location is set at meter before the stop-line for the vehicles which decide to stop before the stop-line group 1. For vehicles which decide to go through the signalized intersection, the starting observation location is set at 50 meter before the stop-line group 2.
For group 1, the value deceleration rate begin to change around the location of 50m before the stop-line. Higher value of N E means driver palys more attention on traffic condition when driving. From the trajectory data, the less value of N E , the fluctuation of deceleration rate is more pronounced and deviates the expection of driver greater. Furethermore, it can conclude that if the drivers concentrate enough on the traffic condition when driving, the trajectories of vehicle are similarity, and consist with the expectation of driver.
For group 2, the value acceleration rate increases continuously around the location of 50m before the stop-line. It can conclude that if the drivers concentrate enough on the traffic condition when driving, the trajectories of vehicle are similarity, and consist with the expectation of driver.
However, when passing through the signalized intersection, the trajectories deviation shows out in different vehicle model, especially in the driver with lower N E value. We can conclude that the vehicle models do not obviously affect the driver attention in the dilemma zone in the simulation. Therefore, the driver attention does not distinctly affect the driver to make the decision to stop before the stop-line or to pass through the signalized intersection.
For group 1, it shows out that the driver stepped on the brake pedal hastily first and then gradually smooth. The higher initial speed of vehicle, the driver will step on the brake pedal deeper and more haste. The lower initial speed of vehicle, the driver has more time to stop the vehicle smoothly before the stop-line.
In addition, the different vehicle models show out different acceleration performance. For group 2, it shows out that the driver stepped on the gas pedal gradually but with different strength. The lower initial speed of vehicle, the driver will step on the gas pedal deeper. Field data was collected at five signalized approaches using video capturing technique to investigate the driver behavior. Frame by frame manual extraction resulted in driver responses at the yellow onset and binary logistic regression model is developed to represent the observed behavior.
The insights from this study findings can be used to enhance the safety and performance of signalized intersections in developing countries. Toggle navigation Menu.
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