A model for simulation and generation of surrounding vehicles in sriving simulators

B ACKGROUND

Traffic safety is a critical issue, with many accidents stemming from failures in the interaction between drivers, vehicles, and traffic systems As the number of driving-related interactions rises, drivers increasingly engage with intelligent transportation systems (ITS), advanced driver assistance systems (ADAS), in-vehicle information systems (IVIS), and NOMAD devices like mobile phones and portable computers These technologies significantly affect driver behavior and vehicle operation To effectively assess the impact of various ITS, ADAS, IVIS, NOMAD systems, and road design on drivers, a thorough understanding of the interactions between drivers, vehicles, and their environment is essential.

Researchers conduct behavioral studies and experiments in various environments, including real traffic systems, test tracks, and driving simulators While real-world settings provide the most authentic experience, they can be unpredictable due to factors like weather and traffic conditions, making it challenging to draw statistically significant conclusions Additionally, some experiments may be too dangerous, costly, or restricted by laws or ethical considerations Test tracks offer a safer alternative with more controlled conditions, reducing statistical uncertainty, but they often lack the realism needed to apply findings to actual road driving In contrast, driving simulators create a controlled and safe environment that allows for the manipulation of test conditions, providing a balance between realism and safety.

A driving simulator replicates the experience of operating a real vehicle, as illustrated in Figure 1.1 It can range from a complete vehicle cabin to a simple setup with just a seat, steering wheel, and pedals, with the driver's environment displayed on a screen The simulator employs a vehicle model to calculate movements based on the driver's inputs, and some systems incorporate motion technology to enhance the realism of these movements Additionally, driving simulators feature a scenario module that defines the road conditions, environment, and various actors and events encountered during the simulation.

Figure 1.1 The VTI Driving Simulator III (Source: Swedish National Road and Transport Research Institute (VTI) (2004))

Driving simulators are used to conduct experiments in many different areas such as:

• Technical systems, such as ITS, ADAS, IVIS, and NOMAD systems

Driving simulators, such as the TRAINER simulator developed for driving license schools, serve as valuable training tools They provide a safe environment to practice unsafe, challenging, or impossible scenarios encountered on real roads From basic maneuvering to emergency situations, the TRAINER simulator enhances driver training by allowing learners to develop essential skills without the risks associated with on-road practice.

For a driving simulator to accurately represent real-world driving, it is essential that the performance of the simulator vehicle, visual elements, and the behavior of surrounding objects are realistic Ambient vehicles must demonstrate trustworthy behavior, as they significantly influence a driver's mental load and overall driving capability This realistic representation is particularly crucial in simulator studies where traffic intensity and composition impact driver performance, such as in research on road design, new technology, or fatigue Moreover, it is vital that not only individual driver behavior is authentic, but also that the overall traffic flow is realistic, reflecting how faster drivers anticipate catching up with more vehicles than those that are slower.

Combining a driving simulator with microscopic traffic simulation can create a realistic representation of surrounding vehicles and traffic dynamics Micro-simulation has gained popularity for analyzing traffic systems, employing various sub-models for car-following, lane-changing, and speed adaptation to reflect driver behavior at a granular level These behavioral models take into account the current road and traffic conditions to generate individual driver decisions, such as acceleration and lane selection Stochastic functions introduce variability in driver behavior, accounting for differences among drivers and changes over time However, traditional methods have relied on deterministic models for simulating ambient vehicles in driving simulators Utilizing stochastic simulation for ambient traffic allows for varied micro-level experiences for drivers, while maintaining comparability at a higher aggregated level This approach may be beneficial for certain experiments, though others may require consistent micro-level conditions for accuracy.

A IM

This thesis focuses on the development and validation of a real-time traffic simulation model designed to generate and simulate surrounding vehicles within a driving simulator The model aims to realistically replicate individual vehicle-driver interactions and the overall traffic flow It emphasizes accurate behaviors in acceleration, lane changes, overtaking, and speed choices, ensuring that the simulated vehicles reflect real-world data in terms of headways, vehicle types, and speed distributions.

D ELIMITATIONS

The simulation model focuses exclusively on two-lane freeways in each direction and rural roads with oncoming traffic, omitting ramps on freeways and intersections on rural roads As a result, this thesis does not address the simulation of urban traffic scenarios.

Driving simulator experiments often incorporate critical situations to assess vehicle responses To effectively create these scenarios, autonomous vehicles must interact with vehicles exhibiting predetermined behaviors However, this thesis addresses the topic only to a limited extent.

T HESIS OUTLINE

Chapter 2 gives an introduction to the field of microscopic simulation of traffic The chapter includes a survey of common car-following, lane-changing, overtaking, and speed adaptation models

Chapter 3 introduces driving simulator experiments and the simulation of surrounding vehicles within these simulators It discusses the benefits and challenges of employing stochastic traffic simulation for accurately representing surrounding vehicles The chapter concludes with an overview of related research in this field.

Chapter 4 introduces the proposed model, beginning with an overview of the simulation framework It then details the technique employed for generating new vehicles, concluding with a discussion of the behavioral models used and the calibration of the relevant parameters.

Chapter 5 outlines the integration of the proposed simulation model with the VTI Driving Simulator III, beginning with a brief overview of the driving simulator before detailing the integrated system.

Chapter 6 presents the validation of the model, beginning with a discussion on the validation process for such models It includes a description and results from validating the interactions between the simulated vehicles and the driving simulator vehicle Additionally, a driving simulator experiment is detailed to assess the behavior of the simulated vehicles The chapter concludes with a discussion and additional observations gathered during the driving simulator tests.

Chapter 7 ends the thesis with a summary and a discussion on future research needs and possibilities.

C ONTRIBUTIONS

This thesis presents a novel traffic simulation model designed to effectively simulate ambient vehicles in a driving simulator, applicable to both freeways and rural roads with oncoming traffic Additionally, the research contributes valuable insights and methodologies to enhance traffic simulation studies.

• A summary over commonly used behavioral models for car-following, lane-changing, overtaking, and speed adaptation

• An investigation of difficulties, benefits, advantages and disadvantages with using stochastic micro simulation of traffic for simulation of ambient traffic in a driving simulator

A novel technique has been developed to generate realistic freeway traffic on a dynamic, moving area surrounding a driving simulator, significantly enhancing the overall simulation experience Building on this innovation, the technique has been further refined to accommodate the generation of vehicles on rural roads, where the absence of a barrier between oncoming traffic poses unique challenges This advanced approach enables the creation of more diverse and realistic traffic scenarios, allowing for a more immersive and effective driving simulation experience.

• A new simple mesoscopic traffic simulation model that simulates individual vehicles using speed-flow diagrams The model is used to simulate vehicles far away from the simulator vehicle

• A new version of the TPMA (Davidsson et al., 2002) car-following model, including a new deceleration model

• An enhanced version of the VTISim (Brodin et al., 1986) overtaking model, which includes new models for the behavior during the overtaking and at abortion of overtakings

• Integration of the simulation model and the VTI Driving simulator III

• Presentation of different approaches that can be used to validate models for simulating surrounding vehicles in driving simulators.

P UBLICATIONS

Some parts of this thesis have been published in other publications The first version of the framework for generation and simulation of vehicles on freeways was originally presented in

Janson Olstam, J and J Simonsson (2003), Simulerad trafik till VTI:s kửrsimulator - en fửrstudie (Simulated traffic for the VTI driving simulator - a feasibility study, In Swedish) VTI Notat 32-2003 Swedish National Road and

Transport Research Institute (VTI), Linkửping, Sweden

A partly enhanced version of this framework was later presented in

Janson Olstam, J (2003) “Traffic Generation for the VTI Driving Simulator” In Proceedings of: Driving Simulator Conference - North

America, DSC-NA 2003, Dearborn, Michigan, USA

The generation and simulation framework for simulation of rural road traffic for driving simulators was first presented in:

Janson Olstam, J (2005) “Simulation of rural road traffic for driving simulators” In Proceedings of: 84th Annual meeting of the Transportation

Section 2.3.1 in the thesis includes a survey over car-following models The main part of this survey has been presented in:

Janson Olstam and A Tapani (2004) conducted a comparative analysis of car-following models, published in VTI Meddelande 960A and LiTH-ITN-R-2004-5 This research was a collaborative effort between the Swedish National Road and Transport Research Institute (VTI) and Linköping University’s Department of Science and Technology in Linköping, Sweden.

Modern societies require efficient traffic and transportation systems to address the persistent issues of congestion and traffic jams, which are prevalent in both large and small cities To mitigate these problems and enhance traffic systems regarding capacity, accessibility, and safety, traffic planners rely on predictive tools for evaluating various road designs and management strategies Over the past few decades, researchers have developed a range of models and tools to tackle these challenges, aided by advancements in personal computer technology Traffic models typically utilize either analytical or simulation approaches; while analytical models employ queue theory, optimization, and differential equations, they often fall short in capturing the temporal dynamics of traffic systems Conversely, simulation models excel in modeling traffic fluctuations over time, incorporating stochastic functions to accurately reflect the evolving nature of traffic dynamics.

Traffic simulation is a valuable and economical tool for analyzing traffic systems, enabling the evaluation of various road designs, regulations, ITS applications, and traffic management strategies These models allow for safe experimentation with both existing and hypothetical traffic scenarios However, to ensure reliable outcomes, traffic simulation models require thorough calibration and validation, a process that can be time-consuming and may impact their overall cost-effectiveness.

C LASSIFICATION OF TRAFFIC SIMULATION MODELS

Traffic models can be classified in various ways, with one common method categorizing them based on the level of detail in representing traffic streams The three primary categories are Microscopic, Mesoscopic, and Macroscopic traffic simulation models.

Microscopic traffic models provide a detailed representation of traffic flow by simulating individual vehicles and their interactions These models include sub-models for various driving behaviors, such as acceleration, speed adaptation, lane-changing, and gap acceptance, to accurately depict vehicle movements and their relationship with infrastructure Notable examples of such models include AIMSUN, VISSIM, Paramics, and MITSIMLab, each contributing to the understanding of traffic dynamics.

Mesoscopic models provide a detailed representation of traffic streams, focusing on individual vehicles or groups of vehicles while utilizing lower-detail interactions compared to micro models These models analyze the relationships between vehicles and infrastructure based on macroscopic factors such as flow, speed, and density Notable examples of mesoscopic simulation models include DYNASMART, developed by Jayakrishnan et al in 1994, and CONTRAM, introduced by Taylor in 2003.

Macroscopic models represent traffic streams with a low level of detail, focusing on aggregated variables such as flow, speed, and density rather than individual vehicles These models utilize speed-flow relationships and conservation equations to analyze how traffic propagates through networks Notable examples of macroscopic simulation models include METANET/METACOR and the Cell Transmission model, which have been developed by researchers like Papageorgiou, Salem, and Daganzo.

M ICROSCOPIC TRAFFIC SIMULATION

Microscopic traffic simulation models, also known as micro traffic simulation models, focus on simulating individual vehicles by treating drivers and their vehicles as a single unit These models capture the interactions between vehicle-driver units and their surrounding infrastructure They consist of various behavioral models that address specific interactions, with the car-following model being the most critical, as it manages the longitudinal dynamics between two vehicles Other significant behavioral models include those for lane-changing, gap-acceptance, overtaking, ramp merging, and speed adaptation The selection of sub-models is influenced by the type of road being simulated, as lane-changing models are essential for urban or freeway scenarios but unnecessary for two-lane highways without barriers A more detailed exploration of the most common behavioral models will be provided in Section 2.3.

Micro simulation models primarily focus on urban and freeway networks, with notable examples including AIMSUN, VISSIM, Paramics, MITSIMLab, and CORSIM However, there are only a few models specifically designed for two-lane highways with oncoming traffic Leading rural road models include the Two-Lane Passing (TWOPAS) model, Traffic on Rural Roads (TRARR) model, and the VTISim model The VTISim model is currently undergoing further development as part of the Rural Road Traffic Simulator (RuTSim) project.

To accurately model the diverse behaviors and preferences of drivers, each vehicle driver unit is assigned unique driver characteristic parameters, such as vehicle length, desired speed, following distance, and acceleration and deceleration rates These variations within the driver population are typically represented by a distribution function, from which individual parameter values are derived For instance, it can be assumed that the desired speeds on freeways adhere to a normal distribution, with a mean of 111 km/h and a standard deviation of 11 km/h.

Micro models typically operate on a time-discrete basis, although some event-based models have also been developed, such as those by Brodin and Carlsson (1986) In a time-discrete model, time is segmented into small intervals, usually ranging from 0.1 to 1 second During each interval, the model updates the status of every vehicle based on established behavioral models Once the interval concludes, the simulation clock advances, transitioning into the next time step.

Microscopic simulation models have been widely utilized for assessing capacity and level-of-service across various road designs and management strategies Over the past decade, these micro models have increasingly been applied to evaluate diverse Intelligent Transportation System (ITS) applications.

Speed Adaptation, also known as Adaptive Cruise Control systems, plays a crucial role in enhancing road safety (Liu et al., 2000; Champion et al., 2001) Research has explored the integration of micro-simulation with various safety indicators to analyze the safety of different road and intersection designs, as demonstrated in studies by Archer (2005) and Gettman et al (2003).

Micro models, while designed to simulate individual vehicles, primarily produce macroscopic outputs like average speeds, flows, and travel times Consequently, much of their calibration and validation occurs at a macroscopic level Although various behavioral models have been calibrated and validated to some degree at a micro level, there has been limited focus on the calibration and validation of combined behavioral models, such as the interaction between car-following and lane-changing models, to ensure they yield valid results at a micro level.

B EHAVIORAL MODEL SURVEY

Car-following models

A car-following model governs driver behavior based on the vehicle in front within the same lane A vehicle is deemed to be following when its movement is restricted by the preceding vehicle, making it necessary to adjust speed to prevent a collision Conversely, a vehicle is considered free when it is not influenced by another vehicle and can travel at its desired speed The follower's behavior is typically defined by its acceleration, though some models, like Gipps (1981), focus on speed While certain models only address behavior during direct following, others provide a comprehensive view of driver actions in various scenarios Effective car-following models categorize vehicle states and corresponding actions, often utilizing three primary regimes: free driving, normal following, and emergency deceleration In the free regime, vehicles pursue their desired speed, while in the following regime, they modify their speed based on the vehicle ahead In emergency deceleration, vehicles reduce speed to avert collisions The notation used in this section includes acceleration (a_n), position (x_n), and speed (v_n) for vehicle n.

∆v v n −v n − 1, difference in speed, [m/s] desired v n Desired speed, vehicle n, [m/s]

1 s n − Effective length (L n − 1 + minimum gap between stationary vehicles), vehicle n-1, [m]

Classification of car-following models

Car-following models are categorized into various classes based on their underlying logic, with the Gazis-Herman-Rothery (GHR) family being the most extensively researched Often known as the general car-following model, the GHR model was first introduced in 1958, marking a significant development in traffic flow theory.

Since its introduction by Chandler et al in 1958, the GHR model has undergone several enhancements This model primarily governs the actual behavior of following vehicles, establishing a stimulus-response relationship between a leader and a follower According to the GHR model, a follower's acceleration is influenced by its current speed, the speed differential between the leader and the follower, and the distance maintained between them Specifically, the acceleration of the follower at any given time t is determined by these factors.

− − − , (2.1) where α>0, β and γ are model parameters that control the proportionalities A

The GHR model can be categorized into symmetrical and unsymmetrical types A symmetrical model applies identical parameter values during both acceleration and deceleration phases, while an unsymmetrical model utilizes distinct parameter values for these two scenarios For example, an unsymmetrical GHR model is employed in various applications.

MITSIM (Yang et al., 1996) to calculate the acceleration in the following regime, and is formulated as

The MITSIM model incorporates parameters α ±, β ±, and γ ±, which are essential for its functionality Specifically, parameters α +, β +, and γ + are applied when the velocity condition v n ≤ v n − 1 is met, while α −, β −, and γ − are utilized when v n > v n − 1 Additionally, the model features an emergency driving regime alongside a free driving regime, enhancing its adaptability to various traffic scenarios.

Collision avoidance models, also known as safety distance models, focus on maintaining a safe distance between vehicles on the road According to Pipes' rule, drivers should maintain at least one car length of distance for every ten miles per hour of speed to ensure safe following.

A safety distance model, as illustrated in 2001, typically derives its specifications from Newton's equations of motion This distance is often calculated to prevent collisions, particularly in scenarios where the leading vehicle decelerates sharply One of the most recognized safety distance models is Gipps' model from 1981, which determines the follower's speed based on the constraints of both their own vehicle and the leader's vehicle, selecting the minimum of these speeds.

In the context of vehicle dynamics, the maximum desired acceleration and deceleration for vehicle n are represented by a_n and d_n, respectively, while d̂_n−1 estimates the maximum deceleration desired by the preceding vehicle, n-1 The safe speed regarding the leading vehicle is determined through Newtonian motion equations, which calculate the highest speed the following vehicle can maintain This ensures that, after accounting for reaction time, the follower can safely decelerate to zero and prevent a collision if the leader comes to a complete stop.

In 1963 a new approach for car-following modeling were presented,

Brackstone et al (1998) classify models of follower behavior into psycho-physical or action point models, specifically GHR models These models propose that a follower responds to even minor changes in relative speed and continues to react to the leader's actions despite significant distances However, the follower's response ceases when the relative speed reaches zero To enhance GHR models, additional regimes such as free driving and emergency deceleration can be integrated, or psycho-physical models can be employed Psycho-physical models focus on thresholds or action points, indicating that drivers alter their behavior only when specific spacing or relative velocity thresholds are met (Leutzbach).

In 1988, the thresholds and corresponding regimes are commonly illustrated using a relative space/speed diagram of a follower-leader vehicle pair, as shown in Figure 2.2 The bold line in the diagram represents a potential trajectory for the vehicle.

Figure 2.2 A psycho-physical car-following model (Source: (Leutzbach, 1988))

Representative examples of psycho-physical car-following models are the ones presented in Wiedemann and Reiter (1992), see Figure 2.3, and Fritzsche (1994), see Figure 2.4

Figure 2.3 The different thresholds and regimes in the Wiedemann car-following model

Figure 2.4 The different thresholds and regimes in the Fritzsche car-following model

Fuzzy logic offers a valuable approach to car-following modeling by acknowledging that drivers often cannot perceive exact values such as speed or distance Instead, they rely on estimations like "above normal speed" or "close." Traditional models assume drivers know precise metrics, but fuzzy logic introduces a more realistic perspective, categorizing speeds into ranges like very low, low, moderate, high, or very high These fuzzy sets often overlap, requiring the use of membership functions to translate actual values into linguistic terms, thereby enhancing the human-like representation of driver behavior.

Figure 2.5 Example of membership functions for driving speed

Fuzzy logic excels in integrating fuzzy sets with logical rules to create diverse behavioral models For instance, a rule could categorize speed into levels such as low, moderate, and very high.

Following I Closing in Free driving

To enhance driving task performance, it's essential to establish clear linguistic rules, such as using "large" to indicate an increase in speed However, a significant challenge lies in the calibration of fuzzy sets Efforts have been made to "fuzzify" both the GHR model and another specific model to address this issue.

MISSION (Wiedemann and Reiter, 1992) However, no attempts to calibrate the fuzzy sets have been made, (Brackstone and McDonald, 1998)

Since the 1950s, various car-following models have been developed, each employing different approaches Despite the existing models, research in this field remains active due to the varying requirements for different applications For instance, models intended for macroscopic outputs, like average flow and speed, have less stringent requirements compared to those designed for microscopic outputs, which focus on individual speed and position changes.

Traffic simulation and car-following models are essential for analyzing how network changes impact traffic metrics like average flow, speed, and density The focus of these simulations is on macroscopic measures, necessitating that car-following models produce representative macroscopic results Leutzbach (1988) provides a macroscopic verification of GHR-models, demonstrating that by integrating the car-following equation, a relationship between average speed, flow, and density can be established This relationship can then be validated against real data or outputs from other macroscopic models Specifically, for a GHR-model with parameters β = 0 and γ = 2, the integration leads to the well-known Greenshields relationship, as referenced by May (1990).

Lane-changing models

Lane-changing models are crucial in understanding drivers' behavior when deciding whether to change lanes on multi-lane roads, playing a vital role in both urban and freeway environments These models take into account various factors that influence a driver's decision to change lanes, as identified by Gipps and other researchers By analyzing these factors, lane-changing models can effectively predict and describe the complex decision-making process involved in lane-changing maneuvers.

(1986) proposed that a lane-changing decision is the result of answering the questions

• Is it necessary to change lanes?

• Is it desirable to change lanes?

• Is it possible to change lanes?

Gipps (1986) introduced a decision tree framework for lane-changing decisions that incorporates various factors, including the driver's intended turn, the presence of reserved lanes or obstructions, and the urgency of the lane change based on the distance to the intended turn This framework is supported by several lane-changing models, including those proposed by Barceló et al (2002), Hidas (2002), and Yang.

1997) are based on the three basic steps proposed in Gipps (1986)

The Gipps (1986) model asserts that lane changes cannot occur if the gap in the target lane is below a specified threshold, which is effective when lane changes are desired However, in scenarios where a lane change is crucial yet not feasible, vehicles in the target lane may assist the stranded vehicle by reducing their speed, thereby creating a sufficient gap for the trapped vehicle to merge This phenomenon has been highlighted in the work of Hidas.

(2002) Hidas (2002) describes a further developed variant of the model presented in Gipps (1986), which also includes the cooperative behavior for vehicles in the target lane, see Figure 2.6

Figure 2.6 Structure for lane-changing decisions proposed in Hidas (2002)

An enhanced version of the model introduced by Hidas (2005) builds upon the original framework established in Hidas (2002), which combines necessary and desirable steps into a single necessary step with outcomes categorized as unnecessary, desirable, or essential This modeling approach is echoed in the work of Yang and Koutsopoulos (1996), where lane changes are classified as either mandatory or discretionary Mandatory lane changes align with Hidas's essential category, representing necessary actions to navigate lane blockages, make intended turns, or avoid restricted lanes In contrast, discretionary lane changes, aimed at gaining speed advantages or avoiding lanes near on-ramps, correspond to the desirable path outlined in Hidas's framework.

(2002) structure In both structures, the differences between mandatory and discretionary lane changes is in the gap-acceptance behavior and the possibility

Is lane change to target lane feasible?

Is lane change to target lane feasible?

Simulate driver courtesy in target lane

No that vehicles in the target lane may renounce their right of way in favor for a vehicle performing a mandatory lane change

Toledo et al (2005) highlighted that traditional lane-changing models typically focus on adjacent lane changes, evaluating whether drivers should switch lanes or remain in their current one, often lacking a tactical approach to lane-changing behavior They proposed a model that allows drivers to select a target lane that is not necessarily adjacent but is deemed most beneficial, enabling them to make multiple lane changes to reach this optimal lane This approach aligns with the decision framework established by Gipps (1986), merging necessary and desired lane choices into a single target lane selection, as less convenient lanes—such as those leading to upcoming turns—are considered less advantageous The model employs a utility function to assess the benefits of each lane and utilizes a discrete choice model to predict lane selection, which will be further elaborated upon in the context of drivers' lane-changing desires.

El Hadouaj et al (2000) developed a lane-changing model that expands upon the work of Toledo et al (2005), suggesting that drivers consider traffic conditions across all lanes, rather than just their own and an adjacent lane This model evaluates the traffic situation not only in the immediate vicinity of the driver but also in more distant areas, dividing the surrounding space into 20 distinct regions Lane changes are determined based on the calculated benefits from these areas, which are assessed using a function that incorporates speed and stability The foundation of this model is rooted in psychological studies of driver behavior conducted at the French research institute INRETS and the Driving Psychology Laboratory (LPC).

Modeling the urgency to change lane

The necessity to change lanes is influenced by the proximity of an obstacle or a planned turn, which can be modeled in various ways Gipps (1986) categorized this into three zones: close, middle distance, and remote, determined by two time distances to the intended turn or obstacle.

Figure 2.7 The three different lane-changing zones proposed by Gipps (1986)

After extensive trials, optimal headway values of 10 seconds and 50 seconds were established (Gipps, 1986) This division of zones was subsequently adopted and refined in the works of Hidas (2002) and Barceló and Casas (2002) Additionally, a comparable zone division has been recognized in other studies.

Zone 3 - close Zone 2 – middle distance

Vehicles in zone 1, located 50 seconds away from their intended turn, can change lanes freely without concern for obstacles In contrast, vehicles in zone 2, which are closer to their turn, exhibit more cautious lane-changing behavior and typically do not switch to lanes that are further from their designated turning lane.

In zone 3, lane-changing decisions are solely aimed at entering the appropriate lane Vehicles in this zone that are not in the correct lane for their intended turn tend to become more aggressive, accepting smaller gaps in traffic This behavior will be explored in more detail in the Gap-acceptance sub-section.

In 1997, Yang introduced a novel approach for modeling the urgency of vehicles to change lanes by tagging them to a mandatory state based on a probability function, rather than utilizing different zones This method employed an exponential probability function, where the likelihood of tagging a vehicle as mandatory primarily relied on the distance to the intended turn or obstacle Wright (2000) later adopted this strategy, opting for a linear relationship instead of the exponential distribution to enhance computational efficiency.

Modeling drivers’ desire to change lane

The drivers desire to change lane can be modeled in several ways, for example by using

In Gipps' 1986 car-following model, which builds upon the framework established in 1981, the focus is on determining the lane that minimally impacts driver speed The model incorporates the influence of heavy vehicles by treating them as if they are the preceding vehicles in their respective lanes Additionally, it introduces a relative speed criterion for lane changing, utilizing default values of 1 m/s for shifts toward the center lane and -0.1 m/s for moves toward the curb This means that a vehicle will only consider changing lanes to the left if it is traveling at least 1 m/s faster than the vehicle ahead in its current lane.

In Kosonen (1999), a variant of the car-following model was introduced to determine the most preferable lane for vehicles This approach utilized a pressure function, which approximates the potential deceleration rate induced by the leading vehicle.

The pressure function models drivers' lane-changing decisions based on the desired speed (v des), the obstacle's speed (v obs), and the relative distance (s) This approach is illustrated in Figure 2.8.

The lane-changing logic proposed by Kosonen (1999) involves calculating the parameter P using equation (2.6) This model incorporates calibration parameters c l and c r, which dictate the driver's inclination to change lanes to the left or right, respectively.

Overtaking models

On roads lacking barriers between oncoming traffic, it is essential to evaluate the entire overtaking process rather than just the lane change itself This requires a comprehensive model that addresses various aspects of overtaking decisions, which can be broken down into multiple sub-models or inquiries.

Lead gapLag gap overtaking decision can for instance be the answer of the following questions, (Brodin et al., 1986):

• Is the overtaking distance free from overtaking restrictions?

• Is the available gap long enough?

• Is the driver-vehicle unit able to perform the overtaking?

• Is the driver willing to start an overtaking at the available gap?

Drivers typically avoid overtaking in restricted areas, but not all adhere to these laws, necessitating models that account for lawbreakers Overtaking decisions are influenced by the size of the available gap; if it is shorter than the required overtaking distance, drivers are unlikely to proceed Additionally, the performance of the overtaking vehicle, such as its maximum acceleration and speed, plays a crucial role Even if a vehicle is capable of overtaking, drivers may hesitate if the distance is excessively long, such as over one kilometer Furthermore, a driver's willingness to take an overtaking opportunity can vary significantly, with different drivers reacting differently to the same gap at different times.

Gap-acceptance models are essential for understanding drivers' willingness to accept available gaps, particularly in overtaking scenarios where variability in behavior is significant While simpler models may assume a common critical gap for all drivers, research indicates that individual drivers exhibit varying levels of gap acceptance over time Studies by McLean (1989) highlight that the variance in gap-acceptance behavior is often greater within a specific driver over time than between different drivers, suggesting that inconsistent models, where each overtaking decision is made independently, may better represent real-world behavior For instance, Bottom et al (1978) found that over 85% of the variance in gap acceptance is attributed to temporal changes in individual drivers, while Daganzo (1981) corroborated this by showing that approximately 65% of the variance is also due to over time changes Despite these findings, challenges remain in accurately modeling gap acceptance, particularly in estimating appropriate distributions that account for both over time and among driver variance.

Gap-acceptance behavior varies among drivers and changes over time, influenced by factors such as the type of overtaking and the speed of the overtaken vehicle McLean (1989) identifies five basic descriptors for classifying overtaking decisions, which are also referenced in the research by Brodin and Carlsson (1986).

When overtaking, a driver's behavior varies based on the type of vehicle being passed; for instance, drivers tend to feel more comfortable overtaking trucks compared to cars.

• Speed of overtaken vehicle: The speed affects both the required overtaking distance and the probability of accepting an available gap

• Type of overtaking vehicle: Overtaking behavior can be expected to differ between for example high performance cars and low-performance trucks

When considering overtaking maneuvers, drivers exhibit different behaviors based on the type of overtaking involved In scenarios where a vehicle can execute a flying overtake—beginning the overtaking process as it approaches a slower vehicle—the driver's approach differs significantly from situations requiring initial acceleration to initiate the maneuver Understanding these distinctions is crucial for safe driving practices.

Drivers' willingness to initiate an overtaking maneuver is influenced by the type of gap limitation present Specifically, they tend to be more inclined to accept a gap restricted by a natural sight obstruction compared to an equivalent gap constrained by oncoming vehicles.

The likelihood of accepting an overtaking gap is influenced not only by the gap's size but also by various other factors, resulting in a probability function for each combination of these descriptors To accurately estimate these functions, a substantial amount of data is required Several studies, including an overview by McLean (1989), have been conducted to assess overtaking probabilities For instance, Figure 2.10 illustrates probability functions for overtaking scenarios involving an oncoming vehicle, based on estimations for Swedish roads as presented by Carlsson (1993).

Figure 2.10 Probability functions for overtaking decisions, combinations of descriptors with oncoming vehicle in sight, (Carlsson, 1993)

The analysis indicates that the probability of successful overtaking in flight is greater than that of accelerated overtaking within the same available gap.

Speed adaptation models

Most micro simulation models incorporate a desired speed parameter to represent drivers' preferred driving speeds, typically using a normal distribution to account for variations among individuals However, this desired speed is not static; it fluctuates based on road design On urban roads and freeways, the posted speed limit primarily influences drivers' desired speeds, while on rural roads, such as two-lane highways, factors like road width and curvature also play significant roles To accurately model these variations in desired speed relative to road design, a speed adaptation model is essential.

A flexible modeling approach for road speed limits involves assigning each driver a specific desired speed corresponding to various speed limits, allowing for variations in desired speeds Alternatively, a relative desired speed distribution can be used, where a driver's desired speed is derived by adding a relative speed to the posted limit, as demonstrated in studies by Yang (1997) and Ahmed (1999) Similarly, Barceló and Casas (2002) propose a method where desired speeds are calculated by multiplying the posted speed limit by an individual speed acceptance parameter, which is normally distributed among drivers.

Rural road geometry significantly influences drivers' desired speeds, with factors such as road width and curvature playing crucial roles Brodin and Carlsson (1986) propose a speed adaptation model that incorporates the speed limit, road width, and horizontal curvature to determine a driver's desired speed for each road section In this model, each driver starts with a basic desired speed, which is then adjusted based on these factors, effectively reducing the median speed Unlike previous models by Yang (1997), Ahmed (1999), and Barceló and Casas (2002), this approach also rotates the desired speed distribution curve around its median This allows the model to account for variations in how strongly different drivers are influenced by speed limits, particularly highlighting that drivers with higher desired speeds are more significantly impacted by speed limits than those with lower desired speeds.

Figure 2.11 Example of shift and rotation of a desired speed distribution

The extent of curve rotation is influenced by various factors related to road conditions Key parameters such as road width, speed limit, and horizontal curvature play a crucial role in determining the necessary adjustments for safe navigation.

3 Surrounding traffic in driving simulators

The road environment significantly impacts driver behavior, influencing factors such as desired speed, lateral positioning, and overtaking actions Additionally, the presence of other road users affects not only travel speed and time but also driver awareness For driving simulators to accurately reflect real driving conditions, they must provide a realistic depiction of the driving environment However, achieving this realism can conflict with the design of effective simulator experiments that yield valuable insights This chapter introduces driving simulator experiments and scenarios, discusses the advantages and challenges of using stochastic traffic simulation for surrounding vehicles, and highlights specific demands for traffic simulation in this context It concludes with a survey of related research on simulating ambient vehicles in driving simulators.

D RIVING SIMULATOR EXPERIMENTS

Experiments, scenarios, and scenes

A driving simulator scenario defines the road and traffic environment, detailing aspects such as road geometry, surface conditions, weather, and surrounding elements like trees and houses It encompasses the behavior of other road users and their interactions Essentially, a scenario represents a series of traffic situations that begin when specific conditions are met and conclude upon the fulfillment of different criteria, as noted by van Wolffelaar (1999) This concept can also be referred to as a constellation of scenes, as described by Alloyer et al (1997).

In 1997, a scene is defined as a detailed specification that includes the location where the scene occurs, the actors involved, the events that will transpire, and the sequence in which these events unfold For instance, Bolling et al provide an example that illustrates this definition.

In a 2004 scenario set in a low-complexity urban environment, a bus at a stop activates its left indicator four seconds before a simulator driver arrives The driver encounters a significant oncoming traffic flow, complicating the overtaking of the bus If the driver yields, the bus accelerates to 50 km/h and proceeds to the next stop; otherwise, it remains stationary Throughout the journey, heavy oncoming traffic continues to hinder overtaking attempts, illustrating a detailed specification of the road environment and the timing and location of various scenes.

A driving simulator experiment involves a carefully structured experimental design that defines the number of participants, the driving scenarios, and the independent variables to be tested, such as Advanced Driver Assistance Systems (ADAS), road friction, or road types The design must also specify how these independent variables are varied among participants One approach is a between-group design, where one group experiences the independent variable (e.g., driving with an ADAS) while a control group drives the same scenario without it Alternatively, a within-group design allows all participants to experience all conditions, such as driving both with and without an ADAS Mixed designs can also be employed, combining between-group and within-group elements for different independent variables.

Design issues

Designing effective driving simulator experiments and scenarios is a complex task, with limited written resources available on key considerations The process often relies heavily on the extensive experience of various driving simulator facilities Establishing universal guidelines for experiment and scenario design is challenging due to the specific applications involved Nonetheless, efforts have been made to create standardized methodologies for driving simulator experiments, such as those developed in the European HASTE project.

2004) and the European ADVISOR-project (Nilsson et al., 2002), in which common methodologies for studying assessments of IVIS and ADAS, respectively, were defined and tested

Driving simulator scenarios are meticulously designed to ensure consistency, with all variables predetermined except for the driver's actions This controlled environment allows for uniform experiences among participants, enabling researchers to draw statistically significant conclusions from experiments involving a limited number of subjects.

To achieve meaningful results in driving simulator experiments, it is essential to limit the number of independent variables to two or three Excessive independent variables can complicate the analysis, making it challenging to identify clear cause-and-effect relationships.

To gain comprehensive insights, it is advisable to conduct multiple experiments For instance, rather than a single experiment comparing mobile phone usage to non-usage, one could investigate the effects of using handheld versus hands-free phones, as well as the impact of mobile phone usage in various road environments.

Here is a rewritten paragraph incorporating the main points and complying with SEO rules:"Driving simulator experiments can be categorized into two distinct types: those that incorporate critical situations or events, and those that do not Critical situations are often utilized to facilitate accelerated testing, allowing researchers to study driver behavior in rare or high-risk scenarios that may not occur frequently in real-life driving By simulating these situations, driving simulators can significantly reduce the time required to gather data, making them an invaluable tool for accelerating research and improving road safety."

U SING STOCHASTIC TRAFFIC IN DRIVING SIMULATOR SCENARIOS

The stochastic traffic – Driving simulator dilemma

Ambient vehicles in driving simulators have typically relied on deterministic models due to the Stochastic Traffic – Driving Simulator Dilemma, which highlights the challenge of needing a sufficient number of participants for statistically significant results while minimizing participant numbers for economic reasons Driving behavior is inherently variable, both between different drivers and within the same driver, necessitating the use of behavioral models that incorporate stochastic elements Implementing stochastic simulations for ambient vehicles enhances realism by providing participants with unique micro-level driving experiences, though this may increase variation in test conditions Despite this, participants will still encounter comparable traffic conditions at a macro level, such as intensity and composition The key challenge is to strike a balance between realism and reproducibility, ensuring that experiments yield both valid and useful results while considering the importance of micro-level conditions in different simulator studies.

Stochastic traffic simulation and critical events

Driving simulator experiments often expose participants to critical situations, such as an animal crossing the road or other vehicles suddenly braking These scenarios require precise positioning and speed of surrounding vehicles to ensure realism When a predetermined event occurs, it is essential that the vehicles' types, positions, and speeds align with the scenario specifications While deterministic simulations allow for complete control over vehicle movements, incorporating stochastic elements complicates scene generation since the exact vehicles present during an event cannot be predetermined Consequently, these situations must be created "on-line" as the simulation progresses, enhancing the challenge of accurately replicating real-world driving conditions.

Alloyer et al (1997) introduced a framework for the online creation of scenes, dividing the scene specification into three key components: the set, the cast of principal actors, and the script of actions The set describes the physical environment where the scene occurs and identifies the actors present Casting involves selecting appropriate traffic elements, vehicles, and pedestrians for various roles The script outlines all actions that will take place within the scene While the set and script can be predetermined in non-stochastic simulations, casting must be conducted online during the simulation process, involving several steps.

• Choosing suitable vehicles to be included in the scene, i.e., vehicles of suitable vehicle type and with suitable position and speed

• Moving the chosen vehicles into the given positions and to the given speeds

• Moving “non-scene” vehicles out of sight from the driving simulator vehicle

Selecting appropriate vehicles for a driving simulator is influenced by traffic conditions and scene complexity Identifying vehicles coming from the opposite direction is straightforward, as they can be repositioned out of the simulator's view However, selecting vehicles traveling in the same direction poses a greater challenge; these vehicles must match the correct type and their speed should closely align with the expected speed in the simulation.

The arrangement of available vehicles frequently varies from the specified sequence, necessitating a strategic rearrangement to position the correct vehicle types accurately It is essential to create this correct order discreetly for the simulator driver, minimizing the number of overtakes required to align the ambient vehicles properly In cases where suitable vehicles are unavailable, new ones must be generated to maintain the desired order.

Positioning vehicles accurately and at the correct speeds is crucial and challenging, requiring discretion to avoid alerting the simulator driver to upcoming events The initial step involves rearranging vehicles into the proper order, ideally out of the simulator's view If overtaking is necessary within sight, it should be managed by creating appropriate gaps in the traffic flow Utilizing road features such as intersections, ramps, or traffic lights is generally more effective than overtaking for seamlessly integrating or removing vehicles from the traffic stream Therefore, an effective online scene creation method should prioritize the use of intersections and ramps over overtaking maneuvers.

To ensure optimal performance, vehicles must be accurately positioned and adjusted to the correct speed based on the scene specifications This involves either accelerating or decelerating the vehicles to appropriately modify the distance between them and the simulator vehicles.

D EMANDS ON TRAFFIC SIMULATION WHEN USED IN DRIVING

Microscopic traffic simulation is an evolving field, with various commercial and non-commercial models available; however, these models are not directly applicable for simulating surrounding vehicles in driving simulators The simulation of ambient traffic in driving simulators requires more advanced microscopic behavioral modeling compared to traditional traffic simulations, which typically focus on aggregated data like average travel times and queue lengths While traffic simulation models may include simplifications, such as instantaneous lane-changing, which do not significantly impact macro-level outcomes, these assumptions can undermine the realism needed at the micro level for driving simulators Accurate microscopic behavior is crucial, as it forms the basis of the simulator's output, and it is essential to ensure that surrounding vehicles behave safely, preventing the driver from encountering unexpected critical situations not defined in the scenario.

Traffic simulation typically focuses on geographically limited areas, ranging from a single intersection to parts of a city or highway Vehicles are generated and removed at designated origins and destinations within the simulated road network In driving simulators, the emphasis shifts to the immediate vicinity of the vehicle, allowing for the simulation of vehicles only within this localized area As the simulator moves, the geographic boundaries for vehicle generation also shift, necessitating an algorithm that generates faster vehicles behind the simulator and slower ones in front This ensures that the frequency of fast and slow vehicles remains accurate while preventing slower vehicles generated behind the simulator from lagging indefinitely Such methodologies have been effectively utilized in models like those presented by Espié.

Microscopic traffic simulation may not be necessary for all vehicles surrounding the simulator vehicle; instead, vehicles located farther away can be effectively modeled using less time-consuming methods, such as mesoscopic or macroscopic approaches For instance, Espié (1995) employed a macroscopic model to simulate distant vehicles This strategy of utilizing microscopic simulation solely for the most relevant areas has been validated in various traffic simulation applications, as discussed by Burghout (2004), who provides an overview of integrating micro-, meso-, and macro simulation models in traffic research.

R ELATED RESEARCH

Rule-based models

Rule-based models, also referred to as knowledge-based systems or expert systems, utilize a set of conditional rules structured as "if (condition) then (action)" to simulate driver behavior (Wright, 2000) By evaluating each rule, these models determine the appropriate actions based on the true conditions identified For instance, a subset of rules can effectively represent free driving behavior.

1 IF (speed < desired speed) THEN (increase speed)

2 IF (speed > desired speed) THEN (decrease speed)

3 IF (new speed limit) THEN (change desired speed)

Drivers often accelerate when traveling below their desired speed, but this deterministic model assumes uniform behavior among all drivers In reality, driving behavior varies significantly both between different drivers and within the same driver over time To address this variability, a probability value is typically incorporated into each rule, indicating the likelihood that a specific action will be taken when conditions are met (Wright, 2000).

In many cases the actions to be executed will be in conflict with each other If for example the following rule is added:

4 IF (speed > front vehicle speed) THEN (decelerate to front vehicle speed) a very common conflict will be that the driver is driving slower than her desired speed but faster than the front vehicle In these cases a conflict resolution criteria is needed For speed control a most restrictive choice is most commonly used The decelerate-to-front-vehicle-speed rule has for example higher priority than the increase-speed-to-obtain-desired-speed rule Another way to solve the conflicts is to make use of the rules’ probability values One way is to use a weighted average of the outcome of the different rules This can however lead to, for example, unintelligent speed choices

Rule-based systems offer significant advantages due to their simplicity and flexibility, allowing for easy modifications through the addition, alteration, or removal of rules However, modeling complex behaviors often necessitates a substantial number of rules, which can complicate visualization and debugging processes Michon (1985) provides a basic estimation of the number of rules required to model the entire driving task, encompassing aspects from gear shifting to route selection, suggesting that such a comprehensive model could require around 10 rules.

Rule-based approaches have been utilized in studies by Boer et al (2001) and van Wolffelaar (1999) These approaches are often combined with fuzzy logic to create fuzzy if-then rules, as illustrated in Section 2.3.1 with a fuzzy rule-based car-following model A notable example of this combined methodology can be found in the work of Al-Shihabi and Mourant (2002).

State machines

State machine models represent systems through a defined set of states, with only one active state at any time Each state can lead to one or more possible next states, depending on the system's structure For example, a simple state machine for a driver's speed control behavior includes four states: free driving, speed up, slow down, and stopped Transitions between these states occur when specific conditions are met, ensuring that state changes are determined by the evaluation of transition conditions from the current state (Wright, 2000).

State machines, with their linear logic, struggle to model complex systems that require simultaneous actions, such as driver behavior (Cremer et al., 1995) To address these limitations, researchers have developed Hierarchical Concurrent State Machines (HCSMs), which incorporate hierarchy, concurrency, and communication between states In HCSMs, the traditional distinction between states and state machines is eliminated, allowing for multiple, concurrently executing child state machines For instance, a HCSM for car driving might include child HCSMs for speed control and steering, alongside others for lane-changing and navigation This concurrency enables multiple active states but can also lead to conflicting outputs, necessitating robust conflict resolution principles In a hierarchical structure, conflict resolution occurs primarily at the lowest child HCSM level, with higher levels assuming that conflicts are managed below.

Figure 3.2 a) Illustration of state machine for speed control b) Illustration of a hierarchical concurrent state machine for speed and steering control

Hierarchical State Machines (HCSMs) address several limitations of traditional state machines while maintaining a high level of determinism This deterministic nature is beneficial for producing consistent driving simulator scenarios; however, it restricts the ability to model realistic driver behavior, which inherently varies between individuals and changes over time.

HCSM has for example been used in the autonomous driver behavioral models used in the simulators HANK (Cremer et al., 1997) and NADS (Ahmad et al.,

2001) located at the University of Iowa.

The eco-resolution principle

Researchers at the French research institute INRETS have developed ARCHISIM, a versatile model that functions as both a traffic simulation and a driving simulator This model operates on an eco-resolution principle, which posits that traffic situations arise from the behaviors and interactions of individual drivers Grounded in psychological studies, ARCHISIM's conceptual framework focuses on decision-making during driving, emphasizing that each driver aims to minimize interactions with their environment and other drivers Notably, psychological research has identified specific behavioral patterns, such as a guiding "law" for lane driving.

Steering v is the current speed v t is the target speed a) b)

(Source: El hadouaj and Espié (2002))

The driver assesses potential interactions with other vehicles and infrastructure, considering both observed and anticipated scenarios She estimates the interaction's duration, determining how long it will last; for instance, if a slower vehicle ahead signals to change lanes, the interaction is deemed short, allowing the driver to remain in her lane Action is only taken when the interaction is expected to last longer and cannot be avoided The overarching goal is to minimize interactions in both the short and long term In the context of lane driving, the ARCHISIM model employs specific decision rules to guide lane selection.

Calculate-gain-for-each-lane(area parameters)

Chosen lane = lane with highest gain value

(Source: El hadouaj and Espié (2002))

The lane gain is determined by local traffic conditions, primarily focusing on the area's maximum speed limits and the stability of road user behavior, which is assessed by the variation in speed among drivers in the vicinity.

Interaction + long duration + suppression possibility ⇒ interaction suppression Interaction + short duration + suppression possibility ⇒ short term adaptation Interaction + long duration + impossibility of suppression ⇒ long term adaptation

This chapter outlines the proposed simulation model, beginning with the simulation framework that details the representation and updating of vehicles and drivers Section 4.2 focuses on the algorithms implemented for generating new vehicles, while Section 4.3 concludes the chapter with an overview of the behavioral models used, including the results from calibrating various parameters of these models.

T HE SIMULATION FRAMEWORK

Representation of vehicles and drivers

In micro simulation models, vehicles and drivers are represented as integrated vehicle-driver units, characterized by specific traits that differ across vehicle types The current model encompasses various vehicle categories, including cars, buses, trucks, and trucks with trailers, categorized by their axle count—3-4 axes and 5 or more axes Notably, buses and trucks without trailers are considered to share similar characteristics.

Vehicle characteristics include length, width, and the power/weight ratio (p-value), which is crucial for assessing performance Length and width are determined by the visual profile in the simulator's visual system, while the p-value represents the ratio of a vehicle's power at the wheels to its mass For most vehicle types, this ratio indicates acceleration capacity, whereas for cars, it reflects acceleration behavior under normal conditions A higher p-value is particularly relevant in scenarios like overtaking, where increased acceleration is often required The power/weight ratio is generally assumed to be normally distributed among similar vehicle types, with an average of approximately 19 W/kg for cars.

A for a complete listening of parameter values

The driver characteristics in vehicle-driver units include basic desired speed and desired time gap The basic desired speed represents the speed a driver aims to maintain on a dry, straight, and clear road, which is then adjusted based on a speed adaptation model for specific road sections This speed is normally distributed among drivers of the same vehicle type, with car drivers typically having a basic desired speed of approximately N ~ 111.11.5 km/h When determining the desired speed for a vehicle, its acceleration capacity is evaluated to ensure it can achieve the desired speed; if not, the vehicle-driver unit is assigned a new power-to-weight ratio.

The desired time gap refers to the interval a driver prefers when trailing another vehicle, a key factor in car-following models discussed in Section 4.3.2 This time gap is typically lognormally distributed among drivers of a specific vehicle type For comprehensive details on standard values for various vehicle and driver parameters, please refer to Appendix A.

Brake lights and turning signals

In traffic simulations, modeling turn signals and brake lights is essential for driving simulators, as these signals must be visible to the driver The usage of turn signals varies significantly among drivers and different traffic situations, such as lane changes and intersection turns Additionally, external factors like traffic flow impact signal usage; for instance, the necessity to indicate intentions decreases at night when fewer vehicles are present compared to busy rush hour scenarios.

In this study, brake lights are considered activated when deceleration rates exceed the engine's deceleration rate of 0.5 m/s² Additionally, drivers are presumed to utilize turn signals with varying probabilities, which differ for lane changes to the left and right, as well as between freeways and rural roads For instance, on freeways, it is assumed that drivers are more likely to use the left turn signal than the right.

The moving window

To create a realistic driving experience, the traffic simulation must operate in real time, necessitating a highly efficient simulation model This model focuses on simulating only the vehicles within a designated area surrounding the driving simulator, which moves in tandem with the simulator vehicle This dynamic area can be visualized as a moving window centered on the simulator vehicle, enhancing the immersive experience for the driver.

Figure 4.1: a) Illustration of traditional traffic simulation b) Illustration of traffic simulation for a driving simulator using the moving window The black vehicle is the driving simulator

The moving window concept in driving simulation aims to enhance efficiency by limiting the simulation of distant vehicles, as those far away do not influence the driving experience However, the window's size must be carefully balanced; it should at least match the sight distance to prevent vehicles from abruptly appearing in front of the simulator vehicle Additionally, a sufficiently large window is essential for realistic traffic dynamics and accommodating speed variations of the simulator vehicle A narrow window may result in faster vehicles exiting the simulation without reappearing when the simulator increases speed, complicating the modeling of traffic flow and conditions, such as queue spillback at merging areas It's important to note that the moving window does not dictate which vehicles are displayed on the simulator screen; that function is managed by the scenario module, with the moving window typically being broader than the area from which vehicles are visualized.

To optimize computational efficiency while maintaining a sufficient observation window, the simulation area is divided into an inner and two outer regions The inner region, known as the simulated area, features vehicles that closely mimic real driver behavior through advanced models for car-following, overtaking, and speed adaptation In contrast, vehicles in the outer regions are simulated using a simpler mesoscopic model, which requires less computational effort, as their behavior is deemed less critical to the simulation's accuracy.

As vehicles approach the simulated area, they are designated as candidate vehicles, and the surrounding regions are referred to as candidate areas Once vehicles exit the system at the boundaries of these candidate areas, they are removed from the model, and new vehicles are generated to maintain the flow, as detailed in Section 4.2.

Driving direction of driving simulator vehicle

Figure 4.2 The different areas The black vehicle is the driving simulator, the grey vehicles are simulated vehicles and the white vehicles are candidate vehicles.

The simulated area

In the inner region of the simulated area, vehicles are modeled using established time-driven micro simulation techniques, ensuring frequent updates for realistic driving behavior This simulation employs various behavioral models, primarily derived from the TPMA (Traffic Performance on Major Arterials) model and the VTISim model, as detailed in Section 4.3.

The candidate areas

The candidate areas in a driving simulator are primarily relevant for traffic traveling in the same direction as the simulator vehicle, with oncoming vehicles in the distance assumed to have no significant impact on the driver While oncoming vehicles behind the simulator may occasionally influence the simulation due to congestion on rural roads, they are generally considered redundant It is crucial, however, to simulate oncoming vehicles throughout the entire area on rural roads, as they significantly affect queue discharging rates in the direction of the driving simulator When utilizing candidate areas for oncoming traffic, these vehicles are expected to travel at the desired speed of the platoon leader within the designated area.

Candidate vehicles moving in the same direction as the simulator vehicle are updated using a straightforward mesoscopic model Initially, these vehicles were assumed to travel at their desired speeds, which was effective for low traffic flows on freeways (Janson Olstam, 2003; Janson Olstam et al., 2003) However, this assumption led to excessively high speeds on rural roads and during peak flows on freeways, resulting in an underutilized candidate area in front of the simulator and congestion behind it To address this issue, a speed-flow curve is now employed to determine the speeds of candidate vehicles, utilizing speed-flow relationships derived from representative data for Swedish roads as presented by the SRA.

Simulated area (Micro model) Candidate area

(Meso model) Generation of new vehicles

Driving direction of driving simulator

(2001), see examples in Figure 4.3 These speed-flow relationships vary with road type, vehicle type, speed limit, number of lanes, road width, and sight class

The model does not utilize all dependent variables; for example, the speed-flow relationship for cars is applied to all vehicle types On rural roads, the model employs the relationships for the highest sight class (class 1), regardless of the actual sight class of the simulated road Additionally, the relationships in the model are influenced by factors such as road type, road width, and speed limit.

Figure 4.3 Examples of speed-flow relationships for a freeway with speed limit 90 km/h and a 8-10 m wide rural road with speed limit 90 km/h (SRA, 2001)

The actual speeds of candidate vehicles are determined by their desired speeds and the average speed derived from the appropriate speed-flow function, effectively modeling the delay caused by surrounding traffic in the area.

Two different methods to calculate a vehicle’s speed have been tested In the first one, the speed of vehicle n is calculated as

The desired speed of vehicle n, denoted as v_des(n), is determined by the equation v_des(n) = f(q) + v - f, where q represents the traffic flow and f(q) indicates the average travel speed at a traffic flow of q vehicles per hour This approach presumes that a vehicle can adjust its speed significantly above or below the average speed experienced under free-flow conditions Alternatively, the second method employs a technique that not only shifts the speed distribution curve but also rotates it around its median, akin to the speed adaptation model proposed by Brodin and Carlsson in 1986.

Section 2.3.4 Following this approach the speed of vehicle n is instead calculated as

( Q des Q 0 Q ) 1/ Q n n v = f q + v −f , (4.2) where Q is a parameter that controls the rotation of the speed distribution curve

In this method, faster vehicles are more significantly impacted than slower ones Although vehicles exceeding the average speed under free flow conditions will maintain this speed at traffic flow q, the gap between their speed and the average will decrease The parameter Q is initially set to -0.2, reflecting the value used for speed adaptation to speed limits in the model by Brodin and Carlsson (1986) While both models demonstrate good performance, additional evaluation is necessary before making any recommendations.

Apart from this reduction of speed corresponding to the speed-flow function, the candidate vehicles travel unconstrained with regard to surrounding traffic

When a candidate vehicle approaches another, it can seamlessly overtake without any time delay Each vehicle operates in its designated lane, as depicted by the multiple lanes shown in the simulator in Figure 4.2.

A candidate vehicle can only enter the simulated area if it maintains a safe distance from the nearest vehicle already within that area The criteria for determining this safe distance varies based on whether the candidate vehicle approaches from behind or in front of the existing simulator vehicle.

Vehicles aiming to enter the simulated area from the candidate area utilize a car-following model to determine their ability to do so without deceleration A vehicle is permitted to enter if the model indicates non-negative acceleration; otherwise, it adopts the model's acceleration and positions itself at the boundary of the two areas, awaiting another opportunity in the next time step To prevent excessive deceleration upon entry, the candidate vehicle adjusts its speed while ensuring a minimum gap from the vehicle ahead, which must exceed a specified distance for stationary vehicles Additionally, in a freeway setting, cars can also enter the simulated area from the left lane, applying the same criteria for entry as used for the right lane.

In the candidate area in front of the simulator vehicle, a distinct approach is employed for the nearest simulated vehicle This vehicle treats the first candidate vehicle like any other simulated vehicle, utilizing a car-following model to adjust its speed Additionally, it applies a lane-changing or overtaking model to determine whether it should attempt to overtake the candidate vehicle While this method is akin to the one used in other candidate areas, it specifically applies the car-following model to the following vehicle within the simulated area rather than directly on the candidate vehicle.

Vehicle update technique

The simulation model employs a traditional time-discrete update method, which is divided into two main parts: updating the speed and position of all vehicles, followed by updating their behaviors, including acceleration, lane changes, and overtaking decisions This separation ensures that the updated information from vehicles does not influence the behavior updates of others, maintaining the integrity of the simulation process.

Figure 4.4 Flow chart over the vehicle update procedure

Remove vehicles which has passed out of the system

Lane Changing OR Passing OR Overtaking model

The speed and position of vehicles are determined using Newtonian equations of motion, with the assumption of constant acceleration and speed throughout the time step Consequently, the speed and position for the subsequent time step are calculated based on these parameters.

In the simulation, the speed \( v_n(t) \) and position \( x_n(t) \) of vehicle n at time t are determined using the equation \( = − + ⋅ − (4.3) \), with T representing the duration of a time step For candidate vehicles, acceleration \( a_n \) is set to zero, and their speed is calculated using either equation (4.1) or (4.2) The time step T varies based on the vehicle's location, with simulated vehicles being updated every 100 milliseconds Vehicles within the simulator driver's sight receive more frequent updates for better visualization, while candidate vehicles are updated less frequently, currently at a rate of once per second.

So far, we have only treated the update of the longitudinal speed and position

The lateral position of a vehicle is primarily influenced by lane changes, with vehicles typically positioned in the center of their lane Two modeling approaches for lane-changing movements have been evaluated: one follows a sine-curve pattern, while the other utilizes a second-degree polynomial at the start and end, with a linear function in between Both methods effectively simulate lane changes on freeways, where these movements last approximately 4-6 seconds, as noted by Liu and Salvucci (2002) However, on rural roads, lane changes can occur much more rapidly, particularly during evasive maneuvers or when aborting an overtaking attempt.

During the user evaluation, see Section 6.3, it was observed that none of the two functions seem to represent lateral movements at quick lane changes correctly

A significant limitation of current functions is their assumption that all initiated lane changes are successfully completed, failing to account for situations where a driver aborts an ongoing lane change To address this issue, a more sophisticated steering model is required, potentially drawing inspiration from the approaches discussed by Boer et al (2001) or utilizing a control theory-based framework.

Figure 4.5 The two different functions for lateral lane-changing movements The dashed grey lines symbolize the lane lines.

V EHICLE GENERATION

Generation algorithm

In the driving direction of the simulator vehicle, new vehicles are generated both behind and in front of it, utilizing a unique generation process distinct from traditional simulation models Specifically, when generating vehicles behind the simulator, only those traveling faster than the simulator are created, as slower vehicles cannot catch up Conversely, for the area in front of the simulator, there is no requirement to generate faster vehicles, as they would not be relevant to the simulation's context.

In traffic simulation models, calculating vehicle arrival times becomes complex when faster vehicles are generated behind a simulator vehicle and slower ones in front Traditional methods rely on time headway distributions, where the average time headway corresponds to the inverse of traffic flow However, if faster vehicles' arrival times are calculated this way, it would inaccurately reflect the average distance between all vehicles, as those generated behind the simulator represent only a subset of the total vehicle population This oversight could lead to a higher frequency of new vehicle generation, skewing the traffic composition from the intended parameters To address this issue, a new generation algorithm has been developed that accurately calculates reasonable arrival times for newly generated vehicles behind the simulator vehicle.

1 Generate a new vehicle with a desired speed, v i des , and time headway, ∆t i , to the vehicle in front

2 Calculate the vehicle’s speed, v i , given its desired speed and the traffic flow, according to either equation (4.1) or (4.2)

3 If the speed is lower than the simulator vehicle’s present speed: increase i and go to step 1, otherwise let n =i

4 Calculate the time to arrival as

, where v DS is the present speed of the simulator vehicle, [m/s]

5 Discard all vehicles except the last generated

Figure 4.6 Illustration of the algorithm for generation of new vehicles at the edge behind the driving simulator

The algorithm generates multiple slower vehicles alongside one faster vehicle during each iteration; however, only the faster vehicle is retained, as all slower ones are discarded To optimize computational efficiency and prevent the algorithm from becoming "stuck" when the simulator vehicle is moving at high speeds, new vehicles are only created behind the simulator when it is traveling slower than the maximum speed in the current desired speed distribution Additionally, the number of attempts to generate new vehicles per time step is limited to a maximum of 10, ensuring n ≤ 10.

To ensure timely arrivals, the speed of the generated vehicle (v_n) must differ by at least 5% from the speed of the simulator vehicle (v_DS) Specifically, if the speed falls within the range of v_DS < v_n ≤ 1.05⋅v_DS, the calculations for arrival time will utilize a speed of 1.05⋅v_DS.

At the edge in front of the simulator, new vehicles are generated according to a corresponding algorithm But the stop criterion is then a speed lower than the simulator’s present speed.

Generation of new vehicles on freeways

The time headways ∆t i represent a snapshot of traffic conditions and may vary from the desired time headways outlined in Section 4.1.1 These time headways are derived from a distribution that differs between freeway and rural road environments This article will detail the characteristics of these time headway distributions in the following sections.

For the freeway environment the time headway distribution presented in Blad

(2002) is used for generating the time headways ∆t i This time headway function is also used in the TPMA-model This time headway distribution can be expressed as

= ⋅ ⋅  + ⋅ + ⋅ , (4.4) where x is the time headway and p 1 and p 2 is parameters that depends on the traffic flow Q according to

For lane flows exceeding 1800 vehicles per hour, the function is adjusted according to the parameters p1 and p2, which are sourced from Blad (2002) The values for the right and left lanes are specified as 4.6.

= , (4.7) in order to fit real data in a better way corr Q ( ) is a correction factor calculated according to

( ) 7.910 8.780 10 3 3.535 10 6 2 4.404 10 10 3 corr Q = − ⋅ − Q+ ⋅ − Q − ⋅ − Q , (4.9) for the right and left lane, respectively

To effectively utilize the time headway distribution functions, a model for estimating traffic flow distribution across two lanes is essential We adopt the model introduced by Blad (2002), which is based on earlier work by Carlsson and Cedersund (2000) This model calculates the flow in the right lane, denoted as Q right.

Q = ⋅k −e − ⋅ , (4.10) where k and l is calculated as

The parameter α represents the proportion of trucks and buses, while β indicates the proportion of trucks with trailers The flow in the left lane is determined by subtracting the right lane flow from the total flow Figure 4.7 illustrates the time headway distributions at a total flow rate of 1000 vehicles per hour.

Figure 4.7 Time headway distributions for the right and left lane on a two-lane freeway at a total traffic flow of 1 000 vehicles/h

On freeways, oncoming vehicles do not engage with driving simulators, allowing for their visualization through playback loops of recorded or simulated vehicle streams In this study, we opted to simulate oncoming vehicles due to the simplicity it offered in terms of programming However, utilizing a playback loop may prove to be a more efficient approach.

On freeways, oncoming vehicles are generated at the boundary between the simulated area and the candidate area in front of the simulator vehicle The arrival time of new vehicles is determined using specific equations, factoring in both the desired speed of the vehicles and the current speed of the simulator It is assumed that oncoming vehicles will drive at their desired speed upon entering the model, necessitating a lengthy warm-up simulation period due to the potential for vehicles to be generated in close proximity with significant speed variations This can cause abrupt decelerations and oscillations within the vehicle stream, a loading issue that has been overlooked in this study However, user evaluations, as discussed in Section 6.3, revealed no unusual or unrealistic behavior from oncoming traffic, suggesting that the employed method is adequate for the intended application.

To optimize simulation efficiency, oncoming vehicles are removed from the model once they are no longer visible in the simulator vehicle's mirrors, with a distance of 2 kilometers deemed sufficient for this purpose.

Generation of new vehicle and vehicle platoons on rural roads

Rural roads often restrict passing and overtaking opportunities, leading to the formation of vehicle platoons Consequently, a simulation model for rural road traffic needs to create realistic vehicle platoons instead of simply generating individual vehicles.

A platoon generation model is utilized to create vehicles moving in the oncoming direction, while realistic vehicle streams in the simulator's direction are generated differently This approach necessitates a more complex model to update candidate vehicles, as it must account for both vehicles within the simulated area and newly generated ones traveling in platoons Rather than explicitly generating platoons, individual vehicles are produced, leading to the formation of vehicle platoons naturally when slower vehicles enter the simulated area from the candidate zone ahead of the simulator vehicle.

Generation of vehicles in the simulator direction

In the vehicle direction simulator, vehicles are generated based on the algorithm outlined in Section 4.2.1 The time headways (∆t i) are modeled as exponentially distributed, with the mean determined by the inverse of the traffic flow, while maintaining a minimum free time gap of 6 seconds.

We use the platoon generation model used in the VTISim model (Brodin et al.,

1986) for generating realistic vehicle platoons in the oncoming direction In this model the queuing model presented in Miller (1967) is used to estimate the mean platoon length as

The parameter λ describes the overtaking possibilities on the current road and is calculated as

The road standard measure, denoted as A, is essential for simulating traffic flow, where q f represents the flow in the studied direction and q o signifies the flow in the opposite direction Additionally, à c indicates the average time gap between constrained vehicles based on the current vehicle composition, while p hv reflects the proportion of heavy vehicles It is crucial to calibrate the road standard measure A for each new road to ensure accurate simulations, as these standards vary between different roadways.

The calibration parameter à c is calculated as c i i i I à pà

The equation ∑ represents the total time for various vehicle types, where I denotes the set of all vehicle categories The variable p i indicates the proportion of each vehicle type, while the calibration parameters are set to specific values: 1.2 seconds for cars, 1.5 seconds for trucks and buses, 1.75 seconds for trucks with 3-4 axles, and 2.25 seconds for trucks with 5 or more axles.

The mean platoon length allows for the calculation of the proportions of free and constrained vehicles, represented as àˆ − 1 and 1−àˆ − 1, respectively Platoons are created by initially generating one free vehicle, followed by the addition of constrained vehicles until another free vehicle appears Subsequently, the vehicles within the platoon are rearranged so that the slowest vehicle leads Additionally, the time headways between vehicle platoons, specifically for platoon leaders, are assumed to follow an exponential distribution.

The mean free time headway (t f) is established alongside a minimum time headway of 6 seconds for free vehicles (t min) Additionally, the time headways between constrained vehicles are modeled using a lognormal distribution, characterized by a mean value of t c.

Vehicles operating in a platoon are expected to maintain their preferred time headway, which is linked to their desired time gaps The average constrained time headway (tc) is determined by the settings of the vehicle and driver, while the mean free time headway (tf) is calculated accordingly.

= − − ⋅ , (4.18) where q is the traffic flow in the current direction and àˆ is calculated according to equation (4.13).

Initialization of the simulation

To create a realistic initial traffic scenario in simulations, it's essential to conduct a warm-up phase where new vehicles are generated using standard traffic simulation methods This approach ensures that the traffic conditions reflect real-world situations On rural roads, the same platoon generation algorithm applied to oncoming traffic during the actual simulation is also utilized in the driving simulator's direction.

In warm-up simulations, an end condition is essential, typically defined by a user-specified warm-up run time In this study, however, the end condition is determined by the number of vehicles passing in front of the observation window This minimum vehicle count is calculated based on the average time required to travel the specified distance, represented by the formula min des n q d.

The equation v = q / d (4.19) illustrates the relationship between traffic flow (q), the total width of the moving window (d), and the average desired speed for the current traffic composition (v des) This condition ensures that the actual traffic flow does not deviate beyond permissible limits.

B EHAVIORAL MODELS

Speed adaptation

Drivers' desired speed fluctuates along a road based on the speed limit and road characteristics Each driver has a fundamental desired speed, representing their preferred travel speed under optimal conditions The specific desired speed for a given road section is determined using the speed adaptation model developed by Brodin and Carlsson (1986) and subsequently refined by Tapani.

In 2005, it was established that the basic desired speed of vehicles is influenced by factors such as road width, curvature, and speed limits Specifically, on freeways, only the speed limit is considered to impact the desired speed The model indicates that the median basic desired speed, denoted as v0, is initially adjusted to account for road width, resulting in a reduced speed v1.

(4.20) where , v 1m is a calibration constant equal to 27.75 m/s, w is the road width, and a is a calibration constant set to 0.042 The speed v 1 is then reduced with respect to curvature to a speed v 2 according to

The mean curve radius (r) is measured in meters, with a calibration constant (b) set at 0.15 Freeways typically feature curve radii exceeding 1,000 meters Consequently, the speed (v2) is adjusted to comply with the current speed limit, resulting in a new speed (v3).

The equation (4.22) defines the variable z as the ratio of the speed limit to v², where d is a calibration constant set at 0.05 Additionally, the calibration constant c varies based on the speed limit and the type of road, with specific calculations for rural roads.

1.3 g 90 0.015 c= − v − ⋅ , (4.23) where v g is the speed limit For freeways the parameter c has been recalibrated

(Janson Olstam et al., 2003) and is now calculated according to

As seen in equation (4.24) drivers are assumed to drive at their basic desired speed when driving on freeways with speed limits of 110 km/h or higher

The desired speed v 3n for a certain vehicle n at a certain part of a road is finally calculated as

3 n 0 Q n 1 Q 0 1 Q Q v = v − −α ⋅ v −v , (4.25) where 0≤α≤1 is a vehicle type dependent parameter Current values on α are

0 for cars, 0.3 for trucks and buses, and 0.5 for trucks with trailer The parameter

Q is a dispersion measure calculated according to

The calibration constants q1, q2, and q3 are set at 0.6, -0.8, and -0.2, respectively, as indicated in equation (4.26) Equation (4.25) illustrates that the desired speed is influenced by both a shift in the basic desired speed distribution and a rotation around its median Specifically, when values of Q are less than 1, this leads to an anti-clockwise rotation around the median.

This implies that fast vehicles will be more affected than slow vehicles For

Q = the desired speed distribution is the result of a parallel shift of the basic desired speed distribution.

Car-following

The car-following model is based on the car-following model presented in

The car-following model, as described by Kosonen (1999) and Davidsson et al (2002), is primarily categorized as a safety distance model It operates under three distinct regimes: Free, Stable, and Forbidden, as illustrated in Figure 4.8.

Figure 4.8 The three different regimes in the car-following model

Different regimes are characterized by headways, which are crucial for understanding traffic dynamics The forbidden area is determined by a headway that varies based on the speeds of both the follower and the leader This area represents an estimation of the braking distance required for the follower to decelerate from its speed to match that of the leader, using a standard deceleration rate In this study, the forbidden headway is calculated to enhance traffic safety and flow.

In the context of vehicle dynamics, the relationship between the speeds of the follower (v_n) and leader (v_n-1) vehicles is crucial The minimum time gap (t_min) plays a significant role, along with the length of the follower vehicle (L_n) and the average normal deceleration rate, currently set at 2 m/s² Additionally, the minimum distance between stationary vehicles (s_stop) is an important factor to consider for safe vehicle operation.

The stable area is defined as the area enclosed by the forbidden area and the free area The width of the stable area, W stable , is calculated as

=  < (4.28) where T s is the minimum stable time headway, W mis the minimum stable space headway, and d f is the function presented in equation (4.27)

When vehicles travel at headways exceeding the sum of the forbidden headway and the width of the stable area, they are classified as free, allowing them to adjust their speed accordingly The original TPMA model utilized discrete speed changes of 2.5 km/h for acceleration and deceleration, which lacks realism on a micro level In this study, a continuous function is employed to calculate acceleration Specifically, when a vehicle's speed is below the desired level, the acceleration model proposed by Brodin and Carlsson (1986) is applied.

The power-to-weight ratio for vehicle n is represented by p n, while C A, C R 1, and C R 2 denote the air and rolling resistance coefficients that vary based on vehicle type Additionally, g signifies the gravitational acceleration constant, and the function i x( n ) indicates the road incline at the position x n of vehicle n.

When the speed of a free vehicle instead is higher than desired the vehicle uses a deceleration rate given as

To achieve the desired speed, a driver maintains a constant speed in a stable area, avoiding acceleration or deceleration If the vehicle exceeds the speed of its leader and surpasses the forbidden time headway, it enters a forbidden area and must decelerate to prevent a collision and return to the stable zone The rate of deceleration is influenced by the ratio (r) of the actual space headway to the forbidden headway, with a higher deceleration rate occurring as this ratio decreases The deceleration is calculated using a piecewise linear function.

The engine parameters define various deceleration rates: the engine deceleration rate is set at 0.5 m/s², the normal deceleration rate at 3 m/s², and the maximum deceleration rate at 9 m/s² to prevent collisions Calibration constants d max, d heavy, d normal, and d engine are established at 0.15, 0.3, 0.6, and 0.75, respectively When a follower enters a forbidden area while the leader moves faster, the follower will utilize the engine deceleration rate to safely return to a stable zone.

The car-following model implicitly accounts for driver reaction times by establishing a stable area, where vehicles will not begin to brake until they have exited this zone Conversely, in acceleration scenarios, it is assumed that drivers react instantly, indicating a stable state of zero delay.

W = in these situations, see equation (4.28)

The car-following model is derived from the calibrated TPMA model, with only minor calibration and validation adjustments made These modifications demonstrate that our model produces results comparable to the original TPMA model, as illustrated in Figure 4.10.

∆ x- l n- 1 [m ] revised version original TPMA version

Figure 4.10 Relative position between a leader and a follower when applying the original and the revised TPMA car-following model

The car-following model discussed is applicable to both freeway and rural road settings Ongoing research aims to create a more adaptable car-following model specifically for rural roads, as noted by Lundgren and Tapani (2005) This new model is expected to eventually supplant the current car-following model in rural environments.

Lane-changing

The lane-changing model is derived from the TPMA model introduced by Davidsson et al (2002) and Kosonen (1999), utilizing a pressure function as outlined in equation (2.6) and illustrated in Figure 2.8 to assess drivers' willingness to change lanes In the original framework, drivers would refrain from changing lanes unless their speed was less than their desired speed, necessitating deceleration before executing a left lane change when approaching a slower vehicle This study modifies the original approach by incorporating a minimum speed difference condition between a driver's desired speed and the speed of the vehicle in front, establishing new criteria for lane-changing behavior.

IF(v n − 1 P fl AND t lane >t min ) THEN desirable to change to the left

To optimize lane changing, the condition IF(c r ⋅P bl > P fr AND t lane > t min) should be met, where P fr, P fl, and P bl represent the pressure values for the front right, front left, and back left of the vehicle, respectively The minimum time required before initiating a lane change is currently established at 10 seconds.

Different values have been tested on the lane-changing parameters c l and c r , and in the end the parameters have been set to the values presented in Gutowski

In 2002, the coefficients for right and left lane changes were established at c r = 0.86 and c l = 0.56, respectively Additionally, a constraint was introduced to prevent a vehicle from changing lanes to the left if it would have opted for a right lane change when traveling in the target lane.

The gap-acceptance component of the lane-changing model is based on the TPMA model, utilizing distinct critical gaps for right and left lane changes as well as for lead and lag gaps These critical gaps are determined using the formula cr n des t = t ⋅ γ, where t des n represents the desired time gap for the vehicle attempting to change lanes The calibration parameter γ, which varies depending on the direction of the lane change and the type of gap, is set according to the values outlined in Table 4.1, aligning with the recommendations from Hillo and Kosonen (2002).

Table 4.1 Used values on the critical gap parameter γ

Overtaking

The overtaking model is divided into two key components: the first focuses on the decision-making process regarding whether to initiate an overtaking maneuver in the current driving context, while the second assesses driver behavior during the overtaking process, determining whether to complete the maneuver or abort it.

The overtaking model used is the one originally presented in Brodin and Carlsson

In 1986, a model was introduced to describe vehicle interactions on the road When a vehicle approaches a slower one, it may attempt a flying overtaking maneuver If this isn't feasible, the following vehicle must reduce its speed to match that of the leading vehicle, in accordance with a car-following model The opportunity for accelerated overtaking arises later when conditions permit Flying overtaking can only occur when the following vehicle is directly behind the slower vehicle, while accelerated overtaking is possible when the following vehicle is in a trailing position This maneuver can be initiated when the following vehicle reaches a sight maximum or encounters an oncoming vehicle.

Drivers who overtake a vehicle in a platoon can utilize the oncoming lane to perform multiple overtakes However, a vehicle will only accept an overtaking opportunity if four specific conditions are met.

The road must be free of overtaking restrictions from the vehicle’s position and 300 meter ahead Restrictions further away are assumed not to affect the overtaking decision

The estimated overtaking distance has to be shorter than the available gap

There must also be a sufficient space in the oncoming lane

3 Ability to execute an overtaking

To ensure safe overtaking, the estimated overtaking distance should not exceed 1000 meters, preventing excessively long maneuvers An accelerated overtaking maneuver is permissible only when the desired speed of the overtaking vehicle surpasses that of the vehicle in front by a minimum of 0.5 m/s.

4 Willingness to execute an overtaking

An overtaking is only performed if the driver accepts the available gap The probability that a driver accepts a gap is determined by a stochastic probability function

The estimated overtaking distance is calculated differently for flying and accelerated overtakings At a flying overtake the driver estimates the overtaking distance as

− , (4.32) where ∆d is the distance which the overtaking vehicle must travel relative the overtaken vehicle At an accelerated overtake the driver instead estimates the overtaking distance as

= ∆ + ⋅ ⋅ , (4.33) where a n is the acceleration of vehicle n calculated according to equation (4.29)

The probability that a driver will execute an overtaking is a function of the available overtaking gap The probability is determined by the following stochastic probability function

The formula P d = e − ⋅ − (4.34) defines the available gap (d gap) in meters, which is determined by the minimum distance to oncoming vehicles and natural sight obstructions The constants A and k are influenced by factors such as the type of overtaking maneuver, sight limitations, the type and speed of the vehicle being overtaken, and the width of the road.

Calibrated values for Swedish road conditions has been presented in Carlsson

(1993) and is also presented in Appendix B

To minimize the frequency of overtaking among vehicles in a platoon, the likelihood of initiating an overtaking maneuver is adjusted based on the vehicle's position within the platoon Consequently, the overall probability of overtaking for vehicles in a platoon is determined by their specific placement in the formation.

The overtaking probability (P) in a vehicle platoon is influenced by the number of vehicles ahead (N) and a calibration parameter (κ), set at 0.6, as per equation (4.35) This probability, calculated through equation (4.34), remains unchanged during situations involving multiple overtakes On roads with wide shoulders, defined as those having a shoulder width greater than 2.25 meters, the overtaking probability is notably high, even over short distances This is because drivers on such roads often initiate overtakes, assuming that oncoming vehicles will maneuver into the shoulder to facilitate the overtaking process Additionally, vehicles on these roads can also utilize the shoulder to allow faster vehicles to pass in the normal lane, a scenario modeled in the passing model outlined in Section 4.3.5.

The overtaking decision model operates as an inconsistent driver model, where each overtaking decision is made independently and does not rely on prior overtaking choices For a deeper understanding of the differences between inconsistent and consistent overtaking models, refer to Section 2.3.3.

When decided to start an overtaking the driver starts to accelerate and changes to the oncoming lane after a short delay, currently set to 2 seconds

During overtaking maneuvers, drivers exhibit distinct speed choices and acceleration behaviors compared to regular driving They are inclined to exceed their desired speed, with an average increase of 10 km/h during these situations Additionally, car drivers experience a notable enhancement in their acceleration, attributed to an improved power-to-weight ratio, which is integrated into the free acceleration model.

The power/weight ratio is currently increased to at least 30 W/kg or with a maximum increment of 6 W/kg

When overtaking, it is crucial for the overtaking vehicle to continuously assess the distance to both the oncoming vehicle and the remaining space available for the maneuver This key factor was not addressed in the model proposed by Brodin and Carlsson.

In 1986, a new sub-model was introduced to enhance the original model, emphasizing that drivers must react when the time to collision (TTC) with an oncoming vehicle is shorter than the estimated time remaining for overtaking This estimated time for overtaking is crucial for assessing safe driving actions.

In the equation provided, ∆ represents the distance related to lane changes, where d min denotes the critical lag gap necessary for safely changing lanes to the right, and t change indicates the duration required to revert to the normal lane It is assumed that the vehicle crosses the boundary between the oncoming and normal lanes halfway through the lane change time The vehicle's acceleration, a n, is derived from equation (4.29) Initially, the remaining overtaking time, t left, was directly compared to the time to collision However, due to observed dangerous overtaking behaviors during user evaluations, a safety margin of 1 second has been implemented for all vehicles, although this parameter requires further calibration for optimal safety.

In scenarios where the time-to-collision (TTC) is less than the time left (t left) and the driver has not yet overtaken the lead vehicle, the driver is expected to abort the maneuver and merge back into the normal lane behind the lead vehicle Conversely, if the vehicle is side-by-side or has already passed the lead vehicle, the driver will increase their desired speed to safely complete the overtaking without colliding with any oncoming vehicles This adjustment results in a recalculated temporarily desired speed to ensure safety during the maneuver.

The minimum distance required for safe overtaking, denoted as d left, is calculated using the time to collision (TTC) and an added safety margin (t safety) If a vehicle's power-to-weight ratio is insufficient to accelerate to the desired speed, as determined by equation (4.29), a temporary adjustment is made to its power-to-weight value.

If the required power-to-weight ratio for achieving a new speed surpasses the maximum allowable ratio for the vehicle type, the driver must abort the overtaking maneuver and safely return to the normal lane behind the vehicle being overtaken.

Passing

On roads with wide shoulders exceeding 2.25 meters, drivers can safely shift to the shoulder to allow other vehicles to pass in the normal lane However, not all drivers utilize this option consistently, as some choose to pass onto the shoulder only occasionally This behavior aligns with the inconsistent passing model outlined by Brodin and Carlsson (1986).

When a vehicle approaches another vehicle on the road and there are wide shoulders available, the leading vehicle has an 85% probability of moving onto the shoulder to allow the following vehicle to pass Additionally, if there is an extra lane present, vehicles will typically shift to the rightmost lane to facilitate the passing of others.

Oncoming avoidance

When driving on rural roads, vehicles must be cautious of both oncoming traffic and overtaking vehicles On roads with wide shoulders, drivers typically steer onto the shoulder if they feel an oncoming vehicle is too close In contrast, on narrower roads, drivers may slow down and use their horn or high beams to signal In critical situations, they attempt to move to the shoulder or ditch to avoid a collision Our model indicates that on wide-shouldered roads, drivers will move to the shoulder if the time-to-collision (TTC) is less than twice the time for a lane change plus a safety margin Conversely, on roads without wide shoulders, drivers signal with high beams, and if the TTC is below 1.5 times the time for a lane change, they brake and maneuver as far into the shoulder as possible to allow the overtaking vehicle to pass safely.

5 Integration with the VTI Driving simulator III

The simulation model has been successfully integrated and tested within the VTI driving simulator III This chapter provides an overview of the functioning of the integrated system, beginning with a brief introduction to the VTI driving simulator III, followed by a detailed description of the integrated system, and concluding with an explanation of how the simulation model interacts with the driving simulator system.

T HE VTI D RIVING SIMULATOR III

Since the 1970s, VTI has been at the forefront of driving simulator development, culminating in the VTI Driving Simulator III, the latest generation of high-fidelity simulators This advanced simulator features a cut-off vehicle cab, a sophisticated vehicle model, and an integrated motion system, complemented by PC-based visual and audio systems Its visual setup includes three screens offering a 120° horizontal and 30° vertical field of view, along with three rear mirrors The motion system provides linear, pitch, and rolling movements, while a vibration table simulates road surface contact For detailed technical specifications, visit the VTI website at www.vti.se.

Figure 5.1 The motion system of the VTI Driving simulator III (Source: Swedish

National Road and Transport Research Institute (VTI) (2004))

T HE INTEGRATED SYSTEM

Figure 5.2 illustrates the integration of the simulation model with the driving simulator The system operates by having the vehicle model compute the simulator's state variables, including acceleration, position, and lateral position, based on the driver's actions with the steering wheel and pedals This data is then transmitted to the scenario module, which manages the movement of other dynamic elements in the environment, such as vehicles, animals, and pedestrians.

All data regarding moving objects, including the simulator vehicle, is transmitted to the visual system, which processes this information to generate current views displayed on various screens for the driver in the simulator.

Figure 5.2 Schematic picture over the integrated system

The integrated system simulates all autonomous vehicles within a traffic simulation model, where the scenario module communicates information about both autonomous and non-autonomous vehicles This module also manages the simulation loop, allowing for a vehicle's simulation to transition from the autonomous traffic model to a controlled scenario simulation This framework facilitates the integration of autonomous vehicles with those exhibiting predetermined behaviors Further exploration of this integration, particularly regarding traffic simulation and scenarios involving predetermined vehicle behaviors, is addressed in Section 3.2.2 However, this thesis does not delve into how to effectively combine traffic simulation with critical events to enhance realism and reproducibility.

The system allows for the control of a vehicle to be shifted between the scenario module and the simulation model, while also implementing a feature that prevents simulated vehicles from overtaking the driving simulator or any other vehicles This capability enables the simulation of realistic oncoming traffic, ensuring that no overtaking occurs within the line of sight of the simulator vehicle.

C OMMUNICATION WITH THE SCENARIO MODULE

The current setup involves the traffic simulation model operating on a separate computer that communicates with the scenario module through an Ethernet network Future plans aim to integrate the traffic simulation model directly into the system for improved efficiency and performance.

Pos., speed, … of ambient veh The current view

Pos., speed, … of DS-vehicle

The current DS-vehicle scenario module relies on ethernet communication, which utilizes two protocols: TCP/IP for command transmission and UDP/IP for state variable updates TCP/IP ensures reliable delivery of commands like start, stop, and freeze by confirming that IP packets reach their destination, allowing for effective communication with the simulation model In contrast, UDP/IP is used for real-time data transmission, offering faster speeds but less reliability, as it does not guarantee packet delivery or order To mitigate this unreliability, increasing the send frequency compensates for potential packet loss or disorder, enabling the receiver to discard outdated packets without affecting performance.

“losing” a package since it quickly gets a new package with up to date information

To minimize delays between actions in the driving simulator and their visualization, the main simulator loop operates at a high frequency of 200 Hz, requiring the scenario module to maintain up-to-date information on simulated vehicles This necessitates either handling potential data loss from the traffic simulation model or increasing the data transmission frequency Vehicle position and behavior updates must run on separate processor threads to optimize performance, with high-frequency position updates managed within the scenario module through extrapolation of data from the traffic simulation model However, synchronizing clocks between different computers running the scenario and traffic simulation models poses challenges, particularly due to differences in operating systems, such as the Windows machine used for traffic simulation, which struggles with clock accuracy This clock drift has caused noticeable positional inconsistencies when driving near simulated vehicles To address this, efforts are underway to compile the traffic simulation model for Linux, facilitating better integration and eliminating the need for ethernet communication, a common source of errors during integration.

The developed model's primary output focuses on the behavior of simulated vehicles, necessitating validation at a microscopic level Validating the model microscopically ensures accurate macroscopic results, although the reverse is not guaranteed This chapter explores various methods for validating the model, details two specific validation approaches employed, and concludes with observations from tests conducted in the driving simulator.

H OW SHOULD THE MODEL BE VALIDATED ?

In this application, the key aspect is that simulator drivers must perceive surrounding vehicles and their behaviors realistically; otherwise, their actions may differ from those in real-life driving However, defining what constitutes "realistic" behavior presents a challenge, as does determining the level of realism required for the model to be considered valid The ultimate aim is to develop a model where simulator drivers cannot distinguish between vehicles operated by humans and those controlled by computers Nonetheless, achieving such a model may be an unrealistic aspiration.

The driving simulator must ensure not only valid results but also safe interactions between vehicles to prevent dangerous situations or collisions Unlike real-world scenarios, where such incidents may occur, the simulator should expose drivers only to critical events defined in the scenario module, with exceptions for risky maneuvers by the driver To assess the realism of vehicle behavior in the simulator, outputs from behavioral models can be compared with real driver data, obtained through instrumented vehicles or other simulators This involves measuring the positions, speeds, and accelerations of vehicles and applying car-following models for validation However, gathering sufficient and usable data for these comparisons is challenging and costly, limiting the scope of such studies in this project Consequently, the focus has been on utilizing pre-calibrated and validated behavioral models, although some may require revalidation Currently, the outputs from these models have only undergone visual validation through two- and three-dimensional simulations.

A key metric related to observed realism in driving simulators is the comparison between the number of vehicles that overtake the simulator driver and those that the driver overtakes While it may be difficult to assess whether the overtaking frequency matches real road conditions at a specific speed, an unrealistic ratio of vehicles caught up versus those overtaken can trigger a noticeable reaction For instance, if a driver believes they are faster than average, they would expect to overtake more vehicles than are overtaking them This catch-up data can be effectively measured during simulation runs and compared with real-world statistics Validation of this metric has been conducted in this study, with results detailed in Section 6.2.

To validate a driving simulator, participants can drive on a specific road in both real life and the simulator If the simulator is accurate, their speed choices, headways, overtaking, and lane-changing behaviors should align closely between the two environments However, this method primarily validates the overall simulator system rather than the traffic simulation model itself If discrepancies arise, it may be challenging to determine whether they stem from the traffic model or other components of the simulator system.

To ensure the realism of simulated vehicle behavior, incorporating the opinions of simulator drivers in the validation process is essential The human perspective is invaluable for identifying unrealistic actions and assessing the authenticity of simulated vehicles While individual feedback may be subjective, gathering insights from multiple participants can mitigate bias and enhance the overall evaluation of realism.

In this study, we aimed to validate our simulation model through a driving simulator experiment, where participants provided feedback on the behavior of simulated vehicles The design and findings of this user evaluation are detailed in Section 6.3.

N UMBERS OF ACTIVE AND PASSIVE OVERTAKINGS

Simulation design

The simulation model utilized data from a 2.5-hour simulation of a straight and flat road, where the driving simulator vehicle operated autonomously, without human intervention During the simulations, the desired speed of the driving simulator varied across different replications, utilizing three distinct basic speeds: 25.8 m/s, 30.8 m/s, and 35.8 m/s.

In a rural setting, the sight distance was considered infinitely long, meaning that available overtaking gaps were consistently limited by oncoming traffic The simulated road, typical of Swedish rural areas, was 9 meters wide with a speed limit of 90 km/h Three distinct traffic flow levels were analyzed, specifically 200, 400, and 600 vehicles per hour per direction.

The freeway simulation featured a straight, flat road with a speed limit of 110 km/h, incorporating three distinct traffic flow levels: 500, 1000, and 1500 vehicles per hour These flow rates were selected to represent both low and high traffic conditions commonly experienced on Swedish roads.

In the simulations, heavy vehicles constituted 12% of traffic, including 4% trucks, 4% buses, and 2% each of two truck types with trailers, reflecting typical traffic conditions on Swedish roads Each combination of desired speed and flow was tested through 10 replications, resulting in a total of 90 replications for each road environment.

In a rural setting, the calculation of active and passive catch-ups involved tracking the number of overtakings during the simulation The total catch-ups were determined by adding the queue lengths both in front of and behind the simulator vehicle at the last time step Conversely, in a freeway environment, passive catch-ups were quantified by counting the vehicles that overtook the simulator vehicle in the left lane, adjusted for those temporarily passed on the right Active catch-ups were measured in the reverse manner.

The time mean speed distribution, denoted as f(v,t), is essential for calculating the expected number of active and passive catch-ups, as outlined in equations (6.1) and (6.2) This distribution was generated through a simulation model utilizing a driving simulator positioned beside the road It was assumed that the time mean speed distribution follows a normal distribution, with mean and standard deviation values derived from point measurements taken during 10 simulation runs.

( ) f v t varies with the traffic flow and the procedure above was therefore repeated for each studied flow.

Results

The results from the rural road environment, illustrated in Figures 6.1 to 6.3, show that the simulated values align closely with the analytical calculations of the expected number of active and passive catch-ups While the simulated values are generally slightly lower than those derived from the analytical expression, this discrepancy is justifiable The analytical model assumes that a vehicle catching up to another can overtake it immediately, without any delays.

Number of vehicles that catches up with DS per km

1 Number of vehicles that DS catches up with per km

The analysis presents the simulated and calculated data regarding the frequency of passive and active catch-ups per kilometer for a driving simulator vehicle (DS) operating on a straight, flat rural road with oncoming traffic at a rate of 200 vehicles per hour.

Number of vehicles that catches up with DS per km

1 Number of vehicles that DS catches up with per km

The simulation results illustrate the number of passive and active catch-ups experienced by a driving simulator vehicle on a straight, flat rural road with oncoming traffic at a density of 400 vehicles per hour The left figure depicts the calculated passive catch-ups, while the right figure shows the active catch-ups per kilometer driven.

Number of vehicles that catches up with DS per km

1 Number of vehicles that DS catches up with per km

The simulated and calculated number of passive and active catch-ups per kilometer for the driving simulator vehicle (DS) was analyzed on a straight, flat rural road with oncoming traffic at a rate of 600 vehicles per hour.

The freeway simulation results, illustrated in Figures 6.4 to 6.6, indicate a strong correlation between simulated and analytical values for passive catch-ups, particularly under moderate flow conditions where overtaking occurs without delay However, the alignment for active catch-ups is less consistent; while agreement is observed at lower travel speeds, discrepancies grow as speeds and traffic flow increase Notably, Figures 6.4 and 6.5 reveal that these differences are more pronounced at higher flow levels, suggesting that the assumption of delay-free overtaking becomes increasingly less valid under such conditions.

Number of vehicles that catches up with DS per km

2.5 Number of vehicles that DS catches up with per km

The simulation and calculation of passive and active catch-ups per kilometer for a driving simulator vehicle (DS) are illustrated in Figure 6.4 This analysis was conducted on a straight and level freeway with a traffic flow of 500 vehicles per hour, following a normal distribution characterized by a mean of 107.6 and a standard deviation of 12.

Number of vehicles that catches up with DS per km

2.5 Number of vehicles that DS catches up with per km

The simulation results depict the number of passive and active catch-ups per kilometer for a driving simulator vehicle on a straight, flat freeway This analysis was conducted with a traffic flow of 1000 vehicles per hour, following a normal distribution with a mean of 104.6 and a standard deviation of 11.9.

Number of vehicles that catches up with DS per km

2.5 Number of vehicles that DS catches up with per km

In a driving simulator study, the number of passive and active catch-ups per kilometer was analyzed on a straight and flat freeway, with a traffic density of 1500 vehicles per hour The results indicate the simulated and calculated catch-up behaviors, represented by a normal distribution with a mean of 100.2 and a standard deviation of 11.9.

The variation in active catch-ups appears to be limited to freeway environments, suggesting that the issue may be specific to these areas An unresolved question remains regarding whether the problem stems from inaccuracies in the model or its implementation Additionally, it's important to recognize that the analytical expression serves merely as an estimation of catch-up numbers, indicating that the expected figures could be the source of the discrepancy.

A key indicator of potential errors in the simulation model is the observation that the simulated mean speed decreases more rapidly with increasing flow than what is seen in real-world scenarios This discrepancy is illustrated in Figure 6.7, which compares speed-flow data from the freeway simulations to average data from a Swedish freeway as reported by SRA (2001).

The simulated space mean speed begins to decline prematurely, indicating that the vehicles are more constrained than expected Despite testing various lane-changing parameters and desired time gaps to reduce speed-decreasing interactions, no improvements have been observed This suggests that additional calibration and validation of the freeway model is necessary.

Figure 6.7 Comparison of simulated freeway speed-flow data and speed-flow relationships presented in SRA (2001)

Figure 6.8 illustrates speed-flow data from rural road simulations, showing that despite slightly lower simulated speeds, the results align more closely than those of freeways This reinforces the notion that the challenges lie within freeway modeling.

Figure 6.8 Comparison of simulated rural road speed-flow data and speed-flow relationships presented in SRA (2001).

U SER EVALUATION

Experimental design

The group of participants consisted of 3 women and 7 men The age varied from

The study involved participants aged 27 to 76, with a majority concentrated between 40 and 60 years, resulting in a mean age of 50.9 years and a standard deviation of 15.4 Notably, none of the participants had prior experience using a driving simulator, and their typical driving mileage varied significantly.

2000 km to 20 000 km per year, with a mean of 13 300 km/year and a standard deviation of 6 300 km/year See Table E.1 in Appendix E for a complete list of the participants’ background information

Participants began their simulation experience with a 5-minute drive on an empty rural two-lane highway, followed by another 5 minutes on an unoccupied freeway This initial warm-up period allowed them to familiarize themselves with the simulator Subsequently, they drove for 15 minutes on each road type, this time with simulated surrounding traffic Participants were instructed to drive as they normally would in both environments After a total of 40 minutes of driving, they completed a questionnaire and participated in interview questions to provide feedback on their experience.

To minimize order effects in driving studies, it would be beneficial to have half of the participants navigate the road environments in reverse order This approach reduces the likelihood that experiences from the first environment influence the results of the second environment.

Scenario design

The rural road scenario featured a 9 km stretch of Sweden's national road Rv34, extending from Mồlilla to Hultsfred This road lacks a barrier between oncoming traffic lanes, necessitating the use of the opposite lane for overtaking It is characterized by numerous horizontal curves and limited sight distances, as illustrated in Figure 6.9 The road measures 9 meters in width, with a 7-meter carriageway, and all intersections along this stretch have been eliminated The posted speed limit is set at 90 km/h for the entire length, with no critical events programmed during the drive.

Figure 6.9 Screen shot from the rural environment

The study focused on a segment of the European road E4 between Linköping and Norrköping, featuring a consistent speed limit of 110 km/h This freeway, characterized by two lanes in each direction, had all on and off ramps removed for the scenario The selection of roads Rv34 and E4 was based on their representation of Swedish rural roads and freeways, respectively.

The study analyzed traffic conditions in two environments with identical input traffic, differing only in road type The rural road experienced a flow of 300 vehicles per hour per direction, while the freeway accommodated 1300 vehicles per hour, reflecting typical Swedish rush-hour conditions The vehicle composition consisted of 90% cars, 5% buses, and 5% trucks, although trucks were visually represented as buses or vans due to the unavailability of truck visuals Vehicle-driver parameters outlined in Appendix A were utilized for simulating both environments.

In a rural setting, the simulator vehicle began its journey from a parking space, while on the freeway, it started from the shoulder The rural scenario featured a clear road, with no other vehicles present within a 600-meter distance behind the simulator and 100 meters ahead Similarly, on the freeway, there was an unobstructed area extending 800 meters behind and 100 meters in front of the vehicle.

Evaluation design

The formulation and design of questions play a crucial role in shaping participants' responses, influencing both the content and quality of the answers It is essential to consider not only which questions are posed but also how they are articulated Additionally, the mode of questioning—whether oral or written—can significantly impact the responses In this experiment, participants engaged with both a written questionnaire and oral interview questions, allowing for a comprehensive analysis of their answers.

The questionnaire utilized a linear rating scale ranging from 1 to 7 to gather subjective measurements, similar to the scale used in Wright's (2000) user validation study An English translation of the original Swedish questionnaire is available in Appendix C and can be requested from the author The initial question focused on the realism of sensations such as steering, accelerating, and braking, aimed at minimizing comments on these aspects in subsequent questions about surrounding traffic Participants were then asked three questions for each road environment, assessing the realism of other drivers' behaviors and comparing the speed and headway choices of simulated versus real drivers.

Interview questions were utilized to effectively gather insights on unusual or unrealistic situations and behaviors, as oral responses are believed to provide richer data Originally in Swedish, these questions can be found in Appendix D Participants were prompted to share any observations of strange or unrealistic situations and to assess whether they believed these scenarios could occur in reality Additionally, they were questioned about the behavior of simulated vehicles during maneuvers such as overtaking and lane changes.

Results and analyses of the questionnaire

Participants responded to a questionnaire using a grading scale from 1 to 7, with the results detailed in Appendix E The findings from questions 2 to 7 will be explored in the subsequent sub-sections.

Question 2 dealt with to what extent the participants think that simulated drivers in the rural road environment behave like real drivers The grading scale went from to “to a little extent” (1) up to “to a large extent” (7) As can be seen in Table E.3 the result is quite good, with a range from 3 to 7 and with the mean of 5.4 The following comments were received:

• “The other vehicles drove relatively aggressive.”

• “Many strange overtakings or tries to overtake.”

These comments agree with the author’s observation during the experiment Some of the simulated drivers started some very risky overtakings and ended or abandon some overtakings late

In question 3, participants evaluated the speed of simulated drivers compared to real vehicles on a rural road using a seven-point scale, where 1 indicated much slower and 7 indicated much faster The responses ranged from 3 to 5, with an average score of 3.6, suggesting that participants generally perceived the simulated drivers as driving slightly slower than actual drivers, a sentiment supported by various comments from the respondents.

While it seemed that all vehicles were traveling at a consistent speed of 80 km/h, the actual speed varied significantly Interestingly, the cars that overtook me did not pass the other vehicles in the same convoy I was part of.

• “It felt ok, but differences between fast and slow vehicles are bigger in real life.”

• “The vehicle platoons traveled a little slow.”

• “They seemed to drive slower than in reality It may depend on the platoons There are more vehicles driving fast on a real rod.”

Question 4 dealt with the headways that vehicles’ that followed behind the simulator vehicle drove at Participants were asked if the other vehicles drove closer, as far away as, or further away than vehicles on a real rural road The scale started at much closer (1) and ended with much further away (7) The answers varied between 3 and 5 with a mean of 3.9 Thus, the participants did not seem to have observed any differences compared to real environments However, as seen in the comments below and as also observed by the author, the mirrors did not display a proper image during the rural road driving This made it difficult to anticipate distances to vehicles behind and thereby difficult to answer this question

• “I did not think about it, so I guess it was normal.”

• “Hard to make any judgment since the mirrors was not as real mirrors.”

Question 5 is equal to question 2 but instead deal with the freeway environment The answers varied between 3 and 7, with a mean of 5.4, see Table E.4 So as for the rural environment, the participants seem to a quite large extent think that the simulated vehicles behave realistic The following comments were received

• “My only comment is that no one overtook me.”

• “Quite calm traffic rhythm in the simulator environment, Harder to predict other driver’s behavior in reality.”

• “It looks like this in dense traffic, heavy vehicles often overtake.”

Question 6 dealt with the difference in speed between the simulated drivers and real drivers on a freeway, that is question 3 but for the freeway environment The answers varied between 2 and 6 with a mean of 3.8 As in the rural environment, it seems like the participants think that the simulated drivers drove a little bit slower than vehicles in reality This is also seen in the comments below

• “There is a larger difference between slow and fast vehicles in reality.”

• “The buses drove a little faster.”

• “More vehicles drive faster in reality It seemed like no one drove faster than 125 km/h.”

Question 7 dealt with the distances to vehicles following the simulator during the freeway driving As can be seen in Table E.4, the participants’ opinions seem to be that the vehicles drove a little bit closer than in reality The answers varied between 2 and 5 with an average of 3.6 The author has observed that vehicles seems to be much closer when looking in the mirror in the driving simulator compared to what they actually are This could be one possible explanation.

Results and analyses of the interview questions

The interview questions were used to get information about strange or unrealistic situations or behavior An English translation of the originally questions in Swedish is available in Appendix D

In a recent study, participants were asked if they had encountered any unusual or unrealistic situations during a simulation While three individuals reported no such experiences, believing all scenarios were plausible, the remaining seven provided descriptions of situations from both rural and freeway environments Their insights were documented in Tables 6.1 and 6.2, respectively, where they also assessed the likelihood of these scenarios occurring in real life.

Table 6.1 Strange or unrealistic situations observed by the participants during the rural road driving

Road type Description Could occur in reality

Rural The blue van was a plug It should have moved out into the shoulder or stopped at a parking lot Yes

Rural More vans than in reality No

Rural An oncoming vehicle moved suddenly from the shoulder back to its normal lane Felt like it was going to change to my lane

Oncoming vehicles did not use the high beam or horn when vehicles from the own direction did not end risky overtakings Instead they went out into the shoulder directly

No Rural I overtook a blue van that after a while overtook me Yes Rural

Many drivers tend to use the oncoming lane more frequently than necessary while overtaking vehicles In practice, they often only position the left side of their car in the oncoming lane, creating potential safety hazards.

Rural There were some very aggressive drivers taking risky overtakings Yes

Rural Very long platoons Yes

Rural One oncoming vehicle seemed to collide with a vehicle in the own direction No

A red Volvo violated an overtaking restriction by initiating and subsequently ending an overtaking maneuver The driver observed no apparent reason for the vehicle to cease the overtaking, as there were no oncoming vehicles in sight.

Rural Oncoming vehicles moved quickly into the shoulder when performing evasive maneuvers Yes Rural Several strange attempts to start overtakings Can happen in reality but not that often, No

Participants perceived certain driving scenarios as strange or unrealistic, primarily linked to overtaking situations Many noted that other drivers exhibited more aggressive behavior than typical, engaging in risky overtakes with minimal safety margins Additionally, vehicles executing evasive maneuvers, such as moving onto the shoulder to avoid oncoming traffic, appeared to move erratically, leading some participants to feel that these vehicles were encroaching into their lane when returning to the normal roadway.

A frequent observation noted that the simulation featured an excessive number of vans compared to real road conditions This discrepancy stemmed from a programming error that treated all personal car types as equally likely The limited visual profiles for personal cars, combined with this flawed assumption, led to an unrealistic representation of vans This issue can be resolved by accurately adjusting the probability assigned to each type of personal car.

The challenges faced by a significant number of vans are consistent across both freeway and rural environments, as highlighted in the responses for the freeway setting detailed in Table 6.2.

Table 6.2 Strange or unrealistic situations observed by the participants during the freeway driving

Road type Description Could occur in reality

Freeway More vans than in reality No

I waited for one vehicle to pass in the left lane in order to change to the left lane myself But instead of passing the vehicle decreased the speed

Freeway Quite long platoons in the left lane More flexible queue discharging in reality No

A vehicle in the left lane, after overtaking a car in the right lane, failed to return to the right lane despite having a clear road ahead It only switched lanes after a significant delay.

Freeway The other vehicles drove slowly No

Some vehicles passed other vehicles very slowly

The subject does not think that one behave like that on a freeway, you accelerate in order to pass faster

Freeway One bus drove for a very long time in the left lane Yes Freeway There was a van that almost passed me on the right side Yes

The feedback regarding the freeway environment varied more than that for the rural setting, with no particularly unusual situations reported during the experiment One participant observed longer queues in the left lane, while another noted a more relaxed traffic rhythm in the simulator Many participants remarked on vehicles lingering in the left lane before returning to the right, a behavior they acknowledged also occurs in real traffic When discussing driver behavior in specific scenarios—such as lane changes and overtaking—participants expressed similar observations, highlighting aggressive driving on rural roads and the tendency for vehicles to remain in the left lane on freeways Additionally, there was a mention that no vehicles attempted to overtake platoons by passing one vehicle at a time to improve their position.

In the final interview, participants learned about two driving simulators at VTI and were asked if they believed a human was operating one of the other vehicles during the experiment This inquiry aimed to validate the model by testing whether a simulated driver could be indistinguishable from a real one While three participants thought a human might be driving, with two specifying which vehicle, seven believed all vehicles were simulated The predominant reasons for this belief included the assumption that every vehicle was simulated and the lack of distinguishing features among them, suggesting that achieving a model that fully meets the optimal validation criterion may be unattainable.

D ISCUSSION

Some additional observations

Test driving in the VTI Driving Simulator III revealed that simulated driver behavior on rural roads wider than 11 meters is highly risky In reality, vehicles frequently pass or overtake others on such roads, even with oncoming traffic visible, leading to dangerous situations However, the simulator does not accurately replicate how drivers manage these risky scenarios, indicating a need for improvement in modeling these behaviors Despite recognizing this necessity, further development has been deprioritized due to the decreasing prevalence of wide two-lane highways in Sweden, as many are being converted to 2+1 roads, which alternate between one and two lanes in each direction.

The lane-changing model can exhibit unusual behaviors in certain scenarios, as illustrated in Figure 6.10 In this case, vehicle B is in the left lane to overtake vehicle C, which subsequently shifts to the left lane to pass vehicle D After vehicle C changes lanes, vehicle B moves to the right lane due to reduced pressure from the vehicle in front, only to become trapped there until vehicle A and potentially others have passed.

Figure 6.10 Illustration of strange lane-changing behavior

The current lane-changing model does not seem to be able to model drivers tactical lane choices good enough It is probably necessary to either enhance the

To address the current model's shortcomings, it is essential to consider alternative models that offer a more suitable approach Notable examples include the frameworks proposed by Toledo et al (2005) and El Hadouaj et al (2000), which may provide effective solutions to the existing challenges.

This thesis introduces a model for generating and simulating surrounding vehicles in a driving simulator, effectively simulating rural roads with oncoming traffic and freeways without intersections or ramps The model leverages established time-driven microscopic traffic simulation techniques, incorporating behavioral models from VTISim and TPMA Notably, it features an advanced overtaking model for rural roads, offering a more realistic representation of driver behavior during overtaking maneuvers, including the potential for aborting overtakes.

The model has been successfully integrated and tested within the VTI Driving Simulator III, with user evaluations indicating that participants perceive the simulated vehicles and their behaviors as realistic While some identified drawbacks have been addressed, further improvements are necessary The model has been validated regarding active and passive catch-ups, showing good agreement on rural roads and passive catch-ups on freeways; however, a discrepancy remains in the number of active catch-ups on freeways, the cause of which has yet to be determined.

The proposed model enhances realism in driving simulator scenarios while expanding their application range It enables the execution of various experiments, allowing for more comprehensive research and analysis in driving simulations.

• Studies on how the traffic load affects drivers

• Demonstration of new or changed road designs

Research indicates that the impact of various factors on driving performance can fluctuate based on traffic intensity For instance, drivers may experience decreased concentration due to alcohol consumption, fatigue, or the use of technological devices such as mobile phones and navigation systems.

• Evaluation on how different road designs affect drivers’ acceleration, lane- changing, or overtaking behavior

Combining a traffic simulation model with a driving simulator opens up significant opportunities for improving traffic simulation accuracy By collecting data on all vehicle movements from the driving simulator, researchers can analyze behaviors such as car-following, lane-changing, and overtaking This valuable information can be utilized to develop more realistic behavioral models, enhancing the overall effectiveness of traffic simulations.

The integration of a driving simulator with a traffic simulation model serves as a robust tool for analyzing the impact of various Advanced Driver Assistance Systems (ADAS) on driver behavior The driving simulator allows researchers to observe how ADAS affects drivers, and this behavior can then be incorporated into the traffic simulation model By conducting experiments with the driving simulator, researchers can verify the consistency of driver behavior when other vehicles are equipped with ADAS Ultimately, the overall impact on the traffic system can be evaluated through the traffic simulation model alone Ongoing research, such as that by Gettman and Head (2003), highlights the importance of utilizing traffic safety indicators alongside traffic simulations.

Archer (2005), and Lundgren and Tapani (2005), also makes it possible to study the overall safety impact of an ADAS

The current model is limited to simulating road links without intersections or ramps, necessitating the inclusion of on and off ramps for practical application This requires an intricate representation of lane-changing and acceleration behaviors during merging scenarios A challenge arises with merging models that employ priority rules, such as allowing the closest vehicle to the merging point to proceed first, which may not reflect actual driver behavior in a simulator Therefore, adopting a methodology similar to the ramp merging model proposed by Kuwahara and Sarvi is recommended for improved accuracy.

In 2004, a model was proposed where vehicles on the ramp adjust their speeds to find suitable gaps, while vehicles in the main stream modify their speeds and headways to facilitate the merging of ramp vehicles Additionally, Hidas (2005) introduced a cooperative lane-changing approach that could enhance this model To create a more comprehensive representation of rural roads, it is essential to extend the model to incorporate intersections and roads featuring barriers between oncoming lanes, such as 1+1 and 2+1 configurations.

The developed model is currently limited to driving simulator scenarios that lack critical events, highlighting a significant research gap in creating scenarios that integrate stochastic vehicle simulation with critical events The approach involves simulating vehicles in the interval leading up to predetermined critical situations, transitioning from stochastic to controlled vehicle behavior as they approach these events A key challenge is to generate these specified scenarios from an unknown initial state without alerting the subject to impending events To facilitate this transition, the simulation model must be enhanced to include intersections and ramps, which are essential for effectively managing the addition or removal of vehicles in the traffic flow Without these features, it would be nearly impossible to create specified situations discreetly.

Enhancing the model to simulate various weather and road conditions is essential for accurate driving simulations For instance, when testing on winter roads, both the simulator vehicle and surrounding traffic must react to the altered conditions If the ambient traffic behaves as if winter conditions are absent, it could lead to unrealistic scenarios where vehicles drive faster and avoid skids, undermining the effectiveness of the simulation.

Ahmad, O and Y Papelis (2000) "An autonomous driver model for the overtaking maneuver for use in microscopic traffic simulation" In

Proceedings of: Driving Simulator Conference, DSC'00, Paris, France Ahmad, O and Y Papelis (2001) "A Comprehensive Microscopic Autonomous Driver Model for Use in High-Fidelity Driving Simulation Environments"

In Proceedings of: 81st Annual Meeting of the Transportation Research

Ahmed, K I (1999) Modeling Drivers' Acceleration and Lane Changing

Behavior Doctorial thesis at Department of Civil and Environmental

Engineering, Massachusetts Institute of technology, Cambridge

Alloyer, O., E Bonakdarian, J Cremer, J Kearney and P Willemsen (1997)

"Embedding Scenarios in Ambient Traffic" In Proceedings of: Driving

Simulator Conference, DSC'97, Lyon, France

Al-Shihabi, T and R R Mourant (2002) "Toward More Realistic Driving Behavior Models for Autonomous Vehicles in Driving Simulators" In Proceedings of: 82nd Annual Meeting of the Transportation Research

Archer, J (2005) Indicators for traffic safety assessment and prediction and their application in micro-simulation modelling: A study of urban and suburban intersections Doctorial thesis at Department of Infrastructure, Royal

Institute of Technology, Stockholm, Sweden ISBN: 91-7323-119-3 Bailey, A C., A H Jamson, A M Parkes and S Wrigth (1999) "Recent and future development of the leeds driving simulator" In Proceedings of:

Driving Simulator Conference, DSC'99, Paris

Bang, B and T Moen (2004) Integrating a driving simulator and a microscopic traffic simulation model Trondheim, Norway, SINTEF (unpublished paper)

Barceló, J and J Casas (2002) "Dynamic network simulation with AIMSUN" In Proceedings of: International Symposium on Transport Simulation, Yokohama http://www.aimsun.com/Yokohama_revised.pdf

Blad, P (2002) "Part E: Traffic Generators" In: TPMA - Model-1 final report F Davidsson, I Kosonen and A Gutowski Stockholm, Sweden, Centre for Traffic Research (CTR): pp

Boer, E R., A Liu and D Salvuvvi, D (2001) "Toward an Integrated Model of Driver Behavior in a Cognitive Architecture." Transportation Research

In 2004, Bolling et al conducted a simulator study on mobile telephones, published in VTI meddelande 969A by the Swedish National Road and Transport Research Institute in Linköping The study can be accessed online at http://62.119.60.67/templates/Report 2797.aspx?reportid544, with the last access recorded on February 8, 2005.

Bonakdarian, E., J Cremer, J Kearney and P Willemsen (1998) "Generation of Ambient Traffic for Real-Time Driving Simulation" In Proceedings of:

IMAGE Conference, Scottsdale, Arizona, USA

Bottom, C G and R Ashworth (1978) "Factors affecting the variability of driver gap-acceptance behaviour." Ergonomics Vol 21(9): 721-734

Brackstone, M and M McDonald (1998) "Car-following: a historical review."

Brodin, A and A Carlsson (1986), The VTI traffic simulation model - A description of the model and programme system VTI meddelande 321A

Swedish National Road and Transport Research Institute (VTI),

Burghout, W (2004) Hybrid microscopic-mesoscopic traffic simulation

Doctorial thesis at Department of Infrastructure, Royal Institute of

Carlsson, A (1993), Beskrivning av VTIs trafiksimuleringsmodell (Description of

VTIs traffic simulation model, In Swedish) VTI Notat T 138 Swedish

National Road and Transport Research Institute (VTI), Linkửping Carlsson, A (1995) Omkửrning av floating car (Number of overtakings of a floating car, in Swedish) Linkửping, Sweden, VTI (unpublished working paper)

Carlsson, A and H.-Å Cedersund (2000), Makromodeller fửr pồ- och avfarter

(Macro models for on- and off ramps, In Swedish) Centre for Traffic

Champion, A., S Espié and J.-M Auberlet (2001) "Behavioral Road Traffic Simulation with ARCHISIM" In Proceedings of: Summer Computer

Champion, A., R Mandiau, C Kolski, A Heidet and A Kemeny (1999) "Traffic generation with the SCANeRII simulator: towards a multi-agent architecture" In Proceedings of: Driving Simulator Conference, DSC'99, Paris, France

Champion, A., M.-Y Zhang, J.-M Auberlet and S Espié (2002) "Behavior Simulation: Towards High-Density Network Traffic Studies" In: Traffic and Transportation Studies (Proceedings of ICTTS 2002) K Wang, C.P.,

X G., L Nie and H Yang Reston, Virgina, USA, ASCE: pp 988-995 Chandler, R E., R Herman and E W Montroll (1958) "Traffic Dynamics: Studies in Car following." Operations Research Vol 6: 165-184

Cremer, J., J Kearney and Y Papelis (1995) "HCSM: A Framework for Behavior and Scenario in Virtual Environments." ACM Transactions on Modelling and Computer Simulation Vol 5(2): 242-267

Cremer, J., J Kearney and P Willemsen (1997) "Directable behavior models for virtual driving scenarios." Transactions of The Society of Computer

Daganzo, C F (1981) "Estimation of gap-acceptance parameters within and across the population from direct roadside observation." Transportation

Daganzo, C F (1994) "The cell transmission model: a dynamic representation of highway traffic consistent with hydrodynamic theory." Transportation

Daganzo, C F (1995) "The cell transmission model, part II: Network traffic."

Davidsson, F., I Kosonen and A Gutowski (2002), TPMA Model-1 final report Centre for Traffic Research, Royal Institute of Technology, Stockholm, Sweden http://www.infra.kth.se/ctr/projekt/tpma/tpma_en.htm

El hadouaj, S., A Drogoul and S Espié (2000) "How to combine Reactivity and Anticipation the Case of Conflicts Resolution in a Simulation Road Traffic" In Proceedings of: MABS’2000 workshop, Boston, USA

Researchers have made significant contributions to the field of road traffic simulation, with notable works including "A generic road traffic simulation model" by El Hadouaj and S Espié, presented at the ICTTS conference in Guilin, China in 2002 Another influential study is "ARCHISIM: Multiactor parallel architecture for traffic simulation" by S Espié, showcased at The Second World Congress on Intelligent Transportation Systems in 1995 These studies have laid the groundwork for the development of advanced traffic simulation models, enabling more accurate predictions and improved traffic management systems.

Espié, S., F Saad, B Schneztler and F Bourlier (1995) "Microscopic traffic simulation and driver behaviour modelling: The ARCHISIM project" In Proceedings of: VTI Konferens 2A part 3, Linkửping

FHWA (1996), CORSIM User Manual V1.01 Federal Highway Administration, McLean, USA http://www.itsdocs.fhwa.dot.gov//JPODOCS/REPTS_TE/4Y001!.PDF Fritzsche, H.-T (1994) "A model for traffic simulation." Transportation

Gettman, D and L Head (2003), Surrogate Safety Measures From Traffic

Simulation Models FHWA-RD-03-050 Federal Highway Administration,

McLean, USA http://www.tfhrc.gov/safety/pubs/03050/index.htm Gipps, P G (1981) "A behavioural car-following model for computer simulation." Transportation Research B Vol 15(2): 105-111

Gipps, P G (1986) "A model for the structure of lane-changing decisions."

Gregersen, N P., T Falkmer, J Dols and J Pardo (2001), Driving simulator scenarios and requirements TRAINER-project: System for driver

Training and Assessment using Interactive Evaluation tools and Reliable methodologies - Deliverable 4.1, http://www.trainer.iao.fraunhofer.de/deliverables/TRAINER%20D4.1_Fin al.zip, Accessed February 8, 2005

Gutowski, A (2002) "Part D6: Calibration of a freeway Link Model using Box's Complex method" In: TPMA - Model-1 final report F Davidsson, I Kosonen and A Gutowski Stockholm, Sweden, Centre for Traffic Research (CTR): pp

Hidas, P (2002) "Modelling lane changing and merging in microscopic traffic simulation." Transportation Research C Vol 10(5-6): 351-371

Hidas, P (2005) "Modelling vehicle interactions in microscopic simulation of merging and weaving." Transportation Reseacrh C Vol 13(1): 37-62 Hillo, K and I Kosonen (2002) "Part D4: Calibration of ramp operations" In:

TPMA - Model-1 final report F Davidsson, I Kosonen and A Gutowski

Stockholm, Sweden, Centre for Traffic Research (CTR): pp

Hoban, C J., R J Shephard, G J Fawcett and G K Robinsson (1991), A model for simulating traffic on two-lane rural roads - User guide and manual for TRARR version 3.2 Technical Manual ATM No 10B Australian Road

Hoogendoorn, S., P and P H L Bovy (2001) "State-of-the-art of Vehicular Traffic Flow Modelling." Journal of Systems and Control Engineering Vol 215(4): 289-303

Janson Olstam, J (2003) "Traffic Generation for the VTI Driving Simulator" In Proceedings of: Driving Simulator Conference - North America, DSC-NA

Janson Olstam, J (2005) "Simulation of rural road traffic for driving simulators"

In Proceedings of: 84th Annual meeting of the Transportation Research

Janson Olstam, J and J Simonsson (2003), Simulerad trafik till VTI:s kửrsimulator - en fửrstudie (Simulated traffic for the VTI driving simulator

- a feasibility study, In Swedish) VTI Notat 32-2003 Swedish National