# An Assessment of Safety-Based Driver Behavior Modeling in Microscopic
Simulation Utilizing Real-Time Vehicle Trajectories

Awad Abdelhalim Corresponding Author
Postdoctoral Research Associate
Department of Urban Studies and Planning
Massachusetts Institute of Technology  Cambridge  MA 02139
Email<EMAIL_ADDRESS>
Montasir Abbas
Professor
Virginia Polytechnic Institute and State University
301 Patton Hall  Virginia Tech  Blacksburg  VA 24061
Tel: 540-231-9002
Email<EMAIL_ADDRESS>
##  1 Abstract

Accurate representation of observed driving behavior is critical for
effectively evaluating safety and performance interventions in simulation
modeling. In this study, we implement and evaluate a safety-based Optimal
Velocity Model (OVM) to provide a high-fidelity replication of safety-critical
behavior in microscopic simulation and showcase its implications for safety-
focused assessments of traffic control strategies. A comprehensive simulation
model is created for the site of study in PTV VISSIM utilizing detailed
vehicle trajectory information extracted from real-time video inference, which
are also used to calibrate the parameters of the safety-based OVM to replicate
the observed driving behavior in the site of study. The calibrated model is
then incorporated as an external driver model that overtakes VISSIM’s default
Wiedemann 74 model during simulated car-following episodes. The results of the
preliminary analysis show the significant improvements achieved by using our
model in replicating the existing safety conflicts observed at the site of the
study. We then utilize this improved representation of the status quo to
assess the potential impact of different scenarios of signal control and speed
limit enforcement in reducing those existing conflicts by up to 23%. The
results of this study showcase the considerable improvements that can be
achieved by utilizing data-driven car-following behavior modeling, and the
workflow presented provides an end-to-end, scalable, automated, and
generalizable approach for replicating the existing driving behavior observed
at a site of interest in microscopic simulation by utilizing vehicle
trajectories efficiently extracted via roadside video inference.

Keywords: Driver behavior modeling, optimal velocity model, microscopic
simulation.

##  2 INTRODUCTION

Traffic modeling and simulation is one of the most powerful tools at the
disposal of transportation engineers today. The modeling and simulation of a
specific site, corridor, or network of interest provides transportation
practitioners with an efficient and effective method to assess the current
performance and evaluate any proposed performance or safety interventions.
Simulation modeling can be sub-categorized into three types:

  * •

Macroscopic Simulation, which provides a high-level representation of traffic
streams,

  * •

Microscopic Simulation, where vehicles are modeled at an individual level, and

  * •

Mesoscopic Simulation, which aims to utilize a combination of macro and
microscopic simulation methods.

While macroscopic and mesoscopic are the more common choices of modeling when
simulating larger networks, microscopic simulation is more often used for
studying the traffic flow in smaller areas, in greater detail. In microscopic
simulation, however, the individual vehicles’ behavior is based on
mathematically-derived driver behavior models that require a tedious process
of data collection and parameter calibration to better replicate the observed
behavior in the specific area of interest. This has generally been the
challenge for the wide-scale adoption of microscopic simulation.

PTV’s Verkehr In Städten SIMulationsmodel (VISSIM) is a discrete, stochastic,
time step-based simulation software that is one of the most popular tools used
for traffic simulation due to its extensive capabilities for modeling and
evaluating different components of the transportation ecosystem (vehicles,
public transit, pedestrians, cyclists, roadside infrastructure, etc.).
VISSIM’s base car-following model is based on the Wiedemann 74 and 99 psycho-
physical models [wiedemann1991modelling]. The car-following behavior of
vehicles in a VISSIM simulation is modified through ten driver behavior
parameters (labeled CC0 – CC9) that represent different thresholds of four
assumed driving states: free-driving, approaching, following, and braking. For
each of those modes, the desired instantaneous acceleration is a result of the
vehicle’s current speed, the speed and distance differences between the
vehicle and the lead vehicle, and specific characteristics of the driver and
the vehicle. The challenge with the Wiedemann model (and other conventional
driver behavior models, e.g. Gazis-Herman-Rothery, Fritzsche) is that they
assume that drivers make longitudinal decisions (i.e. acceleration) based on
assumed momentary stimuli inputs. These models do not account for the driver’s
planned decision process, where a driver could perceive an impending danger,
and plans to avoid that danger, then executes that plan in multiple time
steps. This is especially important when modeling safety-critical or close-to-
critical situations, when an ego vehicle approaches a vehicle that slows down,
forcing the driver of the ego vehicle to start a process of avoidance or
adjustment in their speed trajectory. The failure to capture this behavior
leads to an inaccurate representation of traffic when modeled in simulation,
hindering the ability to evaluate safety interventions.

###  2.1 Objective and Contributions

This study aims to showcase the improvements that can be achieved in VISSIM
simulation of safety-critical behavior utilizing real-time, safety-based
driver behavior modeling. The real-time safety-based Optimal Velocity Model,
which was proposed in a recent study [abdelhalim2021safety] is calibrated for
the site of study using vehicle trajectories extracted from a roadside camera
and implemented in VISSIM as an external driver model. We compare the
performance of our model to the default VISSIM model in terms of replicating
the existing safety-critical behavior at the area of study. We then assess the
impact of different scenarios of signal control and speed enforcement in
mitigating the simulated safety concerns. The following sections of this paper
are as follows: (a) a survey of related literature on driver behavior modeling
in microscopic simulation and trajectory-based traffic safety, (b) a detailed
breakdown of the VISSIM model development and external driver model
implementation, (c) results and analyses of the case study, and, (d)
discussion and conclusions.

###  2.2 Related Work

####  2.2.1 Driver Behavior and Safety Modeling in Microscopic Simulation

Over the past two decades, the growing adoption of microscopic simulation
software has provided researchers with powerful means for evaluating different
components of transportation networks and their interactions. The simulated
vehicle interactions, which form the basis of microscopic driving behavior
models, allowed for the assessment of traffic safety and evaluation of
countermeasures as opposed to solely relying on analyzing crash data from
police reports. The Surrogate Safety Assessment Model (SSAM)
[gettman2008surrogate] is the prime example of such efforts. Using vehicle
trajectories exported from microsimulation as an input, SSAM’s approach
utilizes conflict analysis for near misses, in terms of time-to-collision
(TTC) and post encroachment time (PET), to infer surrogate measures of actual
crash data in terms of frequency, types, and severity of crashes. SSAM,
however, is dependent on the outputs generated by microsimulation. Hence,
adequate parameter calibration for the underlying driver behavior model used
to generate the vehicle trajectories is a crucial step that the lack thereof
was found to result in a significant deviation of simulated safety conflicts
from the observed behavior [vasconcelos2014validation],
[huang2013identifying], [dijkstra2010calculated].

Given the increasing popularity of VISSIM over the years, numerous studies
have been conducted to assess the sensitivity of calibrating its underlying
Wiedemann car-following model to better mimic the existing traffic flow and
behavior and result in more realistic simulated safety conflicts. Fellendorf
and Vortisch [fellendorf2001validation] conducted one of the earliest studies,
where they assessed the impact of the driver model calibration on both a micro
and macroscopic level. The results of their study indicated that a well-
calibrated model can replicate traffic flow with high accuracy, with the
caveat that driver behavior models should at least take national and regional
regulations and driving styles into account to produce reliable
representations in simulation. Lownes and Machemehl [lownes2006vissim,
lownes2006sensitivity] conducted a sensitivity analysis to assess the impact
of modifying VISSIM’s driver behavior parameters on simulated traffic flow
capacity. Their work has highlighted the impact of changes on driver behavior
models at a microscopic level on traffic flow at a macroscopic level, further
making the case for the necessity of parameter calibration to ensure adequate
representation of traffic modeled in the simulation. Other studies have also
highlighted the necessity of taking into account the varying traffic patterns
to be modeled and the specific considerations needed for calibrating VISSIM’s
driver behavior parameters accordingly, such cases include modeling traffic at
urban intersections [manjunatha2013methodology], [arafat2020data] and freeway
merge areas [fan2013using]. The work of Fan et. al. [fan2013using]
particularly stands out in this category, as VISSIM’s default driver behavior
parameters were calibrated for freeway driving, yet separate parameter
calibration for merging sections specifically was necessary, with the results
highlighting the significant improvements obtained. This was attributed to the
default VISSIM model parameters being calibrated from driving data from the
German autobahn, while the study was conducted in China, hence the driving
behavior parameters were not entirely transferable.

The transferability of the calibrated VISSIM driver behavior model parameters
was assessed by Essa and Sayed [essa2015transferability], who calibrated the
VISSIM model parameters to maximize the correlation between observed and
simulated traffic conflicts in one intersection and tested the calibrated
model on a nearby intersection. Their study concluded that while not all of
the calibrated model parameters are fully transferable, the calibrated model
still significantly outperforms the default model in terms of providing a
better correlation between the observed and simulated traffic conflicts.
Hence, any safety assessment without proper model calibration should be
avoided. Essa and Tarek further highlighted this need for rigorous calibration
and the limitations of simulation-based safety assessment in other studies
[essa2015simulated], [essa2020comparison].

The extensive literature in VISSIM, and microscopic model parameter
calibration in general, lacks a clear and transferable framework to overcome
the shortcomings of site-by-site data collection and calibration of driver
model parameters to reduce errors versus observed data. In recent years,
researchers have opted to utilize neural network models to overpass this
tedious process [otkovic2020validation], [naing2021data]. And while such
methods succeed in producing improved results, they lack interpretability,
unlike the traditional driving behavior models which are based on traffic flow
theory fundamentals. There exists, therefore, a need for a generalizable
driving behavior modeling approach for simulation to better mimic the vehicle
trajectories being simulated and their resulting safety conflicts, allowing
for a more accurate assessment of proposed safety interventions. To overcome
this gap identified in driver behavior modeling calibration and its
application in VISSIM, we propose an implementation of a data-driven high-
fidelity external driver behavior model in VISSIM and showcase its utilization
in a case study to assess appropriate safety interventions. The proposed
external driver model is calibrated from video inference for the site of
interest, providing an end-to-end scalable, automated, and generalizable
workflow for replicating the observed behavior in microscopic simulation.

##  3 METHODOLOGY

###  3.1 Area of Study, Data Collection, and the VISSIM Model

In a recent study [abdelhalim2021safety], we utilized an extended VT-Lane
framework to obtain the trajectories and calibrate a data-driven safety-based
driver behavior model for the area of study. Previous works detail the
implementation and evaluation of the computer-vision-based trajectory tracking
framework [abdelhalim2020vt, abdelhalim2020towards, abdelhalim2021framework].
Figure 1 shows the area of this study from the perspective of the roadside
camera used to obtain the video data, illustrating the NEMA movement
enumeration for the site. The traffic volumes and speed distributions obtained
from the inference of 1-hour PM traffic footage were modeled in VISSIM
alongside the existing on-site signal timing plan illustrated in Figure 2.

(a) Site of study and NEMA movement labels.

(b) Trajectories and movement classification.

(c) The VISSIM model developed for this study.

Figure 1:  Site of study and tracked vehicle trajectories. Figure 2:  NEMA
movements and on-site signal timing plan.

###  3.2 Incorporating the Safety-Based Driver Model

VISSIM’s external driver model module is utilized to incorporate our
calibrated safety-based OVM. The C++ generated Dynamic Link Library (DLL) file
is executed during VISSIM’s simulation runs once every simulation step for all
vehicles present in the network. All vehicles in the network are controlled by
the default Wiedemann model that VISSIM utilizes unless they are engaged in
car-following episodes. In this study, a vehicle is considered in car-
following if it is moving at a speed $\geq$ 5 m/sec (18 km/hr), and there
exists a slower leading vehicle moving in the same lane. The threshold ensures
that the model is not utilized for vehicles that are stopping at the
intersection due to signal control, which could be assumed to be in a car-
following model based on estimated TTC. Figure 3 shows a flowchart with the
code execution logic for driver behavior model selection in VISSIM, which is
detailed in Algorithm 1.

The widely used optimal velocity model first proposed by Bando et al.
[bando1995dynamical] calculates the speed of the following vehicle based on
the distance gap given by Equation 1, from which the desired acceleration is
calculated using Equation 2.

$v_{opt}(s)=v_{o}\frac{\text{tanh}\left(\frac{s}{\Delta
s}-\beta\right)+\text{tanh}\ \beta}{1+\text{tanh}\ \beta}$ (1)

$\dot{v}=\frac{v_{opt}(s)-v}{\tau}$ (2)

Where:
$s$ = Distance gap between vehicles in a car-following episode ($m$).
$v_{opt}(s)$ = The theoretical optimal velocity for a given distance gap
($km/hr$).
$v_{o}$ = Desired speed ($km/hr$), $\Delta s$ = Transition width ($m$).
$\beta$ = Form Factor, $\dot{v}$ = OVM acceleration ($km/hr/sec$).
$v$ = Actual speed of a following vehicle ($km/hr$).
$\tau$ = Adaptation time ($sec$).

For our modified safety-based OVM [abdelhalim2021safety] which is incorporated
in VISSIM as an external driver model for this study, the instantaneous
optimal velocity and resulting desired acceleration based on real-time TTC are
calculated using the following equations:

$v_{opt}(ttc)_{i,n}=v_{o}\frac{\text{tanh}\left(\frac{ttc_{i,n}}{\Delta
s}-\beta\right)+\text{tanh}\ \beta}{1+\text{tanh}\ \beta}$ (3)

$\dot{v}=(1-\alpha)\frac{v_{opt_{i,n}}-v_{i,n}}{\tau}+\alpha
f(ttc_{observed})$ (4)

Where:
$ttc_{i,n}$ = Instantaneous time-to-collision between vehiclei and preceding
vehicle in a car-following episode at simulation time step $n$ ($sec$).
$v_{opt}(ttc)_{i,n}$ = The theoretical optimal velocity for vehicle $i$ during
simulation time step $n$ ($km/hr$).
$v_{o}$ = Desired speed ($km/hr$), $\Delta s$ = Transition width ($sec$).
$\beta$ = Form Factor, $\dot{v_{i,n}}$ = Desired acceleration for vehicle $i$
during time step $n$ ($km/hr/sec$).
$v_{i,n}$ = Actual speed of vehicle $i$ during simulation time step $n$
($km/hr$).
$\tau$ = Adaptation time ($simulation\ time\ steps$).

Figure 3:  VISSIM driver behavior model selection logic.

The weighted observed acceleration, $\alpha f(ttc_{observed})$, allows our OVM
to implicitly learn location-specific driving behavior characteristics from a
subset of the observed driving behavior on-site to supplement the base OVM
model’s assumptions while maintaining the benefits of interpretability of the
remaining model parameters (e.g., the calibrated model had a lower desired
speed for vehicles executing turning movements compared to through moving
vehicles, which is logical). We utilized VT-Lane’s ability to classify the
vehicles’ movements across the intersection to calibrate separate model
parameters for through-moving vehicles and vehicles executing turning
movements at the intersection. The parameter calibration process for the model
and substantial improvements achieved compared to the base OVM are detailed in
[abdelhalim2021safety]. The calibrated model parameters for each movement type
utilized by the external driver model in this study are detailed in Table 1.
Algorithm 1 details the steps for the external driver model application during
each simulation time step, where it is applied to all the vehicles in
simulation.

Table 1: Optimal Parameters For The Calibrated Safety-Based OVM | Vehicle Movement
---|---
Through | Turning
$\Delta s$ | 4.63 | 4.76
$\beta$ | 1.10 | 0.10
$\tau$ | 6.11 | 5.83
$v_{o}$ | 38.20 | 31.95
$\alpha$ | 0.18 | 0.01

Result: Desired acceleration of vehicles in VISSIM simulation.

initialization;

for  _$time\\_step_{n}$_ do

for  _$vehicle_{i}$_ do

if  _$speed_{i,n}\ <\ 5\ (m/s)$_ then

$acceleration_{i,n}\leftarrow{}Default$;

else

if  _$vehicle_{i,n}\ \exists\ \Delta\ Distance\ \And\ \iff\ \Delta\
Speed\in\mathbb{R}^{+}$_ then

$v_{opt_{i,n}}\leftarrow{}v_{o}\frac{\text{tanh}\left(\frac{ttc_{i,n}}{\Delta
s}-\beta\right)\ +\ \text{tanh}\ \beta}{1+\text{tanh}\ \beta}$;

$acceleration_{i,n}\leftarrow{}{\scriptsize(1-\alpha)}\frac{v_{opt_{i,n}}-\
speed_{i,n}}{\tau}+\alpha f(ttc_{observed})$;

else

$acceleration_{i,n}\leftarrow{}Default$;

end if

end if

end for

end for

Algorithm 1 VISSIM External Driver Behavior Model

##  4 RESULTS AND ANALYSIS

###  4.1 Observed Vehicle Behavior and Safety Conflicts

A 1-hour simulation (preceded by a 15-minute warm-up) was conducted in VISSIM
and the instantaneous time-to-collision for vehicles involved in car-following
episodes was calculated and stored in an external database. Figure 4
illustrates the location of safety conflicts and the associated average TTC
for car-following instances where the TTC was $\leq$ 3 seconds for each
location. X and Y coordinates are respectively the local longitude/latitude in
the VISSIM model.

(a) VISSIM’s base Wiedemann model.

(b) Safety-Based Optimal Velocity Model.

Figure 4:  Observed average TTC (where instantaneous TTC $\leq$ 3s) for
simulation model.

It can be clearly observed that VISSIM’s base Wiedemann model is extremely
conservative in generating safety conflicts during car-following episodes.
Even when instances of low TTCs do occur, the vast majority take place as
vehicles approach the stop bars at the intersections’ four approaches. The
base VISSIM model generates minimal safety conflicts as vehicles traverse the
intersection and as they continue to accelerate downstream, where following
vehicles seem to always be accelerating at a rate slower than the leading
vehicles, leading to a severe underestimation of safety conflicts as reported
by numerous studies in the literature. Our Safety-Based OVM that was
incorporated in VISSIM generates a more realistic driving behavior that would
be expected at an urban intersection, especially as vehicles accelerate to
clear the intersection and at the merge areas of through lanes with turning
lanes as clearly illustrated in Figure 4 (b).

This distinction between VISSIM’s default behavior and the external driver
model is most evident when looking at safety-critical situations where the TTC
between vehicles involved in a car-following episode momentarily drops to 1
second or less as can be seen in the figure. Out of 2667 vehicles in the
1-hour simulation, 31 vehicles (1.1%) had safety-critical car-following
instances using VISSIM’s default model, compared to 210 (7.8%) when utilizing
the external driver model, where an instance is one simulation timestep (0.10
seconds).

###  4.2 Impact Assessment of Mitigation Measures

Based on this replication of observed driving behavior, we assess the impact
of different mitigation measures on reducing the number of simulated
conflicts. The area of study has a posted speed limit of 35 mph (55 km/hr).
The observed speeds from video inference that were utilized in creating this
simulation model had an 80th percentile speed of 35 mph (55 km/hr) and 95th
percentile speed of 47 mph (75 km/hr), which is expected as there is no speed
enforcement on-site and drivers typically drive above this posted speed limit.
We assess the impact of enforcing speeds at 65 km/hr and 55 km/hr,
respectively. Those enforcement measures are assessed with three scenarios of
signal control, the current signal control previously illustrated in Figure 2,
a scenario with a half-cycle length (70 seconds instead of 140), and a split-
phasing signal control scenario. A sensitivity analysis for those enforcement
and signal control scenarios is conducted for the observed, as well as half,
and double the traffic volumes. For brevity, the conventions for the different
scenarios used hereafter are shown in Table 2. Signal control scenarios are
color-coded and labeled by name.

Table 2: Conventions for Volume/Speed States $\downarrow$ Volume / Speed $\rightarrow$ | Observed | 65 km/hr | 55 km/hr
---|---|---|---
Observed | V_S | V_65 | V_55
Half | 1/2V_S | 1/2V_65 | 1/2V_55
Double | 2V_S | 2V_65 | 2V_55

(a) Count of car-following episodes.

(b) Percentage of episodes relative to total volume.

Figure 5:  Car-following episodes with safety-critical instantaneous TTC
($\leq$ 1.5 sec) for the different simulated scenarios.

Figure 5 shows the counts and percentages of car-following episodes with
instances of safety-critical TTC $\leq$ 1.5 sec. For the existing volume and
given turn movement classifications at the intersection, utilizing a split-
phasing control was found to reduce the number of generated safety-critical
conflicts by over 23%. Enforcing a 65 km/hr speed provides further but not
substantial improvements. Split-phasing was also found to produce
substantially better results in terms of safety in the scenario of lower
traffic volumes. Conversely, it was the lowest performer in the case of double
the observed volume.

Figure 6:  Instantaneous safety-critical conflicts under current signal
control.

Figures 6 to 8 show all of those safety-critical conflicts for the different
simulation scenarios, illustrating instantaneous (not averaged) safety-
critical time-to-collision conflicts and their locations within the
intersection’s area. The split-phasing which was found to significantly reduce
the existing safety conflicts can be seen in Figure 8 almost eliminating the
conflicts generated at the turning lanes. The extended queues for phases 2 and
6 due to split-phasing resulted in an extended shockwave as vehicles approach
and stop at the intersection during a red light, hence it is to be avoided in
case of an increased traffic volume at this intersection.

Figure 7:  Instantaneous safety-critical conflicts under half cycle length.
Figure 8:  Instantaneous safety-critical conflicts under split-phasing.

##  5 CONCLUSIONS

This study provided an assessment of utilizing a data-driven driver behavior
model to provide a high-fidelity simulation of safety-critical behavior. A
safety-based Optimal Velocity Model that was calibrated for the location of
study in Blacksburg, VA, and implemented in VISSIM as an external driver
model. The resulting safety conflicts were compared to that of VISSIM’s
default Wiedemann model, and the results showcase the substantial improvements
that can be achieved in simulation utilizing our proposed model in terms of
replicating the existing safety concerns. We utilized this improved behavior
modeling to quantify the impact of different signal control and speed
enforcement scenarios in mitigating the simulated safety concerns.

Unlike existing studies in the literature, our assessment did not involve a
process of specifically calibrating VISSIM’s model parameters to replicate the
observed or expected safety concerns in the area of study. Conversely, our
safety-based OVM utilized as an external driver model in this study was
calibrated beforehand from video inference, and the direct implementation of
that calibrated model resulted in a highly accurate representation of the
status-quo at the area of study without targeted fine-tuning within VISSIM.
The results highlight the value of this approach of video inference-based
driver behavior modeling which provides a highly scalable, automated, and
generalizable workflow and succeeds in better replicating the observed
behavior in microsimulation. Vehicle trajectories can be efficiently extracted
in real-time via our VT-Lane framework. While additional time is required post
trajectory acquisition to calibrate the model parameters, the task can be
effectively accomplished in near real-time which allows for the assessment of
changes in driving behavior due to traffic disruptions, changes in weather,
and other factors.

We concluded this study by assessing the potential impact of different signal
control and speed enforcement measures to reduce the simulated conflicts at
the intersection of the study across varying traffic volumes. The results
obtained and discussed in this study do not take into account the trade-off
between capacity and operational safety, which could be the subject of future
works. Those results, however, do present the practitioners with an additional
decision-support layer that effectively quantifies the expected safety impact
for the selected interventions as a function of the existing driving behavior
in an area of interest. Future studies will also assess the scalability and
transferability of this approach, which could provide traffic safety
practitioners and transport agencies with a robust decision-support tool for
evaluating the safety impact of different traffic demand management, signal
control, and enforcement measures.

##  6 Author Contribution Statement

The authors confirm their contribution to the paper as follows: study
conception and design: A.A., M.A.; data collection: A.A.; analysis and
interpretation of results: A.A.; draft manuscript preparation: A.A., M.A. Both
authors reviewed the results and approved the final version of the manuscript.
The authors do not have any conflicts of interest to declare.