# Augmented Driver Behavior Models for High-Fidelity Simulation Study of Crash
Detection Algorithms

Ahura Jami1, Mahdi Razzaghpour1, Hussein Alnuweiri2, Yaser P. Fallah1 1
Connected & Autonomous Vehicle Research Lab (CAVREL), University of Central
Florida, Orlando, FL, USA.2 Department of Electrical and Computer Engineering,
Texas A&M University at Qatar, Doha, QatarThis research was supported in part
by the Qatar National Research Fund Project NPRP 8-1531-2-651.

###### Abstract

Developing safety and efficiency applications for Connected and Automated
Vehicles (CAVs) requires a great deal of testing and evaluation. The need for
the operation of these systems in critical and dangerous situations makes the
burden of their evaluation very costly, possibly dangerous, and time-
consuming. As an alternative, researchers attempt to study and evaluate their
algorithms and designs using simulation platforms. Modeling the behavior of
drivers or human operators in CAVs or other vehicles interacting with them is
one of the main challenges of such simulations. While developing a perfect
model for human behavior is a challenging task and an open problem, we present
a significant augmentation of the current models used in simulators for driver
behavior. In this paper, we present a simulation framework for a hybrid
transportation system that includes both human-driven and automated vehicles.
In addition, we decompose the human driving task and offer a modular approach
to simulating a large-scale traffic scenario, allowing for a thorough
investigation of automated and active safety systems. Such representation
through Interconnected modules offers a human-interpretable system that can be
tuned to represent different classes of drivers. Additionally, we analyze a
large driving dataset to extract expressive parameters that would best
describe different driving characteristics. Finally, we recreate a similarly
dense traffic scenario within our simulator and conduct a thorough analysis of
various human-specific and system-specific factors, studying their effect on
traffic network performance and safety.

###### Index Terms:

Driver Behavior Model, Driver Reaction, Intelligent Transportation Systems,
Traffic Simulation, Vehicular Safety Simulation

##  I Introduction

Recent studies of traffic data collected on US roadways have shown a steady
increase in road fatalities, resulting in over 35,000 lives lost and over $240
billion in damages each year[1]. Although motor vehicle accidents constitute
one of the highest causes of death in the USA[2], they are almost always
predictable and preventable. Deploying Advanced Driver Assistant Systems
(ADAS) within an intelligent transportation framework is a low-cost, yet
effective, step toward resolving this issue. Depending on the level of
autonomy of such safety systems, they can either warn drivers by recognizing
potentially dangerous situations or take over vehicle control through
prevention mechanisms. Forward collision and lane departure warnings are two
examples of active safety systems that provide advisory alerts. Forward
collision avoidance and lane-keeping assistance are more advanced versions of
these systems that provide automated control in addition to recognizing
dangerous scenarios.

Vehicle instantaneous position, kinematic information (heading, velocity,
acceleration, yaw rate, etc.), driver-specific information (head pose, eye
gaze, etc.), and environmental data (road type, weather conditions, lighting
characteristics, etc.) are some of the most informative situational elements
used by ADAS[3, 4]. In general, the data used by an ADAS can be separated into
two groups: the host vehicle’s data and its surrounding objects. The host
vehicle’s positional and kinematic data can be collected from the Global
Positioning System (GPS) and the vehicle’s Controller Area Network (CAN) bus,
which provides sensory information such as speed, acceleration, throttle
position, and steering angle. The second type of data, namely information
about remote objects, is obtained using local sensors such as cameras, radar,
and LiDAR, as well as wireless communication between vehicles, known as
Vehicle-to-Vehicle (V2V) communication. The current version of ADAS, which is
already in use in some high-end vehicles, scans the environment and monitors
driving conditions using local sensors. Recent communication advancements in
wireless vehicular networking offer an opportunity for the automotive industry
to be on the brink of a breakthrough in automation and safety improvements
through designing and utilizing Cooperative Vehicular Safety (CVS)
applications. As a cyber-physical system, a modern vehicle uses V2V
communication as a desirable platform for developing a rich, advanced, and
low-cost safety system[3, 5, 6, 7]. Furthermore, using Vehicle-to-Everything
(V2X) communication will expand vehicles’ perception beyond the range of their
onboard sensors.

However, integrating such automated mechanisms into a traditional
transportation system poses several technical challenges. Given the stochastic
nature of host or remote vehicle drivers, it is critical for automated systems
to have a detailed awareness of their surroundings. Furthermore, in order to
improve the performance and efficiency of such systems, they must be designed
within a flexible framework that takes driver behavior models into account.
Another crucial issue that overshadows the design of an adaptive system is the
need for rich and extensive driving data in which these systems are to
perform. When approached through real-world measurement campaigns, the data
collection phase can be very costly and time-consuming[8, 9]. Furthermore,
some of the most critical test scenarios can be extremely dangerous because
they expose real drivers to potentially hazardous situations. A thorough
analysis of driver behavior during a collision scenario, for example, is
required to design an adaptive Forward Collision Warning (FCW) algorithm. A
potentially dangerous collision scene should be designed and tested in a
series of trials. These critical issues motivate the development of a
versatile simulation platform capable of performing any examination without
the use of real drivers.

Figure 1: An architectural overview of the co-simulation framework along with
a snapshot of the simulator environment

Despite the fact that an Intelligent Transportation System (ITS) is
multidisciplinary, traditional simulators were designed solely for studying
traffic management topics. They have limited capabilities for assessing active
safety mechanisms in life-threatening situations. The analysis of such
critical systems necessitates a comprehensive framework that allows for an
assessment with sub-second accuracy in various traffic conditions. There have
been several attempts to incorporate novel ITS applications into traditional
simulators. Veins[10] is a simulation framework that connects the SUMO traffic
simulator[11] to the OMNeT++ event-based communication network simulator[12].
Despite its wide range of applications for the simulation of vehicular ad hoc
networks, this coupled platform cannot support the investigation of many novel
applications, such as Cooperative Collision Warning (CCW) systems, without
requiring significant changes to the underlying software structure.

Another category of vehicular simulators has a particular focus on the
simulation and analysis of different algorithms on a single vehicle. However,
the main disadvantage of such simulators is the lack of complexity of an urban
driving setup, which sets significant limitations on the examination of an
ADAS in a large-scale traffic scenario. Such traffic-related shortcomings may
include the absence of intersections, traffic rules, and most importantly,
other vehicles. TORCS[13] is an instance of a such simulator.

With the astonishing rise and success of machine learning approaches, a new
type of simulator is emerging that focuses on machine learning, specifically
deep learning applications within ITS. They are, however, very similar to the
preceding category in that they lack an extensive traffic setup and are
primarily concerned with autonomous driving and the performance of a single,
fully automated vehicle. CARLA[14], developed by researchers at Intel, and
AirSim[15], developed by Microsoft, are examples of such simulators that are
both open-source and are powered by Unreal Engine 4 (UE4)[16].

This paper’s contributions to overcoming the aforementioned issues are as
follows:

  * •

This paper and its companion [17] propose a comprehensive co-simulation
framework designed specifically for the analysis of automated applications
such as vehicular safety systems within a hybrid transportation network that
includes both human-driven and automated vehicles. It is made up of perfectly
designed modules such as mobility and human driver models, a road
transportation package, inter-vehicular communication protocols, and safety
systems such as FCW.

  * •

Introducing a separate driver model that allows for the simulation of
dangerous road traffic scenarios while overcoming the inherent perfection and
accident-free nature of a Car-Following Model (CFM).

  * •

The proposed co-simulator allows for real-time representation of various
traffic environments.

The technical aspects of these components are discussed in the following
sections. The rest of the paper is organized as follows: In section II we
describe the co-simulation architecture in detail and propose a driver-in-the-
loop approach to simulate human-driven vehicles. Next, we study and introduce
different driving characteristics in section III. In section IV we analyze a
congested traffic dataset and perform a classification of three classes of
drivers. Moreover, we extract descriptive information for different categories
of drivers where we use all this information and recreate a congested traffic
scenario in our simulation in section V. We conclude by analyzing various
drivers’ responses to FCW and their impact on the performance and safety of
the traffic system.

##  II Co-Simulation Architecture

As the current conventional transportation system evolves rapidly into an
intelligent one, the quick and efficient development of many novel ITS
technologies necessitates simulation-based testing and evaluation. The co-
simulation framework presented in this paper is an extension of our previous
work[17], and it was created with the cutting-edge game engine technology
UE4[16] and its integrated NVIDIA PhysX Vehicle[18]. UE4 is a video game
development tool created by Epic Games, a video game and software development
company. Developers can use this tool to create simulations, edit videos or
sounds, and render animations. Nvidia’s PhysX is an open-source real-time
physics engine middleware SDK that is part of the Nvidia GameWorks software
suite. PhysX’s vehicle support has been expanded from suspension/wheel/tire
modeling to a more comprehensive model that couples modular vehicle components
such as the engine, clutch, gears, auto box, differential, wheels, tires,
suspensions, and chassis.

Figure 2: The Fuzzy-PD control structure used to represent a human-driver’s
car following behavior

We used a modular pipeline to decompose the driving task into different
interoperable components, as opposed to many traditional simulators that use a
CFM to handle both vehicle dynamics and driver characteristics[11, 19, 20].
These include a mobility model, a driver model, perception and sensing
packages, and a CCW system that perceives the surrounding environment using
information obtained from the vehicle’s local sensors and inter-vehicular
communication. This active safety mechanism in our simulation framework
assists the driver in avoiding dangerous scenarios by issuing imminent alerts.
Figure 1 represents an overview of the proposed simulation platform and
illustrates the relationship between its components. The scenario that is
shown on the right side of the figure is a snapshot of the simulation
environment and demonstrates vehicles equipped with CCW in a near-crash
scenario 111A demo of the simulator demonstrating the evaluation and
effectiveness of a CCW in avoiding a crash can be found at
https://vimeo.com/252441087.

###  II-A Mobility Model

The mobility model is responsible for handling the kinematics and dynamics of
a vehicle and its subsystems. This module converts the driver-supplied
throttle and steering angle values into lateral and longitudinal vehicle
movement. We use the UE4 standard physics engine and its integrated component,
NVIDIA PhysX Vehicle, to handle the physical characteristics of vehicles in 3D
environments. The NVIDIA PhysX models a vehicle as a rigid body on a
collection of sprung masses[18]. The complete UE4 physical engine allows for a
near-realistic dynamical response of vehicles within its virtual environment
by adjusting the vehicle’s mechanical setup, such as engine torque and
differential setup, and by incorporating additional components such as tire
models and road friction.

###  II-B Driver Model

The driver model, which represents a human driver and is tasked with
controlling the vehicle while adhering to traffic laws, is essentially the
system’s brain. A driver controls the vehicle during a longitudinal car-
following regime by adjusting the throttle and brake pedals to maintain a safe
speed and distance from the leading vehicle[21]. According to control theory,
the interaction between the driver and the vehicle creates a closed-loop
feedback control system, with the driver acting as a feedback controller[22].
As the most popular type of controller in the industry, PID controllers are
often used to describe robot driver models[22, 23]. Despite their popularity
and ease of implementation, PID-like models alone cannot characterize ideal
human drivers because they are based solely on speed and acceleration errors
and do not take into account driver-specific characteristics. A more accurate
representation of a driver should consider nonlinearities in human response
time, as well as their specific decision processes[24].

Given that each driver has a unique driving style, we propose a mixed-driver
model that is controlled by a CFM-Fuzzy-PD closed-loop feedback controller. As
an alternative to PD control, fuzzy-PD control is often mentioned because some
of the techniques and algorithms used to tune the PD gains require further
tuning by a skilled human driver. The combination of these models allows us to
incorporate the most beneficial features of each subsystem, resulting in a
natural and human-interpretable system, suitable for implementing a driver-in-
the-loop model. The CFM interprets the data and recommends a target
acceleration. The Fuzzy-PD components then determine how quickly to adapt to
the provided acceleration value.

A Fuzzy Inference System (FIS) is a viable option for dealing with the
uncertainties in the car-following regime by mapping the variables that the
driver perceives to the variables that they can control with arbitrary
accuracy using fuzzy reasoning. The Partial-Derivative (PD) component
stabilizes the response time and ensures the controller’s performance. The
proposed CFM-Fuzzy-PD closed-loop feedback controller is depicted in Figure 2.

We begin our discussion of our driver-in-the-loop system with the Intelligent
Driver Model (IDM) component. In our system, IDM is a microscopic model of
traffic flow that provides the reference acceleration $a_{i}(t)$ to the
driver’s fuzzy component[25]. The microscopic traffic model’s goal is to
describe the dynamics of each vehicle as a function of the positions and
velocities of its neighbors[26].

The output of such a model, which can be either the vehicle’s velocity or
acceleration, can be interpreted as the desired velocity/acceleration of the
driver while following other vehicles in a smooth and safe driving regime. The
IDM was designed by [25], which is also implemented in several microscopic
traffic simulators such as MovSim [20] and SUMO [11]. The model is formulated
as follows:

$v_{i}(t)=\frac{dx_{i}(t)}{dt}$ (1)
$a_{i}(t)=\frac{dv_{i}(t)}{dt}=\alpha(1-(\frac{v_{i}(t)}{v_{0}})^{\delta}-(\frac{G(t)}{s_{i}(t)})^{2})$
(2)

with

$G(t)=s_{0}+v_{i}(t)\tau+\frac{v_{i}(t)\Delta v_{i}(t)}{2\sqrt{\alpha\beta}}$
(3)

where $x_{i}(t)$, $v_{i}(t)$, and $a_{i}(t)$ represent the position, velocity,
and acceleration of the host vehicle at time $t$ respectively; $\alpha>0$ is
the comfortable acceleration of the driver, $\beta>0$ represents comfortable
braking deceleration; $v_{0}$ is the desired velocity; $s_{0}$ represents the
minimum gap; $s_{i}(t)=x_{i-1}-x_{i}-l_{i-1}$ is the net distance between host
vehicle $i$ and leader vehicle $i-1$ with a length of $l_{i-1}$; $\tau$ is the
minimum desired safe time headway to the vehicle in front; and $\Delta
v_{i}(t)=v_{i}-v_{i-1}$ represents the velocity between the host and leader
vehicles.

Although IDM includes some of the most important driver characteristics, it
only provides the reference acceleration $a_{i}(t)$ as a desired acceleration
value for the driver. It is up to the rest of the controller to figure out how
fast the driver wants to reach that value. Given a complete dynamical model of
a vehicle, the Fuzzy-PD part of the controller attempts to map the supplied
acceleration values to changes in the throttle and brake pedals. The
statistical analysis in the work of [27] shows that the integral of throttle
position over time has a direct relationship with fuel consumption, and thus
needs to be considered in modeling and identification of human drivers.
However, due to the lack of reliable and publicly available traffic data that
include throttle measurement, we constructed the Mamdani FIS component using a
heuristic and human interpretable approach. As a result, the FIS in this case
is designed to be as simple yet interpretable as possible, with only one input
$\Delta a_{i}(t)$ denoting the difference in accelerations and one output
$\delta p$ denoting changes in accelerator or brake pedal positions. The seven
linguistic variables of this Mamdani FIS are shown in Figures 3(a) and 4(a).
The fuzzy rules are characterized in a way that the normalized Membership
Functions (MF) are within the interval $[-1,1]$. These values are then mapped
to the maximum acceleration and deceleration values of the vehicle itself.
Figure 5(a) shows the output of the FIS for the MFs’ characteristics
represented in Figures 5a-b. These MFs are tuned intuitively to represent
different driving behaviors. It is found that the steeper the slope of the
curve in Figure 5(a), the faster and more aggressively a driver would respond
to acceleration changes dictated by IDM.

Many car-following models including IDM do not consider the driver perception-
reaction time (time taken by a driver to sense the stimulus and start reacting
by either accelerating or decelerating) [26]. Perception-reaction time is a
driver-specific parameter that can be influenced by a variety of implicit and
explicit factors such as the driver’s mood, drowsiness, comfort level, vehicle
condition, and weather. Olson _et al._[28] conducted a study on human reaction
time and found that the average perception-reaction time for $95^{th}$
percentile was $1.6$ seconds. Similarly, we adopt a constant perception-
reaction time of $1.4s$ and a constant pedal switch time of $0.2s$.

A low-pass filter is the final component of this feedback control system.
Because the dynamical behavior of the vehicle is represented by a complete 3D
physics model, factors other than throttle value affect the vehicle’s
acceleration. Tire and suspension models, as well as road characteristics, are
examples of these. The moving average filter used here helps to stabilize the
system’s response by reducing noise artifacts of the vehicle’s acceleration
value. Finally, we disintegrated the IDM into individual states and introduced
a driver state parameter that identifies the appropriate CFM state for the
driver. The driver’s state is determined by information gathered from various
sources, such as vision and safety alerts. A field-of-view represents the
driver’s vision, allowing it to sense the objects within it and schedule an
appropriate action accordingly. These actions actually represent the states
that the driver can enter. Aside from vision, other factors such as safety
warnings may cause a state transition and thus force the driver into another
state. Figure 6 depicts the main driving tasks in the form of a state machine.

(a) Membership functions associated with inputs (a) Membership functions
associated with outputs (a) Output of the fuzzy inference system for above
membership functions Figure 5: Fuzzy inference system membership functions

A visual representation of changes in vehicle kinematic data is shown below
using the proposed driver-in-the-loop model for each state of the IDM (Figure
9). In Figures 7(a) and 8(a) the free flow and following states are also
compared with the case of traditional simulators approach, i.e., a pure CFM.
Figure 9(a) shows the host vehicle’s reaction in a near-crash scenario where
the leading vehicle exhibits sudden braking behavior. As a final note, the
parameters of CFM-Fuzzy-PD system are tuned to represent a moderate driving
behavior.

Finally, the introduction of a separate driver model in such a modular manner
lays the foundation for a simple, human-interpretable system that can be tuned
to represent various driving characteristics. Additionally, it breaks down the
traditional one-to-one approach of CFMs and allows for the introduction of
different classes of drivers.

###  II-C Inter-Vehicular Communication Model

The safety algorithms in CVS Systems use the communicated data between
vehicles to survey the thread zones every $0.1s$ to detect any danger.
Cellular-V2X, also known as C-V2X, is the leading standard candidate for
inter-vehicular communication among the suggested communication protocols
[29]. C-V2X has been specifically designed for ITS applications as a fast-
response and scalable solution due to the time sensitivity of active safety
systems and the need for low latency in their communication protocols. It is
also worth noting that the mandatory deployment of C-V2X devices on all
vehicles is currently being debated at the United States Department of
Transportation.

Figure 6: Main driving tasks represented through a state machine

Communication Logic: This component represents the communication subsystem on
the host vehicle. It determines the transmission power and frequency and
dictates how the recourses of the network should be used to broadcast the next
Basic Safety Message (BSM)222A basic safety message holds essential vehicle’s
state information such as its location and kinematic data [30].. The choice of
communication parameters directly affects the reception probability of BSM
packages within a V2V environment [31, 30]. The baseline transmission rate in
CVS Systems is $10Hz$ [32].

Vehicle Tracking: This module deals directly with the tracking of vehicles
whose information is received over the communication medium. Upon reception of
BSMs by the host vehicle, a local map is constructed from these communicated
data which will keep track of the surrounding vehicles. Various methods have
been proposed to minimize the tracking error. A few notable ones include
simple models such as first and second order kinematic models (constant speed
and constant acceleration), to more complex ones that are based on Kalman
Filter and Gaussian Process[33, 34, 35]. Nevertheless, it has been shown that
in a longitudinal car-following regime, a second order kinematic model can
perform with high accuracy [36]. Consequently, the constant acceleration is
also the model we adopt in our framework.

Effect of Communication Layers: In a communication network model, the
application layer perceives the effect of the lower layers on the communicated
data as a pattern of random losses imposed on the stream of packets that are
received by the host vehicle. Knowing that the transmission delay in a single
hop wireless network is insignificant and that the losses in a broadcast
network are well-randomized, we can describe the effect of the communication
network in an abstract mathematical form using a random loss rate during
transmission [31, 37, 38].

(a) Free Flow (a) Following (a) Emergency state Figure 9: A visualization of
the kinematic responses of the proposed driver-in-the-loop model for three
main driving states (a) Free Flow, (b) Following, and (c) Emergency state.

###  II-D Forward Collision Warning Algorithms

One of the most important collision prevention mechanisms is FCW. CVS systems
can be a low-cost way to integrate FCW systems into existing vehicles. The
exchange of BSMs provides the host vehicle with rich content for complex
predictions. Various automakers are testing and using various FCW algorithms.
Unfortunately, most automakers do not disclose the details of their safety
algorithms, so we can only rely on those available to academic and research
communities. In our companion paper[17], we analyzed the performance of some
of such FCW algorithms, namely the Knipling algorithm[39], CAMP Logistic
Regression[40], and a driver-tuned FCW algorithm from National Highway Traffic
Safety Administration (NHTSA) [41]. In this work, we focus on only two of
these algorithms that showed better performance, i.e., CAMP Logistic
Regression and NHTSA.

##  III Understanding Human Driving Characteristics

Human factors play an important role in any cyber-physical system that
includes humans as part of its physical plant, such as drivers and pedestrians
in an ITS. The past decade has seen a general downward trend in road
fatalities, thanks to the advancement in safety systems of modern vehicles.
However, crash statistics are still alarming, as the recent NHTSA study shows
a total of 42,915 lives lost in 2021 alone. NHTSA study shows a total of
37,133 lives lost in 2017 alone, of which 3,166 cases involved distracted
driving [42]. Another summary of driving statistics shows that up to 660,000
drivers use cell phones while driving during daylight hours, increasing their
chances of being involved in an accident[43]. The study states that
approximately 80% of recorded crashes were the result of drivers’ distraction,
making it the primary cause of rear-end crashes. However, the driver’s
inattention does not necessarily imply the carelessness of that driver[39]. A
driver’s attention may be diverted from the forward path for both driving and
non-driving reasons. Examples of driving-related distractions may include
watching for a pedestrian, looking at signs and landmarks, looking at side
mirrors, or turning the head during a lane change.

Despite the importance and the need for detailed study, distracted driving
does not necessarily describe a specific driver’s driving personality.
Instead, it defines a state in which the driver is no longer paying attention
to the driving task. In other words, one cannot bind distracted driving to
their driving characteristics (as this does not relate to how the kinematics
of vehicles are affected). On the other hand, there exists a category of
dangerous on-the-road driving behavior that is labeled ”aggressive driving.”
NHTSA defines aggressive driving as ”the operation of a motor vehicle in a
manner that endangers or is likely to endanger persons or property”[44]. An
aggressive driver may exhibit behaviors such as speeding, failing to obey
traffic signals, making frequent lane changes, and most importantly,
tailgating which is considered one of the significant causes of crashes that
may result in severe injury or death. Recent NHTSA reports[42] show that
speeding, which is a characteristic of aggressive drivers, has been the cause
of approximately 9,717 deaths, accounting for more than 26% of all traffic
fatalities in 2016 alone.

These alarming statistics compel the implementation of active vehicular safety
systems, which brings us back to the goal of this paper: introducing a
simulation platform for the evaluation and verification of vehicular active
safety systems in various traffic scenarios. The simulation architecture
described in this paper allows for the introduction of two types of drivers,
namely cautious and distracted, as well as three distinct driving behaviors,
namely normal, conservative, and aggressive. As a result of this segregation,
a driver may be in any of six different states at any given time. We use a
driver’s visual perception to determine their cautious and distracted states.
A cautious driver is one who pays close attention to the road ahead and what
is in front of him/her, whereas a distracted driver is one whose vision range
is severely limited, causing him/her to be unaware of his/her surroundings. A
distracted driver has a very high chance of colliding with a decelerating
Leading Vehicle (LV) in a congested traffic scenario or at a traffic light in
such a system.

The driving characteristics of a driver can be extracted from a congested
traffic scenario, which is considered a major contributing factor to
aggressive driving[43]. Impatient drivers who are frustrated by on-the-road
delays caused by either high traffic volume during rush hour or a collision
may respond aggressively by either following too closely or changing lanes
frequently. For this purpose, we use the Next Generation Simulation (NGSIM)
dataset[45] to find appropriate parameters for the IDM car-following model
that will represent the aforementioned categories of drivers. The NGSIM
dataset contains the vehicle paths of over 2000 drivers during an afternoon
rush hour. As a result, the dataset is an excellent candidate for the task at
hand. The details of the NGSIM dataset, as well as its statistical analysis,
are discussed in the following section.

##  IV Dataset Analysis: Parameter Extraction and Driver Classification

The Next Generation SIMulation (NGSIM) program was originated by the Federal
Highway Administration of the U.S. Department of Transportation (USDOT) to
”improve the quality and performance of simulation tools, promote the use of
simulation for research and applications, and achieve wider acceptance of
validated simulation results”[45]. The NGSIM dataset provides high resolution
($10Hz$) positional and kinematic data for 5648 vehicles, which were collected
during afternoon rush hour in three 15-minute intervals ($4:00$ pm to $4:15$
pm, $5:00$ pm to $5:15$ pm, and $5:15$ pm to $5:30$ pm). These vehicle
trajectory data were collected on a sub-second basis on US Interstate 80 in
California on April 2005, using seven stationary cameras mounted on a 30-story
building. The dataset is regarded to contain the most useful features for the
development and validation of microscopic traffic models. The NGSIM dataset
was published in 2007 and is freely available for download.

Before starting our analysis, it is worth mentioning that the NGSIM dataset is
provided in imperial units, which were converted to the metric system for the
results reported here. Additionally, the trajectory and kinematic data of
vehicles exhibited noise artifacts that were filtered using a moving average
filter with a half-second window. The comparison of filtered and unfiltered
sample acceleration data for three different drivers is shown in Figure 10.

(a) Unfiltered acceleration

(b) Filtered acceleration

Figure 10: Comparison of filtered and unfiltered acceleration data

Given the specification of an aggressive driver, i.e., speeding and
tailgating, two main kinematic features that can best describe these
aggressive characteristics are acceleration and the time headway of vehicles.
Time headway is a measurement of the time it would take the following vehicle
to reach the leading vehicle if the leader remains stationary.

$\tau=\frac{s_{i}}{v_{i}}=\frac{x_{i-1}-x_{i}-l_{i-1}}{v_{i}},\ \forall
v_{i}>0$ (4)

It has been shown that drivers tend to keep a constant time headway from their
leading vehicle during a car-following driving regime[46]. The probability
distribution function of this feature for all drivers within the dataset is
represented in Figure 11(a). NHTSA gives several rules of thumbs and
recommendations for a safe time headway. For a scenario such as the one in the
NGSIM dataset (dry and clean pavement), and for the average speed of $35mph$
($~{}55km/h$), the recommended following distance rule is $2-3$ seconds. This
can also be observed in Figure 11(a) with the mode of the histogram sitting
around $2.5s$. Obviously, many drivers follow this rule in an attempt to keep
a safe driving experience. However, we can see that a fraction of drivers have
kept a much smaller time headway to their leading vehicles, while the other
group of drivers has chosen to keep larger time headway. Using the recommended
time headway rule, we classify these drivers into 3 clusters: aggressive
drivers with $(\tau<2.0s)$, normal drivers $(2.0s\leq\tau\leq 3.0s)$, and
conservative drivers $(3.0s<\tau)$. The changes in time headway of three
randomly sampled drivers from all bins, along with the mean of their time
headways are represented in Figure 12(a). We can see that these drivers
attempt to keep a relatively constant time headway all the time.

After categorizing these drivers into three groups, we attempt to extract the
IDM parameters using statistical analysis of time headway and acceleration
data. The average time headway PDF contains enough information to determine
the distribution ratio of the drivers and their minimum desired time headway
$\tau$ (equation 5). We use a gamma probability distribution function of the
following form to fit this data:

$f_{\Gamma}(x|\alpha,\beta)=\frac{\beta^{\alpha}}{\Gamma(\alpha)}x^{\alpha-1}e^{-\beta
x}$ (5)

thus, representing the time headway $\tau$ of each driver as a gamma-
distributed random variable $x$ with shape parameter $\alpha=9.15$ and rate
parameter $\beta=0.31$. Based on the above classification, and the fitted
gamma PDF, the ratio of each category of the driver can be obtained using the
inverse percentile at the edge points 2 and 3 seconds. These ratios are
presented in table LABEL:tab:idm_parameters. A simulated driver will be
assigned a category based on bins’ thresholds and the randomly gamma-
distributed time headway.

Next, we analyze the changes in the acceleration profiles to find the
remaining parameters of IDM. Figure 13(a) represents the Empirical Cumulative
Distribution Function (ECDF) of all the acceleration values of each driver’s
category. In this figure, the solid lines represent the acceleration values
while the dashed lines represent the absolute values of decelerations for each
class of driver. We can see that the aggressive driver has kept higher
acceleration values than the other two drivers. As we move towards the
conservative drivers, the resistance in accelerating/decelerating becomes more
apparent. From this observation, the comfortable accelerations $\alpha$ and
braking decelerations $\beta$ (equation 2) were represented as a uniformly
distributed random variable within the range of $70^{th}$ to $90^{th}$
percentile of accelerations and decelerations respectively. The final
extracted ranges for each category of drivers are shown in table
LABEL:tab:idm_parameters.

(a) Distribution and clustering of mean time-headways of all drivers in NGSIM
dataset (a) Changes in time headway of three sampled drivers (a) ECDF of
acceleration values of all drivers of each category Figure 13: NGSIM dataset
analysis

##  V Performance Evaluation and Simulation Results

To evaluate the performance of our simulation framework based on the
parameters obtained from the previous section (table
LABEL:tab:idm_parameters), we designed a dense highway traffic scenario,
similar to NGSIM, involving 150 gamma-distributed drivers. The highway
scenario was built to be $2km$ long with vehicles looping back to the start
once they have reached the end. This way, we ensured a consistently congested
scenario. The simulations have been executed on a PC with an Intel-R CoreTM
i7-7700 @ 3.60GHz CPU, 32 GB of RAM, and NVIDIA GeForce GTX 1080 Ti GPU.

We combined the six classes of drivers introduced earlier and analyzed their
driving responses in two scenarios: one in which no vehicles have CCW and one
in which all vehicles have CCW. To investigate the effectiveness of
implemented FCW algorithms in preventing near-crash and crash scenarios, we
defined the emergency state (Figure 6) as a driver hard braking reaction when
a warning is issued. This emergency state reaction is simulated by pressing
the brake pedal all the way down (i.e., the throttle is $-1$) after an initial
perception-reaction delay of 1.3s. The maximum braking torque of all vehicles
is $1500Nm$. The work of[4] shows that braking was the primary form of the
reaction of many drivers to an FCW alert. In fact, it is the primary objective
of any collision avoidance algorithm to determine the right time for braking
to avoid a dangerous scenario. The main parameters of the simulation are
presented in table LABEL:tab:simulation_parameters.

TABLE I: Parameters of Intelligent Driver Model for three categories of drivers Driver Type | Aggressive | Normal | Conservative
---|---|---|---
Comfortable Acceleration, $\left(m/s^{2}\right)$ |  $\alpha\in[$1.53,2.75$]$ |  $\alpha\in[$1.43,2.59$]$ | $\alpha\in[1.30,2.41]$
Comfortable Deceleration, $\left(m/s^{2}\right)$ | $\beta\in[1.52,2.73]$ | $\beta\in[1.43,2.59]$ | $\beta\in[1.27,2.41]$
Desired Time Headway, (s) | $f_{\Gamma}(x\mid\alpha,\beta)<2$ | $f_{\Gamma}(x\mid\alpha,\beta)\leq 3$ | $3<f_{\Gamma}(x\mid\alpha,\beta)$
Ratio | 19 % | 43 % | 38 %
TABLE II: Simulation Parameters Duration, minutes | 90
---|---
Number of Vehicles | 150
Exact Number of Drivers |
(Aggressive/Normal/Conservative) | 27 / 66 / 57
Network’s Packet Error Rate (PER) | 30
Implemented FCW Algorithms | CAMP Logistic Regression,
| NHTSA Driver-Tuned Models
Error-dependent Estimator | Constant Acceleration

In addition to Time Headway ($\tau$), we also use Time-To-Collision (TTC) to
evaluate the performance of the two FCW algorithms. TTC is a safety metric
that is frequently used in the literature and can be computed using the
following formula[47]:

$TTC_{i}=\frac{x_{i}-x_{i-1}}{v_{i}-v_{i-1}},\ \forall\>v_{i}>v_{i-1}$ (6)

where indices $i$ and $i-1$ represent the host and the leading vehicles,
respectively.

We start our first simulation analysis without the warning algorithm enabled.
After multiple runs, a factor of $3\%$ distracted drivers resulted in an
average of $42$ accidents, $81\%$ of which were resulted from distraction,
$17\%$ from aggressive driving characteristics, and the other $2\%$ were
caught in a pileup. Of these $42$ counted collisions, $33.3\%$ involved
aggressive drivers, $50\%$ normal drivers, and $16.3\%$ conservative drivers.
It is worth mentioning that the vehicles that were involved in an accident
continued blocking the road for a period of $10$ to $20s$ before being removed
from and respawned back into the simulator at a later time.

For a comparison with NGSIM data, the count density distribution of time
headways of different classes of drivers is shown below (Figure 14). The
following results include both cautious and distracted drivers for each
behavior characteristic. We can observe that the combined distribution with a
mode of $~{}2.5s$ exhibits similar characteristics as the analysis shown in
section IV.

Next, the same scenario was repeated several times but with the vehicles
equipped with FCW systems and the drivers able to react to a warning by hard
braking. We run a series of analyses with a communication network packet error
rate (PER) of $30\%$. Table III shows the collision statistics obtained for
each class of driver and the respective FCW algorithm.

TABLE III: Crash and warning statistics for a simulated 90 minutes long
scenario

Driver Type (Number of Drivers) Aggressive (27) Normal (66) Conservative(57)
Collision Information Total Distracted Leader Hard Braking Total Distracted
Leader Hard Braking Total Distracted Leader Hard Braking Collision Statistics
No Warning Algorithm 14 7 0 21 21 0 7 6 0 CAMP Logistic Regression 6 2 4 8 8 1
5 5 0 NHTSA Early $(0.32g)$ 6 6 0 5 5 0 0 0 0 NHTSA Intermediate $(0.4g)$ 6 3
2 5 5 0 3 3 0 NHTSA Imminent $(0.55g)$ 11 6 7 7 7 2 1 1 0 Warning Information
Total Positive Ratio Total Positive Ratio Total Positive Ratio Warning
Statistics CAMP Logistic Regression 843 156 18.5% 1116 411 36.8% 309 38 12.3%
NHTSA Early $(0.32g)$ 1105 117 10.5% 1063 361 34.0% 193 168 87.0% NHTSA
Intermediate $(0.4g)$ 1290 70 5.4% 958 402 42.0% 208 143 68.7% NHTSA Imminent
$(0.55g)$ 989 122 12.3% 442 208 47.1% 149 57 38.3%

While some collisions were inevitable, all the FCW algorithms were effective
in significantly reducing the number of collisions. Upon the occurrence of a
collision, our algorithms analyzed the scenario to determine who was at fault.
The ”Total” column for each driver’s class in table III refers to the total
number of crashes that type of driver was at fault. We can see that for all
scenarios analyzed, conservative drivers were involved in considerably fewer
accidents, whereas aggressive drivers, despite their smaller numbers $(18\%)$,
were the most at fault. Surprisingly, all accidents in which a normal or
conservative driver was at fault were caused by them being distracted. Hence,
this implies that not all the tested FCW algorithms were effective in
preventing distracted-related collisions. Recall that all drivers had a $1.3s$
perception-reaction delay. This implies that the implemented algorithms may
still fail in complex circumstances, e.g., the vehicle traveling at higher
speeds with its driver being distracted while the leader experiences an
emergency state and suddenly brakes[33]. Amongst the two FCW algorithms, CAMP
Logistic Regression performed worse than all three settings of NHTSA as this
algorithm is not a fully-adaptive algorithm with less flexibility compared to
the driver-tuned NHTSA ones.

Figure 14: Count density distribution of time headways of simulated vehicles
for each class of drivers.

When a driver displays a sudden reaction to a warning by hard braking, it
forces its following vehicles to slow down or potentially hard brake too,
causing more hazards and near-crash scenarios[21]. For the simulation
configuration above, we observed that an accident might result from either a
distracted driver or a sudden slowdown of a leading vehicle, or a combination
of both. Therefore, we consider a warning that successfully averted such a
crash scenario into a near-crash as a positive warning.

Table III shows the statistics with regard to the number of warnings
generated. For the aggressive driver, we can see that the NHTSA Early and
Intermediate had the most warnings generated, though the majority of these
were false warnings. This is also true for the other two algorithms which
imply that for aggressive driving behavior, none of these algorithms are
suitable options. Such a significant fraction of false warnings will result in
the frustration of the driver and ultimately in him/her shutting down the
system. A similar trend follows for normal drivers whereas the NHTSA with
Early alert settings appeared to assist the conservative drivers exceptionally
well with $87\%$ positive warnings and zero accidents at fault.

The overall sensitivity of each FCW algorithm is represented as the
Probability Distribution Function (PDF) of the TTCs when a warning was issued
(Figure 15). While the time headway distributions show similar characteristics
and are close to each other, we can see a noticeable difference in the
distribution of time-to-collision. Figure 16 explains the poor performance and
higher number of accidents for the CAMP Logistic Regression algorithm as the
$90^{th}$ percentile of the warnings being generated when host vehicles were
less than $4s$ away from colliding with their leading vehicles. We can
conclude from this observation that the algorithm was tuned for very
aggressive driving characteristics. However, considering the perception-
reaction delay of a driver, the timings of these warnings were still late even
for an aggressive driver to effectively avoid the collision. This observation
implies that it is crucial to consider different driver-specific parameters,
especially the perception-reaction time when designing adaptive vehicular
active safety systems. Accordingly, this trend is followed by NHTSA Imminent,
Intermediate, and with Early having a $90^{th}$ percentile of $8s$. Note that
all the time headways and time-to-collisions shown in this paper are
calculated via communicated data that are received by host vehicles through
BSM messages.

Figure 15: Sensitivity of each forward collision warning algorithm represented
through empirical distribution functions of time headway Figure 16:
Sensitivity of each forward collision warning algorithm represented through
empirical distribution functions of time-to-collision

##  VI Conclusion and Future Work

With the rapid growth of advanced driver assistants and automated systems,
simulation tools have become an integral part of the development process of
these systems. Simulators not only can improve development efficiency, but
also can offer opportunities to analyze scenarios that otherwise would have
been extremely costly, time-consuming, and on some occasions dangerous to
human subjects. In this work, we extended our co-simulation framework [17] and
deployed it on the state-of-the-art game engine technology UE4. With the help
of NVIDIA PhysX and the UE4 physics engine, we were able to represent a large-
scale traffic scenario with detailed 3D physics and visualization. We
described the individual components of our platform in detail and proposed a
simple human interpretable extension to the traditional car-following models.
The extended model related a human driver to a feedback controller and
employed the Intelligent Driver Model to supply a reference acceleration while
incorporating a Fuzzy-PD system to compensate for the error. In this extended
approach, we integrated the perception-reaction delay time of the driver as an
individual component, along with descriptive driving characteristics through
the parameters of the Intelligent Driver Model and Fuzzy membership functions.
Furthermore, to extract these various driving behaviors, we surveyed different
driving characteristics and examined a traffic dataset from a congested
scenario. We used the drivers’ time headway and acceleration as descriptive
features of their driving style. Using this data, we divided the drivers into
three categories: aggressive, normal, and conservative. We found that a gamma-
distribution function can best describe the dispersal of the drivers within
the environment. Finally, we incorporated all the extracted parameters into
our simulator and equipped the vehicles with forward collision warning
systems. We then analyzed the performance of these systems for each class of
driver with a hard-braking response as a driver reaction to a collision
warning. Of the tested safety algorithms, driver-tuned NHTSA with Early
warning configuration performed remarkably well for conservative drivers with
$87\%$ positive warnings generation and prevented all rear-end collisions.
Conversely, none of the four configurations of forward collision warning
systems showed adequate performance for aggressive driving characteristics.

Many active safety systems make extensive use of the kinematical parameters of
both the host and the leading vehicles. Given the importance of these
parameters in the judgment made by safety algorithms, they must be simulated
with the highest accuracy possible. Unfortunately, car-following models make
significant simplifications to the vehicles’ dynamics, to a level that a
detailed look at their response curve shows unnatural and abrupt changes in
the velocity and acceleration of vehicles, which leads to false warnings even
for safe and collision-free scenarios. The unrealistic kinematical response of
CFMs especially taints those models that are based on calculating the next
speed value. This limitation led to many false warnings in our previous
evaluations. Separation of vehicle dynamics from its driver model allowed for
a more accurate kinematic response which in turn resulted in better studying
of such active safety systems and obtaining test results that were otherwise
not producible by traditional simulators.

It is expected that AVs and HVs will share the road. AVs’ safety and
reliability will be determined by their social awareness and ability to engage
in complex social interactions in a socially acceptable manner. However, AVs
are still inefficient when it comes to collaborating with HVs, and they
struggle to understand and adapt to human behavior, which is especially
difficult in mixed autonomy. We intend to continue this work in this direction
and improve the simulation environment so that it can incorporate data from
real-world traffic and handle more complex interactions between HVs and AVs.

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