Comprehensive Review of Traffic Modeling: Towards Autonomous Vehicles

Abstract

Autonomous vehicles (AVs) have the potential to revolutionize transportation by offering safer, more efficient, and convenient mobility solutions. As AV technology advances, there is a growing need to understand and model traffic dynamics in environments where AVs interact with human-driven vehicles. This review provides a comprehensive overview of the modeling techniques used to simulate and analyze autonomous vehicle traffic. It covers the fundamental principles of AVs, key factors influencing traffic dynamics, various modeling approaches, their applications, challenges, and future directions in AV traffic modeling.

1. Introduction

The advent of autonomous vehicles (AVs) represents a transformative shift in the transportation sector, offering the potential for enhanced safety, efficiency, and convenience. This technological evolution, driven by advancements in sophisticated sensors, artificial intelligence, and real-time data processing, is poised to redefine traditional traffic dynamics and urban mobility [1]. As self-driving cars, trucks, and buses increasingly populate our roadways, it becomes imperative to understand their impact on traffic patterns. Consequently, autonomous vehicle traffic modeling has emerged as a critical area of study, aiming to predict and optimize the interactions between autonomous and human-driven vehicles.

Autonomous vehicle technology is built upon significant progress in machine learning, computer vision, and sensor fusion [2]. These vehicles navigate complex environments by perceiving their surroundings, making decisions, and executing actions without human intervention [3]. The potential benefits of AVs, such as reducing traffic accidents, alleviating congestion, and improving fuel efficiency, are substantial. However, to fully realize these benefits, a deep understanding of how AVs will coexist with conventional vehicles and influence overall traffic flow is necessary [4].

The motivation for modeling autonomous vehicle traffic lies in the need to ensure a smooth and safe integration of AVs into existing transportation systems. Effective models can guide policymakers, urban planners, and engineers in developing infrastructure, traffic management strategies, and regulatory frameworks. These models also help anticipate potential challenges, such as mixed traffic scenarios where human-driven and autonomous vehicles share the road, and devise strategies to address them [5].

This comprehensive review aims to synthesize the current state of research in autonomous vehicle traffic modeling, highlighting various approaches, methodologies, and findings. This review will explore different modeling paradigms employed in AV traffic research, including microscopic models that simulate the behavior of individual vehicles, macroscopic models that treat traffic as a continuous flow, and mesoscopic models that combine elements of both approaches. Each of these models provides unique insights into how AVs affect traffic dynamics.

This review will also examine studies investigating the impact of AVs on overall traffic flow, speed, and congestion. Research has shown that even a small percentage of AVs on the road can significantly improve traffic efficiency. Furthermore, the evaluation of different driving algorithms and their influence on traffic stability and throughput will be analyzed.

Interactions between autonomous and human-driven vehicles, including conflict points, cooperative behaviors, and the potential for new forms of traffic congestion, will be explored in the context of mixed traffic environments. Mixed traffic scenarios present unique challenges, such as the need for AVs to anticipate and react to the unpredictable behaviors of human drivers.

The successful integration of AVs into existing transportation systems requires supportive infrastructure and policies. This review will consider issues related to the requirements for road infrastructures, traffic signals, and regulatory measures needed to facilitate the integration of AVs.

Simulation is a critical tool in AV traffic modeling, enabling the testing of hypotheses, validation of models, and execution of large-scale traffic experiments in virtual environments. This review will provide an overview of various simulation tools and platforms used in AV traffic modeling, emphasizing their role in advancing our understanding of autonomous vehicle dynamics.

Despite significant progress in AV traffic modeling, several challenges persist. These include the need for more accurate and scalable models, the integration of real-world data, and the consideration of human factors in mixed traffic environments. Additionally, ethical and legal issues related to AV deployment, such as liability and privacy concerns, remain to be addressed.

Looking ahead, this review will outline potential research directions, including the development of more sophisticated models that incorporate machine learning and artificial intelligence, the use of edge computing and 5G networks for real-time data processing, and the exploration of new traffic management strategies that leverage the capabilities of AVs. By advancing our understanding of autonomous vehicle traffic dynamics, we can pave the way for a safer, more efficient, and sustainable transportation system.

2. Autonomous Vehicle Technology

Autonomous vehicle (AV) technology, commonly referred to as self-driving or driverless cars, represents a significant innovation in the transportation sector. These vehicles are designed to sense their environment and operate without human intervention, utilizing a sophisticated combination of sensors, cameras, machine learning algorithms, and real-time data processing [6,7]. The Society of Automotive Engineers (SAE) International classifies AVs into six levels of automation, each representing an increasing degree of autonomy [8]:

• Level 0 (No Automation)—the driver is responsible for all driving tasks. The vehicle may provide warnings and momentary assistance but does not control any aspect of driving.
• Level 1 (Driver Assistance)—the vehicle can assist with either steering or acceleration/deceleration using information about the driving environment. The human driver handles all remaining aspects of driving.
• Level 2 (Partial Automation)—the vehicle can control both steering and acceleration/deceleration under certain conditions. The driver must remain engaged and monitor the environment continuously.
• Level 3 (Conditional Automation)—the vehicle can perform all aspects of driving in specific conditions. The driver must be ready to take control when requested by the vehicle.
• Level 4 (High Automation)—the vehicle is capable of performing all driving tasks and monitoring the environment in certain conditions without human intervention. The vehicle may request human intervention in rare cases.
• Level 5 (Full Automation)—the vehicle can perform all driving tasks under all conditions without any human intervention. No driver attention or intervention is required at any time.

The core technologies behind AVs include computer vision, sensor fusion, localization, path planning, and driving control, which collectively enable the vehicle to operate autonomously [9]. These technologies allow AVs to communicate with other vehicles (V2V), infrastructures (V2I), and pedestrians to enhance safety and efficiency. However, despite the rapid advancements, challenges remain in ensuring safety, reliability, regulatory approval, and public acceptance. The increased connectivity also exposes AVs to cyber threats, necessitating robust security measures.

Autonomous vehicles rely heavily on advanced sensor and perception systems to navigate and operate safely. These systems integrate various sensors, including cameras, LiDAR, and radars, to create a comprehensive understanding of the vehicle’s surroundings. While cameras and radars are cost-effective and reliable, LiDAR provides detailed 3D mapping and object detection capabilities, though it is more susceptible to adverse weather conditions [10,11]. The fusion of data from these sensors is crucial for enhancing the accuracy of environmental perception, which is essential for safe operational planning.

Machine learning algorithms play a vital role in processing sensor data and improving the efficiency and accuracy of object detection and image segmentation. For instance, the MultiTaskV3 detection-segmentation network achieves high precision and low power consumption, particularly when implemented on specialized platforms like the AMD Xilinx Kria KV260 Vision AI [12]. However, these systems’ performance can degrade under adverse weather conditions, which affect the quality of data from cameras and LiDAR [13]. To mitigate these challenges, new methods, such as monocular depth estimation using YOLOv7 and attention mechanisms, have been developed to provide low-cost, accurate depth information from RGB images [14].

Robust positioning and mapping systems are also crucial for maintaining submeter-level accuracy across various environments, enhancing AVs’ reliability and safety. However, the broader acceptance and integration of AVs into public roads will depend on addressing concerns related to cost, security, privacy, and environmental impact, as highlighted by studies on the willingness of different populations to adopt AVs [15].

The development of AV technology extends beyond sensor systems and includes advanced control and decision-making algorithms that allow these vehicles to navigate complex environments safely and efficiently. These algorithms reduce accidents caused by human error and improve traffic flow and travel times [16,17]. Given the high-dimensional state space and sparse rewards in urban environments, decision-making for AVs can be particularly challenging. Techniques like Coordinated Convolution Multi-Reward Proximal Policy Optimization (CCMR-PPO) have been developed to address these challenges, optimizing state space and designing multi-objective reward mechanisms to enhance performance in simulations [18].

Specific scenarios, such as navigating roundabouts, involve formulating decision-making as a Partially Observable Markov Decision Process (POMDP) and using algorithms like Partially Observable Monte-Carlo Planning (POMCP) to improve policy predictions and state transitions [19]. AVs must also handle unconventional scenarios, including adverse weather conditions and unsignalized intersections, where traditional planning methods and emerging machine-learning approaches are critical for ensuring safety and reliability. Deep reinforcement learning (DRL) techniques have shown promise in generating decision-making policies that account for interactions with pedestrians, enabling AVs to exhibit natural driving behaviors [20]. Methods like Deep Deterministic Policy Gradient (DDPG) ensure that AVs maintain safe distances and stay centered on the road during path-following tasks [21].

Communication systems are equally essential for AV technology, ensuring safety, reliability, and efficiency in transportation. The Internet of Autonomous Vehicles (IoAV) and the Internet of Vehicles (IoV) are crucial frameworks that enable AVs to interact with each other and their environment through Vehicle-to-Vehicle (V2V), Vehicle-to-Infrastructure (V2I), and Vehicle-to-Everything (V2X) communications [22,23,24]. The integration of 5G networks supports these communications due to their high throughput and low latency, meeting the complex dynamics and real-time requirements of AVs [25]. Furthermore, the use of big data technologies enhances the functionality and safety of AV systems by facilitating the storage and processing of vast amounts of data generated by AVs [22].

Security remains a critical aspect of AV communication, with tamper-resistant broadcasting schemes developed to protect data from unauthorized access and tampering, ensuring secure and efficient information dissemination [26]. The deployment of AV technology also presents opportunities to address social equity by improving transportation access in underserved communities, thereby reshaping urban landscapes and enhancing public transportation systems. Looking ahead, the evolution toward 6G communication promises even greater bandwidth, lower latency, and higher data rates, further enhancing AV capabilities and opening new research and development horizons in vehicular communication [24].

Overall, the convergence of IoT, big data, and advanced communication technologies like 5G and 6G is driving the advancement of AV technology, making it a cornerstone of modern intelligent transportation systems (ITSs) and smart cities.

3. Traffic Flow and Its Characteristics

Traffic flow is a multifaceted concept that can be understood in both broad and narrow senses, each of which provides valuable insights into transportation systems. From a broad perspective, traffic flow encompasses the interaction between various modes of transport and the road infrastructure. This interaction involves not only vehicles but also pedestrians, cyclists, and unmanned systems, all of which navigate through a network of streets, highways, intersections, and traffic control devices. The goal of studying traffic flow at this level is to develop an optimal traffic network that balances the needs of all users while minimizing congestion and improving overall efficiency.

Within this broad context, traffic flow can be viewed in terms of system optimum and user equilibrium. The system optimum seeks to minimize the total travel time for all users across the network, whereas user equilibrium refers to each driver choosing the shortest possible route from their current location to their destination. However, achieving both system optimum and user equilibrium simultaneously in real-world traffic networks can be challenging, if not impossible. Therefore, optimizing transport infrastructures is a key objective in transportation engineering, aimed at enhancing both efficiency and fairness within the system.

In a narrower sense, traffic flow refers to the movement of vehicles along a one-dimensional pathway, such as a road or highway. This concept is often characterized by key parameters: speed (u), density (k), and flow (q). Understanding these parameters and their interrelationships is fundamental to traffic flow theory. A time–space diagram (Figure 1) is a useful tool for visualizing these relationships. It graphically represents the movement of vehicles over time along a specific travel path, with each vehicle’s trajectory depicted as a curve with a non-negative slope. The position of each vehicle at any given time is shown along these trajectories.

The average and instantaneous speeds can be defined for every vehicle. The instantaneous speed of the individual vehicle (u_i) is the slope of the trajectory at the appropriate point on the trajectory (slope of the red line in Figure 1, u_i = dx/dt). The average speed of the vehicle is measured in a selected section of the route (slope of the blue line in Figure 1, u_ai = Δx/Δt). Two average speeds for a group of vehicles are defined for traffic flow in a given period of time and road segment: space and time mean speeds. The time mean speed (u_t) is an average value of the instantaneous speeds (u_i) of vehicles measured at a reference point. If instantaneous vehicle speeds are measured at the reference point (x_r) (in Figure 1, the speed (u_i) at the point x_r is a slope at the point x_r that is similar to the red line), then the time mean speed is calculated as follows:

$$u_t={\displaystyle \frac{1}{n}}\sum _{i=1}^n{u}_i$$

(1)

The space mean speed (u_s) is an average value of the average vehicle speeds (u_ai) of the vehicles measured on the reference road segment. If the reference road segment is the whole space presented in Figure 1, then the average vehicle speeds (u_ai) is a slope similar to the blue line and is calculated as follows:

$$u_s={\displaystyle \frac{1}{n}}\sum _{i=1}^n{u}_{ai}$$

(2)

The vertical distance between the trajectories is the vehicle spacing (s) between the centers of two vehicles. The horizontal distance represents the vehicle headway (h).

The density (k) is the number of vehicles per unit length of the reference road segment. The density is presented in Figure 1 as a vertical cross-section of the space–time diagram at time t_r. It is inverse to the average spacing:

$$k={\displaystyle \frac{1}{\frac{1}{n}\sum _{i=1}^n{s}_i}}$$

(3)

Flow (q) is the number of vehicles that pass through the reference point per unit of time. The flow is presented in Figure 1 as a horizontal cross-section of the space–time diagram at point x_r. It is inverse to the average headway:

$$q={\displaystyle \frac{1}{\frac{1}{n}\sum _{i=1}^n{h}_i}}$$

(4)

The relationships between these key parameters—speed, density, and flow—form the foundation of traffic flow theory. One of the earliest and most influential studies on this subject was conducted by Greenshields in 1935, who explored the relationship between vehicle spacing and speed [27]. This relationship is now recognized as a fundamental relation and is often depicted in a fundamental diagram that illustrates the interdependencies between these variables.

3.1. Classical Traffic Flow Theories

The development of classical traffic flow theory began in the 1950s, marking the start of systematic efforts to understand and model traffic dynamics. A significant milestone in this field was the publication of a comprehensive bibliography in 1961 by the Committee on Theory of Traffic Flow, which was featured in a letter to the Editor of the Journal of Operations Research [28]. This bibliography categorized important publications into ten sections, including hydrodynamic analogies, kinematic waves, car-following dynamics, probabilistic flow models, traffic distributions over networks, and various statistical studies. The foundational topics identified in this early work continue to influence traffic flow research today.

3.2. Shape of the Fundamental Relation

The concept of the fundamental relation in traffic flow, which describes the relationship between key variables such as spacing, speed, density, and flow, was first proposed by Greenshields [27]. This relation is crucial for understanding how traffic behaves under different conditions and forms the basis of many traffic flow models.

In 1955, Lighthill and Whitham, followed by Richards in 1956, developed the LWR model, which uses hydrodynamic analogies and kinematic wave theory to describe the relationship between traffic density (k), flow (q), and speed (u) [29,30]. The static hydrodynamic equation for this model is as follows:

$$q=ku$$

(5)

Vehicle preservation involves the equation of dynamic continuity, for example, for the homogeneous case:

$${\displaystyle \frac{\partial k}{\partial t}}+{\displaystyle \frac{\partial q}{\partial x}}={\displaystyle \frac{\partial k}{\partial t}}+{\displaystyle \frac{\partial \left(ku\right)}{\partial x}}=0$$

(6)

To solve a macroscopic flow model, a third equation, often referred to as the fundamental relation or diagram, is necessary. Greenshields [27] proposed a linear relation that leads to a parabolic relationship between flow and density, where flow is zero when density is either zero or at its maximum (k_max) and reaches a peak at critical density (k_cr):

$$u=u_{\mathrm{m}\mathrm{a}\mathrm{x}}\left(1-{\displaystyle \frac{k}{k_{\mathrm{m}\mathrm{a}\mathrm{x}}}}\right)$$

(7)

The maximum density (k_max), when the flow is stopped, is named the jam density: k_jam = k_max. Then, the fundamental relation is of the following form:

$$q=4q_{\mathrm{c}\mathrm{a}\mathrm{p}}k\left(1-{\displaystyle \frac{k}{k_{\mathrm{j}\mathrm{a}\mathrm{m}}}}\right)$$

(8)

The density–speed and density–flow according to this model are shown in Figure 2. The critical density (k_cr) divides traffic flow into two areas (or phases): free flow and congestion.

In contrast to Greenshields, Greenberg [31] proposed a logarithmic relation between flow and density that better aligns with experimental data in certain scenarios. This model introduces an adjusting parameter to account for variations in traffic behavior:

$$q=q_{\mathrm{c}\mathrm{a}\mathrm{p}}{\displaystyle \frac{ek}{k_{\mathrm{j}\mathrm{a}\mathrm{m}}}}\mathrm{l}\mathrm{n}\left({\displaystyle \frac{k_{\mathrm{j}\mathrm{a}\mathrm{m}}}{k}}\right)$$

(9)

where e is the adjusting parameter, q_cap is the maximum flow, and k_jam is the jam (maximum) density.

Because this equation is not defined at k = 0, some initial zone with instant speed is introduced. Gazis et al. extended the car-following theory to derive a relationship similar to Greenberg’s model, emphasizing that the sensitivity of a following vehicle is inversely proportional to the spacing between vehicles [32].

Underwood further developed the fundamental relations by proposing an exponential model for speed–flow functions [33]:

$$u_s=u_{s0}\mathrm{e}\mathrm{x}\mathrm{p}\left(-bk\right)$$

(10)

which was generalized in the following form [34]:

$$u_s=u_{s0}\mathrm{e}\mathrm{x}\mathrm{p}\left[-{\left({\displaystyle \frac{k}{b}}\right)}^a\right]$$

(11)

where u_s is the space mean speed, u_s0 is the space mean speed at zero flow (maximum speed), and a and b are the parameters. Then, the critical density and capacity are as follows:

$$k_{cr}=b{\left({\displaystyle \frac{1}{a}}\right)}^{{\displaystyle \frac{1}{a}}}$$

(12)

$${q_{\mathrm{m}\mathrm{a}\mathrm{x}}=u}_{s0}b{\left(ae\right)}^{-{\displaystyle \frac{1}{a}}}$$

(13)

This model can be extended to represent capacity drop:

$$u_s=\left\{\begin{array}{cc}\left(u_{s0}-∆u\right)\mathrm{e}\mathrm{x}\mathrm{p}\left[-{\left({\displaystyle \frac{k}{b}}\right)}^a\right]+∆u& for k<k_{cr}\\ \left(u_{s0}-∆u\right)\mathrm{e}\mathrm{x}\mathrm{p}\left[-{\left({\displaystyle \frac{k}{b}}\right)}^a\right]& for k\ge k_{cr}\end{array}\right.$$

(14)

where a, b, and Δu are the parameters.

Edie addressed the shortcomings of Greenberg’s model [31] in low-density areas by proposing a discontinuous exponential form that combines elements of both Greenberg and Underwood’s relations [35]:

$$u_s=\left\{\begin{array}{cc}{u}_{\mathrm{m}\mathrm{a}\mathrm{x}}\exp \left(-{\displaystyle \frac{k}{k_m}}\right)& for k<k_{cr}\\ c\ln {\displaystyle \frac{k_{jam}}{k}}& for k\ge k_{cr}\end{array}\right.$$

(15)

where c and k_m are the parameters.

Drake et al. [36] analyzed and modified Greenshields’ model, introducing a bell-shaped curve to describe the relationship between speed and density, particularly in complex traffic scenarios (Figure 3):

$$u_s=u_{\mathrm{m}\mathrm{a}\mathrm{x}}\mathrm{e}\mathrm{x}\mathrm{p}\left[-{\displaystyle \frac{1}{2}}{\left({\displaystyle \frac{k}{k_m}}\right)}^2\right]$$

(16)

Smulders [37] proposed a hybrid model that combines a parabolic relationship below the critical flow and a linear relationship above it, offering a more nuanced description of traffic flow dynamics (Figure 4).

Daganzo’s model [38], one of the most widely used, presents a bilinear relationship in the density–flow plane, providing a simple yet effective framework for understanding traffic behavior (Figure 5).

While these models laid the groundwork for traffic flow theory, they also have limitations. The LWR model and its modifications are among the simplest traffic flow models but fail to account for more complex phenomena such as capacity drops, hysteresis, relaxation, spontaneous congestion, traffic oscillations, and phase transitions. As traffic systems become more intricate, there is a growing need for models that can capture these advanced dynamics.

3.3. Capacity Drop

The concept of capacity drop refers to the sudden reduction in traffic flow from a free-flowing condition to a stop-and-go state and the subsequent difficulty in returning to the original flow rate. Edie [35] introduced this concept by modifying existing traffic flow theories to account for these abrupt changes in state. This phenomenon is critical in traffic dynamics, particularly in managing and controlling traffic flow effectively. Discontinuous is introduced into the fundamental relation (Figure 6).

The capacity drop phenomenon has been extensively studied through both empirical observations and theoretical models. For example, Gazis and Edie [39] presented a fundamental diagram based on experimental data from the Lincoln Tunnel in New York City, highlighting the existence of a capacity drop as a gap in the diagram. This observation was further confirmed by Hall and Agyemang-Duah [40], who validated the capacity drop in various traffic scenarios.

Numerous studies have explored the capacity drop effect across different settings. Cassidy and Windover [41], Cassidy and Bertini [42], and others [43,44,45,46,47] have reported that the magnitude of the capacity drop can range between 0.5% and 35%, depending on the specific traffic conditions. This wide variation underscores the complexity of the phenomenon and the influence of various factors on traffic flow.

Researchers have proposed several mechanisms to explain the occurrence of capacity drops. Laval and Daganzo [48] suggested that disruptions caused by lane-changing maneuvers, particularly near merging points and moving bottlenecks, can trigger capacity drops. This idea is supported by Saberi and Mahmassani [49], who identified two distinct types of capacity drops: one associated with the inability of the network to maintain peak traffic for extended periods and another linked to incomplete recovery after the network is reloaded.

Yuan et al. [50] further contributed to this understanding by demonstrating that the queue discharge rate increases with vehicle speed within a queue, and the magnitude of the capacity drop decreases as the vehicular speed increases. This finding highlights the dynamic nature of traffic flow and its sensitivity to speed variations.

The capacity drop phenomenon has also been explored through various simulation models. Zhang and Kim [51] used a car-following model to simulate capacity drops, while Hu et al. [52] and Ding and Huang [53] employed cellular automata models. Yuan et al. [54] applied a geometric Brownian motion model to gain deeper insights into the underlying mechanisms of capacity drops.

Recent studies have aimed to provide a more comprehensive understanding of capacity drops. Kontorinaki et al. [55] presented an overview of different modeling approaches that capture the capacity drop phenomenon in first-order traffic flow models. Their work also introduced a new approach, validated using real data from a UK motorway network. Wang et al. [56] offered a thorough review of capacity drops, examining them from both behavioral and simulation perspectives. Their findings demonstrate that capacity drops can be accurately modeled and targeted using both macroscopic and microscopic simulation tools.

More than ten potential causes of capacity drops have been identified, including factors such as limited acceleration, differences in acceleration, variance-driven gaps, proximity to bottlenecks, the number of lanes, lane-changing behavior, and on-ramp flow. Despite significant progress in understanding capacity drops, this area remains an active field of research within traffic flow theory. Ongoing studies continue to investigate ways to mitigate capacity drops and improve traffic management strategies.

3.4. Hysteresis

The concept of hysteresis in traffic flow was first introduced by Newell [57] in 1962. He proposed a car-following model where the relationship between velocity and spacing differs depending on whether a vehicle is accelerating or decelerating. In this model, the deceleration branch is positioned above the acceleration branch in the flow–density diagram, leading to what is known as a clockwise hysteresis loop (Figure 7). This hysteresis effect contributes to instability in long queues, where the process of deceleration and acceleration does not follow a uniform pattern.

The idea of hysteresis was further explored and developed by several researchers. Treiterer and Myers [58] analyzed hysteresis from both macroscopic and microscopic perspectives, providing foundational insights into its behavior under different traffic conditions. Zhang [59] expanded on this by defining three traffic phases—acceleration, deceleration, and strong equilibrium—where the branches of the hysteresis loop can intersect and even reverse positions, resulting in a counterclockwise hysteresis loop. This complexity underscores the variability in traffic behavior during transitions between free flow and congestion.

Numerical simulations have played a crucial role in advancing the understanding of hysteresis. For instance, Zhang and Kim [51] used car-following models to demonstrate the presence of traffic hysteresis, capacity drops, and the emergence of fast waves during transitions from free flow to congestion. Similarly, Buisson and Ladier [60] reported hysteresis phenomena in the macroscopic fundamental diagram of the Toulouse road network, highlighting the influence of road network topology and heterogeneity on the shape of the diagram.

Yeo and Skabardonis [61] validated Newell’s assumptions through the analysis of statistical trajectory data, suggesting that human errors can induce traffic instability, further contributing to hysteresis. Recent work by Laval and Leclercq [62] introduced a measurement approach that accounts for nonstationary states, identifying four types of hysteresis: strong, weak, negligible, and negative. Laval [63] confirmed that the acceleration branch is often observed above the deceleration branch, a pattern associated with counterclockwise hysteresis loops, which may be explained by variations in driver behavior, particularly aggressive or timid driving.

Geroliminis and Sun [64] investigated the causes of clockwise hysteresis loops using data from the Twin Cities metropolitan area freeway network in Minnesota, USA. Their findings suggest that such loops are more likely to occur during peak periods when drivers adhere rigidly to traffic patterns, though the probability of hysteresis decreases when drivers adapt to avoid congestion. Gayah and Daganzo [65] further explored this by showing that the likelihood of hysteresis decreases if drivers adapt to changing traffic conditions, thereby avoiding congestion.

Saberi and Mahmassani [49] identified two distinct types of clockwise hysteresis loops, labeled as H1 and H2. The H1 loop typically appears when network recovery is unstable, characterized by a heterogeneous traffic distribution during recovery and a continuous decrease in the average network flow as the network occupancy is reduced. In contrast, the H2 loop occurs during stable network recovery, where the average flow remains unchanged as occupancy decreases. Saberi and Mahmassani [66] also proposed a characterization of the path-dependent hysteresis pattern in highway networks.

Ahn et al. [67] studied these hysteresis loops by analyzing the evolution of speed–spacing relationships during stop-and-go oscillations, while Chen et al. [68] demonstrated that variable driver characteristics are a significant factor in the periodicity and development of traffic oscillations, which in turn affect the discharge rate at bottlenecks.

Research into hysteresis phenomena continues to evolve, with studies focusing on different aspects and applications. For example, Shim et al. [69] analyzed large-scale vehicle trip data in South Korea, revealing distinct hysteresis patterns in macroscopic fundamental diagrams during weekdays and weekends. Rammutla and Zuidgeest [70] conducted a detailed analysis of hysteresis loops in Cape Town, showing that H2 hysteresis loops signify stable network recovery during peak periods. Maes [71] observed a clockwise hysteresis loop in the study of phenomena under transient traffic conditions caused by incidents on a bidirectional motorway in Brussels, Belgium.

Xu et al. [72] examined the relationship between network flow and density, as well as trip completion rates, discovering that different patterns of hysteresis loops can emerge depending on the traffic conditions, with some even taking on counterclockwise forms. These findings underscore the complexity of hysteresis in traffic networks, where even the length of trips can influence the overall traffic dynamics.

To better understand and simulate hysteresis phenomena, various models have been employed. Zhang and Kim [51] used car-following models, while Hu et al. [52] and Ding and Huang [53] applied cellular automata models. Additionally, He et al. [73] and Mühlich et al. [74] utilized microsimulations, and Zhou and Shi [75] developed a modified full-velocity difference model. More recent approaches, such as the long-memory and short-memory deep learning car-following models by Wang et al. [76], further demonstrate the dependency of hysteresis on small fluctuations in car-following behaviors.

Ultimately, hysteresis in traffic flow is a multifaceted phenomenon, heavily influenced by the interplay of driver behaviors, traffic conditions, and roadway characteristics. Continued research and simulation efforts are essential to fully understand and mitigate its impact on traffic dynamics.

3.5. Three-Phase Traffic Flow Models

In traffic flow theory, a phase is defined as a state that exists in both space and time. Traditional fundamental diagrams, as discussed earlier, typically classify traffic into two phases: free flow and congested flow. However, Kerner and Klenov [77] introduced a more nuanced model called the three-phase traffic theory. This theory expands upon the conventional understanding by introducing an additional phase, thereby providing a more comprehensive explanation of traffic behavior. The three-phase traffic theory is grounded in the concept of synchronized flow and postulates that the steady states of synchronized traffic cover a two-dimensional (2D) region in the flow–density plane, which contrasts with the traditional one-dimensional approach. This theory challenges the idea that a single fundamental diagram can fully capture the dynamics of traffic flow. Instead, it suggests that traffic congestion can be divided into three distinct phases: free flow (F), synchronized flow (S), and wide moving jam (J) (Figure 8). In the first phase of free traffic flow, empirical data have a positive correlation between the flow rate (q) and vehicle density (k). This relationship ends at the maximum free flow (q_max) with a corresponding critical density (k_crit). There are the same phases as in the two-phase models presented in previous sections. The average speed of the vehicle in the phase of a wide moving jam is much lower than the average speed of the free flow. On the downstream front, vehicles accelerate at the speed of the free flow. On the upstream jam front, vehicles come from the free flow or synchronous flow and must reduce their speed. In the synchronized flow phase, both the flow rate and vehicle speed may vary. The downstream front of the synchronized flow is often spatially fixed, usually at a bottleneck at a certain location on the road. The flow rate in this phase could remain similar to that in free flow, even if vehicle speeds are greatly reduced.

Kerner and Klenov developed the first-order phase-transition model to explain the onset of synchronized flow from free flow, which led to the continuum version of the three-phase theory. This was further extended by Kerner et al. [78], who proposed a cellular automata approach consistent with the three-phase theory. Their work provided empirical validation for the theory, showing that traditional two-phase models could not fully explain certain traffic phenomena, such as the persistence of synchronized flow and the spontaneous formation of wide moving jams.

Overall, the three-phase traffic theory offers a more detailed understanding of traffic dynamics by recognizing that traffic flow is not simply a matter of free flow versus congestion. Instead, it acknowledges the complex and transitional nature of traffic, where phases like synchronized flow play a critical role in how congestion develops and dissipates on roadways.

3.6. Other Phenomena

In the study of traffic flow, several phenomena beyond the basic principles have been observed and analyzed. These phenomena provide a deeper understanding of the complexities involved in traffic dynamics.

The relaxation phenomenon, first identified by Smith [79], occurs when vehicles involved in a lane-changing maneuver initially accept short spacings but gradually transition to more comfortable spacings over 20 to 30 s. This behavior has been incorporated into various car-following models and lane-change decision processes, as explored by Gipps [80], Liu et al. [81], Li [82], and others [83,84,85,86,87]. The phenomenon highlights the dynamic nature of driver behavior during lane changes, which must be considered in accurate traffic modeling.

Density oscillations between lanes, initially studied by Gazis et al. [88], represent another important aspect of traffic flow. These oscillations, which occur particularly in queuing situations, were first described in detail by Mauch and Cassidy [89]. They noted that such oscillations stabilize as they propagate upstream, with distinct periodicity. Subsequent studies by Jin and Zhang [90] and others have investigated how network geometry influences these oscillations, using both microscopic and macroscopic models. Lämmer and Helbing [91] extended this research by proposing a self-organization approach to traffic light control, which helps manage oscillations at intersections.

Laval and Leclercq [92] proposed a mechanism to explain the formation and propagation of stop-and-go waves, a common occurrence in congested highway traffic. Their theory describes how oscillations spontaneously appear and transform into these waves, often exacerbated by merging and divergent maneuvers near ramps. Ahn et al. [93] further explored how these oscillations change in amplitude as they propagate along highways, providing a comprehensive theory on their dynamics. These insights are crucial for developing strategies to mitigate the impact of such oscillations on traffic flow.

The concept of phase transitions in traffic flow, which refers to shifts between different states of traffic (e.g., from free flow to congested flow), is a significant area of study. Nagatani [94,95,96] applied deterministic cellular automaton models to simulate these transitions, analyzing the impact of various factors on traffic flow. This work has been expanded by Fukui and Ishibashi [97] and Schadschneider and Schreckenberg [98], who investigated the transitions between moving and jammed phases. Understanding these transitions is critical for predicting and managing congestion in real-time traffic scenarios.

Recent studies have continued to explore these phenomena, applying advanced modeling techniques such as recurrent neural networks (Zhou et al. [99]) and mechanical vibrations (Wang et al. [100]) to analyze traffic oscillations. These efforts aim to develop new control strategies that can dampen oscillations and improve overall traffic flow efficiency. Additionally, ongoing research into phase transitions, such as those by Nagatani et al. [101] and others, continues to provide valuable insights into the dynamic nature of traffic flow, with implications for future traffic management systems.

4. Factors Influencing Autonomous Vehicle Traffic

The factors influencing autonomous vehicle (AV) traffic are multifaceted, encompassing vehicle characteristics, road infrastructures, and human behaviors. These elements interact dynamically, shaping the efficiency, safety, and adoption of AVs in various traffic environments.

The characteristics of AVs significantly influence traffic flow efficiency and the overall adoption of this technology. Key factors such as speed, acceleration, and flow in dedicated lanes are crucial for optimizing traffic management, particularly in setting buffer zones for lane changes [102]. For instance, the design speed and headway of AVs can reduce the buffer zone length, thereby enhancing traffic efficiency. Moreover, AVs have the potential to increase the network capacity by up to 19%, although they may adversely affect critical accumulation by up to 9% in oversaturated conditions [103]. The integration of AVs with public transportation systems and the promotion of ridesharing can further mitigate potential negative impacts on traffic flow and congestion [104].

Beyond technical specifications, psychological factors such as perceived usefulness, ease of use, and initial trust play a pivotal role in the adoption of AVs, indirectly influencing traffic patterns by affecting user behavior [105]. Additionally, demographic factors like gender, education, and income can moderate the impact of these psychological factors on AV adoption intentions, thereby affecting traffic dynamics [106]. The socioeconomic profile of individuals and their familiarity with AV technology are other internal factors that shape AV adoption tendencies, contributing to the broader traffic ecosystem. External factors such as safety, security, and legal issues also shape public attitudes towards AVs, influencing their widespread adoption and, consequently, their impact on traffic flow [107]. The development of intelligent transportation systems, including dedicated highway lanes for AVs, is essential for optimizing their traffic flow efficiency and maximizing the benefits of AV technology [102].

The integration of AVs into the transportation system necessitates significant adaptations in road infrastructures to ensure optimal performance and safety. Enhanced road maintenance and the development of separate corridors exclusively for AVs are critical for simplifying and securing the infrastructure. For example, the uniform distribution of AVs can prolong the maintenance life of pavements, although increased traffic volume may accelerate rutting distress [108]. The number of road lanes is another crucial parameter, affecting network vulnerability and travel delays, with AV implementation proving efficient in reducing delays during road failures [109].

While the elimination of the human factor allows for relaxed geometric design requirements, it also introduces challenges such as an accelerated rutting potential and the need for new infrastructure facilities like safe harbor areas [110]. The strategic placement of roadside sensors is also vital for AVs’ perception and tracking performance, with an optimized sensor placement improving accuracy and reducing costs [111]. The transition to AVs can lead to increased average speeds and reduced travel times, especially at higher market penetration rates [112]. Public acceptance and the development of appropriate strategies and policies are essential to leverage the benefits of AVs and address uncertainties related to infrastructure and demand modeling [110].

Human behaviors and interactions present significant challenges to the decision-making algorithms of AVs, necessitating sophisticated programming to ensure safety and efficiency. The acceptance of AVs is influenced by personal traits such as the desire for control, hedonic motivation, and perceived safety and risk [105]. These factors not only affect the adoption of AVs but also how human drivers and pedestrians interact with them. For instance, pedestrians often rely on visual cues from drivers, which may be absent in AVs, leading to potential confusion and safety concerns [113].

The presence of AVs also alters human driving behaviors. Studies have shown that human drivers exhibit different car-following behaviors when trailing AVs compared to human-driven vehicles, often reducing their time headways. Pedestrian behavior is influenced by various contextual factors, including the weather, road structure, and social norms, all of which must be considered in AV algorithm development [114]. Driver workload during autonomous driving is another factor, with different non-driving-related tasks and collision warnings affecting the workload and takeover readiness of drivers [115]. Additionally, human drivers’ subjective feelings and decision making in mixed traffic environments are influenced by their driving style; for example, aggressive drivers may feel more anxious and behave more aggressively around AVs [116].

Effective interaction modeling between AVs and human-driven vehicles is crucial, as current models often neglect communication and assume passive responses, which can lead to inaccuracies [117]. Public attitudes towards AVs, shaped by factors such as uncertainty, policy impacts, and changes in the road traffic environment, play a critical role in their adoption [118]. Interaction-aware controllers (IACs) in AVs, which predict human drivers’ responses, need validation against natural driving behavior to ensure reliability [119]. Furthermore, demographic, psychological, and mobility behavior characteristics significantly influence public acceptance and the intention to use AVs, highlighting the need for direct experience and education to foster positive attitudes [114].

5. Traffic Flow Models

Traffic flow models are tightly connected with the fundamental relation and diagram and different traffic phenomena and can be classified into three main groups: macroscopic, mesoscopic, and microscopic models. However, they intertwine and interpenetrate. Van Wageningen-Kessels et al. [120] presented an interesting genealogy of traffic flow models. Another survey was presented by Li and Chen [121], where they classified the models also into three groups: headway-related macroscopic modeling, headway modeling, and headway-related microscopic modeling. Li et al. [122] reviewed trajectory data-based traffic flow studies that were conducted over 15 years (2005–2020) and summarized traffic phenomena/models at the microscopic/mesoscopic/macroscopic levels.

Table 1. Traffic flow simulation techniques.

Method	Advantages	Disadvantages
Microscopic Simulation	High level of detail; Can model individual vehicle interactions; Useful for detailed traffic management studies.	Computationally expensive; Requires detailed input data; May not scale well for large networks.
Macroscopic Simulation	Less computationally intensive than microscopic simulations; Good for large-scale simulations; Captures overall traffic behavior.	Lacks detail on individual vehicles; Assumes homogeneous traffic; Less accurate for small-scale simulations.
Mesoscopic Simulation	Balances detail and computational efficiency; Can model large networks with more accuracy than macroscopic models.	Intermediate complexity; May require calibration; Less detailed than microscopic models.
Agent-Based Simulation	Can simulate individual driver behaviors; Flexibility in modeling various scenarios; High granularity.	Computationally demanding; Requires complex calibration; Behavior rules can be hard to define.
Cellular Automata	Simple to implement; Computationally efficient; Suitable for large networks.	Over-simplified; May not capture complex dynamics; Limited in modeling heterogeneity.

presents the most important information on individual techniques used for the simulation of traffic flow.

5.1. Macroscopic Models

Macroscopic models consider traffic flow as continuous, connected with continuous models for fluids. They omit individual vehicles using variables such as density and flow.

The first macroscopic traffic flow model was derived in hydrodynamic analogy by Lighthill and Whitham [29] and, independently, Richards [30]. Their model was later named the LWR model. But the hydrodynamic approach to traffic flow can be justified as a continuum only with a high density of vehicles. A partial differential equation for the conservation of vehicles is as follows:

$${\displaystyle \frac{\partial k}{\partial t}}+{\displaystyle \frac{\partial q}{\partial x}}=0$$

(17)

5.1.1. Kinematic Waves and Lane Changing

Kinematic wave models were among the earliest applications of the hydrodynamic approach in traffic flow theory, serving as a foundational concept that has been extended and refined through subsequent research. Munjal and Pipes [123] initiated this line of inquiry by studying the propagation of on-ramp density waves on uniform unidirectional multilane freeways, laying the groundwork for understanding wave dynamics in traffic systems. Newell [124,125,126] developed a simplified theory of kinematic waves, which has become a cornerstone in highway traffic modeling.

The concept of lane-changing further extended macroscopic modeling, integrating more complex traffic behaviors into the hydrodynamic framework. Holland and Woods [127] introduced a continuum model for a two-lane traffic flow using the theory of kinematic waves, assuming constant but unequal wave speeds in the two lanes. This work bridged the gap between single-lane and multi-lane traffic flow models, offering insights into the differential dynamics of lane changing.

Advancing the theoretical framework, Helbing et al. [128] applied a Boltzmann gas–kinetic traffic equation to model traffic across different density regimes, from low to high vehicle densities. Their approach accounted for forwardly directed interactions and vehicular space requirements, thereby enhancing the applicability of kinetic models in capturing realistic traffic behaviors. Daganzo [129] further expanded the macroscopic modeling by proposing a behavioral theory for homogeneous, multi-lane freeways, predicting distinct groups of lanes dominated by either aggressive or timid drivers. This behavioral segmentation introduced a new layer of complexity to traffic flow analysis.

The theoretical developments by Daganzo [130] also provided significant contributions to the understanding of traffic dynamics. He proved that solutions to well-posed kinematic wave traffic problems with a concave flow–density relation can be interpreted as least-cost paths in space–time, offering a rigorous mathematical foundation for traffic modeling. Laval and Daganzo [48] contributed to this framework by describing a mechanism for precisely tracking lane changers, postulating that lane-changing vehicles create voids in traffic streams, which in turn reduce the overall flow. Their work was complemented by Laval and Leclercq [84], who analyzed the impact of lane changing on the relaxation phenomenon, demonstrating how these interactions influence traffic stability.

Further contributions to the understanding of traffic interactions include the work by Logghe and Immers [131], who modeled non-cooperative vehicle interactions, where slow vehicles act as moving bottlenecks for faster vehicles, leading to anisotropic behavior in the traffic stream. This model highlighted the importance of vehicle heterogeneity in traffic flow dynamics. Laval and Leclercq [92] extended this line of research by describing the spontaneous emergence of oscillations and their transformation into stop-and-go waves, linking microscopic interactions with macroscopic traffic patterns.

Jin [132] provided a comprehensive analysis of the bottleneck effects caused by lane changes in highway merging, diverging, and weaving areas, both theoretically and empirically. His findings underscored the significant impact of lane changing on the overall traffic flow, particularly in complex traffic environments.

Recent advancements have leveraged machine learning and deep learning techniques to further refine traffic flow modeling. Mohanty et al. [133] applied a deep learning neural network architecture to forecast a congestion score, utilizing Newell’s simplified theory of kinematic waves. This approach represents a significant step towards integrating traditional traffic theories with modern data-driven methods. The work by Makridis et al. [134] complements this by proposing a model based on the Lagrangian discretization of the LWR model, ensuring consistency at the macroscopic scale with the propagation of congested waves according to first-order traffic flow theory.

Jin [135] also introduced a link queue model as a system of ordinary differential equations, which captures queue spillbacks and interactions among links. This model is a space-continuous approximation of the kinematic wave model and can be integrated into a multiscale modeling framework for network traffic flows. Meanwhile, Qin et al. [136] proposed a generalized framework of the Lighthill–Whitham–Richards (LWR) model, examining vehicular flow under varying cooperative adaptive cruise control (CACC) penetration rates. They theoretically demonstrated that the kinematic wave speed propagating through the mixed platoon corresponds to the slope of the mixed fundamental diagram.

Further extending the application of kinematic wave theory, Luan et al. [137] proposed a dynamic Bayesian graph convolution network to infer traffic congestion propagation, allowing for simulations of congestion processes in customizable scenarios. This model represents a novel integration of traffic flow theory with advanced machine learning techniques. Shang et al. [138] focused on the energy consumption aspects of traffic flow, proposing a model that reflects the characteristics of traffic kinematic waves induced by congestion, thus linking traffic dynamics with environmental impact considerations.

In summary, these studies collectively demonstrate the evolution of kinematic wave models from foundational theories to modern applications that integrate behavioral dynamics, lane-changing effects, and machine learning techniques. By refining and expanding upon these models, researchers have developed a robust theoretical and practical framework that continues to inform traffic flow analysis and urban planning.

5.1.2. Network Models

Network models are intricately connected with kinematic waves and lane-changing models, forming a comprehensive framework that addresses various aspects of traffic flow dynamics. A key transitional element in this framework is the Newell–Daganzo merge model, which provides a foundational procedure for determining the flow from two merging roads into a single road. This model originated from Newell’s work [139] on the merging process and was further developed by Daganzo through the cell transmission model [140], which introduced a diagram for highway merges and illustrated the application of this theory in practical scenarios. These foundational contributions have significantly influenced subsequent research in traffic flow modeling.

Cassidy and Ahn [141] expanded upon these early models by demonstrating that the combined capacity of two input branches is typically less than the system’s exiting capacity. Their findings highlight the inherent inefficiencies in merging scenarios, which informed later studies aiming to optimize merge strategies and improve overall traffic flow.

The merge problem can be mathematically formulated as a maximization problem as follows:

$$\max q_{\mathrm{o}}=\sum _i{q}_i\le q_{\mathrm{o}\mathrm{m}\mathrm{a}\mathrm{x}} \forall 0\le q_i\le q_{i\mathrm{m}\mathrm{a}\mathrm{x}}$$

(18)

where q_o is the output flow, q_omax is the output capacity, q_i is the input flow of i-th inflow, and q_imax is the capacity of i-th inflow.

Taking into account the merging node with two input roads, the solutions can be presented graphically (Figure 9). The plot presents two input flows, q₁ and q₂, with capacities, q_1max and q_2max, which limit the correspondent flow and are appropriately presented by vertical and horizontal lines. The output capacity (q_omax) is presented by a line marked ‘q_omax = q₁ + q₂’. There are four areas in the plot (Figure 9). The first area, marked by number 1 and green shading, corresponds to free flow in the outlet and both inlets. The second and third areas, marked by numbers 2 and 3, present congestion in the output road and in one of the input roads. Vertical and horizontal arrows show solutions to the output capacity. The fourth area, marked by number 4 and red shading, corresponds to congestion at the outlet and both inlets. The arrows go to the solution with the same point defined by split priority. A common split priority rule is the “zipper rule”, where vehicles merging alternate between the two input flows. The solutions for a merging node with three inputs are similar, but a graphical representation requires a 3D plot.

Similarly, diverge problems can be formulated and analyzed as follows:

$$\max q_{\mathrm{i}}=\sum _j{q}_j\le q_{\mathrm{i}\mathrm{m}\mathrm{a}\mathrm{x}} \forall 0\le q_j\le q_{j\mathrm{m}\mathrm{a}\mathrm{x}}$$

(19)

where q_i is the input flow, q_imax is the input capacity, q_j is the output flow of j-th outflow, and q_jmax is the capacity of j-th outflow.

Solutions of a diverged node with two outputs can also be presented graphically (Figure 10). Figure 10 presents solutions for two variants of the relationship between input and output capacities. The input capacity (q_imax) can be less than the sum of the output capacities (Figure 10a) and more than this sum (Figure 10b). The first area, marked by number 1 and green shading, corresponds to the free flow in the inlet and both outlets. The second and third areas, marked by numbers 2 and 3, present congestion at the inlet and at one of the outlets. The declined or vertical and horizontal arrows show solutions to the output capacity. The extension of the declined arrow passes through the origin; it is the so-called turning proportion, which depends on the traffic composition and the traffic situation. When there is no priority for a free outlet flow, traffic is divided according to the turning proportion. When such a priority is present, congestion at one outlet may not have an effect on free flow at another, and the arrows can be vertical or horizontal. A real solution can be between these two variants. The fourth area, marked by number 4, corresponds to congestion at the inlet and both outlets. The arrows can go to the point of the capacities of both outlets or one of two capacities, similar to the second and third areas.

As traffic networks become more intricate, involving multiple inlets and outlets, the complexity of modeling increases significantly. Early solutions to these complex intersections were proposed by researchers [142,143], laying the groundwork for more sophisticated models that integrate merges and diverges into a unified framework. Tampere et al. [144] analyzed a generic class of first-order node models for simulating traffic flows, while Flötteröd and Rohde [145] introduced an approach to the macroscopic first-order modeling of traffic at complex urban intersections. These contributions have advanced the theoretical understanding of traffic dynamics at intersections, particularly in urban environments.

Zhang et al. [146] investigated dynamic network models where congestion manifests as queueing behind bottlenecks, further contributing to the understanding of how congestion propagates through networks. Their work, along with that of Qu and Zhou [147], who utilized a parallel computing framework for large-scale transportation simulations, underscores the importance of computational methods in handling the complexity of modern traffic networks.

Wang et al. [148] proposed a traffic control strategy for multiple intersections, introducing the concept of a “super intersection” where vehicle movements are coordinated across closely connected intersections. This innovative approach aligns with the increasing need for integrated traffic management solutions in urban areas, where intersections must be managed collectively rather than in isolation.

Ma et al. [149] developed a solution framework for estimating multiclass dynamic demands for the origin and destination in large networks, which is applicable to a wide range of vehicular data. Their framework is particularly relevant for urban planners and traffic engineers tasked with managing demands in increasingly congested cities, where an accurate demand estimation is crucial for effective traffic management.

Further advancements in intersection modeling include Wang et al. [150], who proposed a multi-agent-based cellular automata model for simulating intersection traffic control. Their model incorporates car-following and lane-changing rules tailored to different traffic scenarios, providing a detailed and dynamic approach to traffic simulations.

Chen et al. [151] introduced a cooperative framework to address the scheduling of connected and automated vehicles (CAVs) at unsignalized intersections, where lane-changing behavior is permitted. This framework is particularly relevant in the context of emerging autonomous vehicle technologies, which require new models and approaches to ensure an efficient and safe traffic flow.

Finally, Zhang et al. [152] proposed a two-level solution framework that combines dedicated intersection deployment schemes with intelligent traffic assignment algorithms based on artificial bee colonies. This multi-level approach represents a significant step forward in optimizing traffic flow in mixed environments that include both traditional and connected automated vehicles.

In summary, these studies collectively contribute to a cohesive and evolving framework for understanding and managing traffic flow at intersections and across complex networks. By refining the relationships between merging, diverging, and network models, researchers have developed a comprehensive approach that integrates theoretical insights with practical applications, addressing the challenges posed by modern traffic systems.

5.2. Microscopic Models

5.2.1. Car-Following Models

Li and Chen [121] provided a comprehensive genealogical tree of vehicle headway modeling, particularly focusing on car-following models within microscopic traffic modeling. Their work delineates three primary branches—safe distance, stimulus response, and psychophysical–psychological models—highlighting their development and evolution from the late 1950s to the present. These branches have largely evolved independently, illustrating the diverse theoretical foundations within car-following models.

Earlier, van Wageningen-Kessels et al. [120] had also explored these modeling branches, identifying similar patterns in safe-distance and stimulus–response models, while also introducing a cellular automata branch. This addition reflects the increasing complexity and diversity of approaches in traffic modeling. Han et al. [153,154] further enriched this discourse by providing a historical review of car-following models, particularly in the context of vehicle-to-everything (V2X) environments. They mapped key developments in the car-following theory, including the introduction of artificial intelligence models and intelligent driving models, onto a timeline, thus offering a broader context for understanding the evolution of these models.

In car-following models, the dynamics between a leader and a follower vehicle are central, with the follower’s behavior modeled in terms of position, velocity, acceleration, or combinations thereof. The foundational work by Pipes [155] in 1953 introduced the first microscopic car-following model, establishing a rule based on maintaining a safe following distance. The law specifies the distance from the leader for the follower. This distance (d) is the sum of the length of the leading vehicle (l), a minimum distance at rest (d₀), and a distance proportional to the velocity of the follower (u):

$$d=l+d_0+ku$$

(20)

Building on Pipes’ model, researchers such as Chandler et al. [156], Herman et al. [157], Helly [158], Kometani and Sasaki [159], and others further refined the car-following theory, each contributing to its theoretical and practical evolution. Notably, Newell [160] and Gazis et al. [161] developed models that introduced new dynamics and feedback mechanisms, which have been foundational in the continued development of microscopic traffic models. Bexelius [162] and Wiedemann [163] also made significant contributions, particularly in the context of traffic simulations and the modeling of driver behaviors. These foundational works are discussed in greater detail in subsequent sections.

Recent advancements in car-following models have introduced new methodologies and technologies. For example, Zhu and Zhang [164] discretized a continuous car-following model into a difference equation and proposed a feedback control system, enhancing the model’s applicability in various traffic scenarios. Cao [165] incorporated headway memory and evolution trends into existing models, further refining the predictive accuracy of car-following behaviors. Jiao et al. [166] extended these models for intelligent transportation systems, integrating vehicle-to-vehicle communication and considering driver characteristics to improve the realism of simulations.

Emerging technologies have also influenced car-following models. Tang et al. [167] proposed a model combining Markov theory with a gated recurrent unit neural network, enabling trajectory predictions in micro-traffic simulations. This approach exemplifies the integration of deep learning techniques into traditional traffic modeling. Similarly, An et al. [168] analyzed a mixed traffic flow based on discrete following intervals, proposing a discrete car-following interval model tailored for autonomous vehicles.

Other researchers, such as Ma et al. [169,170], have focused on nonlinear dynamics within car-following models. Their work introduced the concept of backward-looking effects and headway changes with memory, which are crucial for understanding the behavior of autonomous vehicles in dynamic traffic conditions. Hossain and Tanimoto [171] extended this by proposing an information-sharing traffic flow model that considers time delays within intelligent transportation systems utilizing wireless communication.

The intersection of game theory and traffic modeling has also been explored, as demonstrated by Gong et al. [172], who developed a cellular automata model incorporating game theory to simulate mixed traffic flows of human-driven and autonomous vehicles on foggy highways. Li et al. [173] proposed a car-following model that captures the behaviors of connected and automated vehicles, leveraging graph theory to describe the communication topology among vehicles in both fixed and switching communication environments.

Advanced machine learning techniques have further enriched car-following models. Qin et al. [174] combined a convolutional neural network with a long short-term memory network to model and reproduce the hysteresis phenomenon observed in congested traffic flows, particularly in mixed traffic environments with adaptive cruise control vehicles. Son and Ding [175] developed a car-following model to simulate the behaviors of human-driven, autonomous, and connected automated vehicles within mixed traffic scenarios. Their model provides a comprehensive framework for simulating and analyzing car-following behaviors across different vehicle types.

In summary, while car-following models are a central component of microscopic traffic modeling, their evolution has been shaped by a variety of approaches and technologies. From the foundational safe distance models to the latest applications of artificial intelligence and deep learning, these models have continually adapted to meet the challenges posed by increasingly complex traffic systems. The relationships between these studies demonstrate a continuous refinement and integration of new methodologies, making car-following models an essential tool in both theoretical and practical traffic analysis.

5.2.2. Safe-Distance Models

Pipes’ model (Equation (19)), which is a foundational safe-distance model, introduces acceleration that is proportional to the relative velocity between vehicles. This model set the stage for subsequent developments in car-following theories by establishing a basic rule for maintaining safe distances between vehicles.

Building on this, Kometani and Sasaki [159] introduced an important refinement by incorporating a driver’s tendency to avoid collisions in all situations. They added a time delay to account for the follower’s reaction to the leader’s changes, making the distance term (d₀) velocity-dependent. This adjustment provided a more realistic depiction of driver behaviors, acknowledging the delays inherent in human reaction times.

Newell [160] further advanced the field by proposing a nonlinear relationship between acceleration and both the distance to the leader and the difference between the follower’s current and optimal velocities. This approach introduced a more complex dynamic into the modeling of car-following behaviors, allowing for a better understanding of how drivers adjust their speed based on the distance and speed differential relative to the vehicle ahead. Similarly, Gasis et al. [161] also explored nonlinear dependencies but focused on the leader’s velocity, the relative velocity, and the distance between vehicles, adding another layer of sophistication to car-following models by integrating multiple factors into the decision-making process of drivers.

Gipps [176] contributed a significant advancement by dividing vehicle movements into two regimes: one where the vehicle’s velocity is limited by its own capabilities (such as the maximum velocity and acceleration), and another where the velocity is limited by the safe distance to the leader. This dual-regime approach offered a more comprehensive framework for understanding vehicle dynamics under varying traffic conditions.

Newell [177] later proposed a simplified car-following model, which became a pivotal development in the field. In this model, vehicles are assumed to follow the same trajectory, merely translated in space and time. This simplification was particularly important as it allowed researchers to bypass the complexities of the transition process when a leader changes speed, which had been the focus of earlier models. By focusing instead on the sources of speed changes, Newell’s model facilitated the integration of car-following behaviors into multiscale models, thereby broadening the model’s applicability in more complex traffic simulations.

Laval and Leclercq [84] introduced further nuance by incorporating driver behaviors, such as timid and aggressive driving, into their models. This addition recognized the variability in driver behaviors, which can significantly impact traffic flow and safety and allowed for a more realistic simulation of traffic dynamics.

Collectively, these studies illustrate the evolution of car-following models from simple safe-distance rules to more complex and nuanced approaches that account for various factors influencing driver behaviors and vehicle dynamics. The relationships between these models demonstrate a clear progression in the sophistication of car-following theories, each building on and refining the concepts introduced by its predecessors. By integrating these models into broader traffic simulations, researchers have been able to develop more accurate and versatile tools for understanding and managing traffic flow.

5.2.3. Stimulus-Response Modeling

Stimulus-response models are a significant component of car-following modeling, focusing particularly on how changes in a leader vehicle’s velocity influence the behavior of the following vehicle. These models share similarities with safe-distance models but place a greater emphasis on the sources of changes in the leader’s velocity and the subsequent reaction of the follower.

The foundation of stimulus–response models was laid by Chandler et al. [156], who first developed a model where the acceleration of the following vehicle is proportional to the difference in velocity between the leader and the follower, with a time delay accounting for driver reactions. This model posits that the characteristics of the leader vehicle serve as the stimulus, directly influencing the acceleration behavior of the follower.

This initial model was subsequently refined by Herman et al. [157] and Helly [158] and later summarized by Gazis et al. [161], leading to the well-known GHR (Gazis–Herman–Rothery) car-following model. The GHR model, in its most general form, can be expressed as follows:

$$a\left(t\right)=c{v}^m\left(t\right){\displaystyle \frac{∆v\left(t-T\right)}{∆x^l\left(t-T\right)}}$$

(21)

where a and v are the acceleration and speed of the follower at time t; Δx and Δv are the relative spacing and speeds, respectively, between the leader and follower, assessed at an earlier time (t − T); T is the driver reaction time; and m, l, and c are the constants. This model encapsulates the core idea of stimulus–response dynamics, where the follower’s behavior is a direct response to changes in the leader’s movement.

However, as Brackstone and McDonald [178] observed in their comprehensive review of stimulus–response models from 1958 to 1999, these models have been used less frequently in recent years due to inconsistent findings regarding parameter values. Their review highlighted the challenges in applying stimulus–response models across different traffic scenarios, leading to a shift in research focus.

This shift gave rise to new directions in the car-following theory, such as the development of intelligent driver models [179,180,181,182] and the optimal velocity model [183]. These models were eventually integrated into Kerner’s three-phase traffic theory [77,184], which represents a more holistic approach to understanding traffic dynamics, incorporating elements from both traditional stimulus–response models and more advanced theories that account for the complexities of modern traffic systems.

In summary, while stimulus–response models were foundational in the development of car-following theories, the evolution of traffic modeling has seen these models being supplemented and, in some cases, replaced by more comprehensive approaches. The relationships between these models and their successors highlight the progression of traffic flow theory from simple reactive models to more sophisticated frameworks that better capture the nuances of driver behaviors and traffic dynamics.

5.2.4. Psychophysical–Psychological Models

Psychophysical–psychological models, also known as action point models, focus on how drivers perceive and react to changes in their environment, particularly the behavior of the vehicle ahead. These models are grounded in the concept introduced by Michaels [185], who suggested that drivers detect the approach of a leader vehicle primarily through changes in the apparent size of the vehicle and by perceiving relative velocity.

This foundational idea was further developed and refined by several researchers, including Wiedemann [163], Lee [186], Evans and Rothery [187], Bekey et al. [188], and Brackstone and McDonald [178]. Each of these studies contributed to the understanding of how drivers use visual cues to make decisions about speed and the following distance, emphasizing the importance of psychological factors in driving behaviors.

One of the key advantages of psychophysical–psychological models, as highlighted by Van Wageningen-Kessels et al. [120], is their ability to differentiate driving behaviors based on headways. At large headways, the driving behavior is generally uninfluenced by the presence of other vehicles, as the distance is sufficient for the driver to operate independently. Conversely, at small headways, the driving behavior becomes more reactive, but only when the changes in relative velocity and headway are significant enough to be perceived by the driver. This perception-driven approach adds a layer of realism to traffic modeling by accounting for the thresholds at which drivers begin to react to their surroundings.

Once the influence of a leading vehicle is detected, these models often transition to incorporate elements from safe-distance or stimulus–response models. This integration allows for a more comprehensive representation of driving behaviors, as it acknowledges that driver reactions are not only a function of the immediate physical environment but also of the psychological processes that determine when and how these reactions occur.

In summary, psychophysical–psychological models provide a nuanced understanding of driver behaviors by emphasizing the role of perception in determining when a driver will react to changes in the environment. The development of these models by various researchers illustrates a progression towards integrating psychological factors with traditional car-following models, resulting in a more complete and realistic depiction of traffic dynamics. This approach highlights the importance of considering both the physical and mental processes that govern driving behaviors, offering valuable insights for improving traffic flow models and safety interventions.

5.2.5. Lane-Changing Models

While car-following models describe the rules for vehicular longitudinal interactions on the road, lane-changing models focus on lateral interactions, which are crucial for understanding overall traffic dynamics. Lane-changing behavior is often categorized into mandatory and discretionary lane changing. Mandatory lane changes are necessary for reaching a planned destination, such as when a vehicle needs to exit a freeway. In contrast, discretionary lane changing is voluntary and more complex, as it involves evaluating the necessity and desirability of the maneuver in addition to the safety considerations typically associated with mandatory lane changes.

The modeling of lane-changing behavior generally focuses on two key aspects: the decision-making process of the driver and the impact of lane changing on surrounding vehicles. This dual focus is essential for capturing the full range of influences that lane changing can have on traffic flow and safety.

Laval and Daganzo [48] contributed to this area by developing a model that explains the reduction in traffic flow following the onset of congestion at freeway lane drops, as well as the relationship between the speed of moving bottlenecks and their capacities. Their work provided significant insights into how lane-changing behavior can exacerbate congestion under certain conditions. Laval and Leclercq [84] further expanded on this by modeling the relaxation phenomenon using a macroscopic lane-changing model, which helped to understand how traffic stabilizes after a disruption caused by lane changes.

Initial lane-changing decision models were predominantly rule-based, focusing on a stepwise process where drivers first select a target lane and then assess whether there is an acceptable gap in the traffic to make the lane change. Gipps [80] proposed a model that considered the structure of lane-changing decisions within urban infrastructures, accounting for variables such as traffic signals, obstructions, and different vehicle types. This early work laid the groundwork for understanding how lane-changing decisions are influenced by various environmental factors. Fritzsche [189] added to this by analyzing bottleneck situations, while Yousif and Hunt [190] developed a model for lane-changing behavior on multi-lane unidirectional roadways, building on the framework established by Gipps. Holland and Woods [127] introduced a continuum model for a two-lane traffic flow, which, although not microscopic, provided valuable insights into lane-changing behavior at a macroscopic level.

Despite these advancements, early models were often simplistic and did not fully capture the complexities of cooperative or forced lane-changing behavior. For example, Wang and Prevedouros [191] presented software programs capable of replicating lane-changing behavior, but these models were limited in scope and did not address the full range of factors influencing lane changes.

To address these limitations, later models incorporated more sophisticated theories, including utility theory, artificial intelligence, and game theory. Hunt and Lyons [192] developed a driver decision-making model using neural networks, which allowed for more nuanced simulations of lane-changing behavior. Maerivoet and De Moor [193] introduced cellular automata models that included multi-lane traffic, further advancing the field by enabling more detailed and realistic simulations.

Hidas [194] presented a multi-agent simulation system in which driver–vehicle objects are modeled as autonomous agents. This system included detailed lane-changing and merging algorithms that considered both forced and cooperative lane-changing, providing a more comprehensive understanding of how drivers interact with each other in complex traffic environments.

Utility theory has also been applied to lane-changing decisions, as demonstrated by Ahmed and Toledo et al., who explored how drivers make decisions based on perceived utilities or benefits. Sun and Elefteriadou [195] developed a classification scheme for driver types, which aimed to predict the likelihood of a driver attempting a discretionary lane change based on their background information. Their work also identified the factors and parameters that influence whether a driver executes a particular lane-changing maneuver, depending on whether it is mandatory or discretionary.

The application of game theory to lane-changing behavior has provided further insights into the strategic interactions between drivers. Kita [196] and Liu et al. [197] were among the first to apply game theory to model merging behavior, highlighting the competitive and cooperative strategies that drivers might use. Building on this, Wang et al. [198] developed a lane-changing control approach for connected and automated vehicles that incorporates both cooperative and non-cooperative game theory formulations. Gong et al. [172] compared a lane-changing strategy based on game theory with the traditional STCA (symmetric two-lane cellular automaton) strategy, demonstrating the potential benefits of game-theoretic approaches in improving traffic flow and safety.

In summary, the evolution of lane-changing models reflects a progression from simple, rule-based frameworks to more complex and integrated approaches that incorporate elements of utility theory, artificial intelligence, and game theory. These models have significantly advanced our understanding of how lane-changing decisions are made and how they impact traffic flow, particularly in increasingly automated and connected traffic environments. The relationships between these studies illustrate the continuous refinement of lane-changing models, with each new development building on and extending the capabilities of previous models.

5.3. Mesoscopic Models

5.3.1. Cellular Automata Models

Cellular Automata (CA) models have been extensively applied to traffic flow modeling, providing significant insights into various traffic dynamics and behaviors. These models collectively contribute to the theoretical and methodological framework of traffic flow analysis, each study building on the others to advance the field.

The BML model, introduced in 1992, serves as a foundational CA model for traffic systems, offering a basic framework for understanding traffic flow. However, its limitations in practical applications prompted further research. Yang’s modification of the BML model, which includes sections of roads, intersections, and vehicle density, represents an important advancement, facilitating the analysis of self-organization phenomena in traffic systems [199]. This modification integrates theoretical concepts of self-organization with practical modeling needs, enhancing the model’s applicability.

Building on this foundation, Liu et al. proposed an improved CA model that incorporates realistic human reactions, significantly enhancing the simulation of congested traffic flow, particularly in medium- to high-density regions [200]. This improvement bridges the gap between theoretical modeling and real-world traffic behavior, offering a more accurate representation of traffic dynamics. Similarly, Yun-Xiang et al. introduced a probabilistic CA model for air traffic flow, integrating the safety distance parameter to better align simulation results with real-world data [201]. This integration highlights the importance of incorporating safety considerations into traffic flow models, further refining their practical utility.

Alexandrovna and Sha’s method for modeling traffic flow on highways and intersections considers driver behavior and vehicle signals to predict possible accident scenarios [202]. Their work contributes to the theoretical understanding of driver–vehicle interactions, offering a methodological framework for accident predictions within CA models. Chechina et al. extended the application of CA models by developing a multi-lane model for urban road networks, which predicts the impact of infrastructure changes on traffic flow [203]. This study emphasizes the practical relevance of CA models in urban planning and infrastructure development.

Valente et al. focused on simulating urban traffic in Cluj Napoca, incorporating various vehicle types and traffic conditions to produce accurate simulations [204]. Their work underscores the adaptability of CA models to diverse urban environments, reinforcing the models’ versatility. Nishida et al. introduced a mixed slow-to-start model that uses fuzzy CA to study the impacts of vehicle density and mixing ratios on traffic jams, blending traditional CA modeling with fuzzy logic to enhance the understanding of traffic congestion dynamics [205]. Storani et al.’s comparison of a hybrid traffic flow model, which integrates both macroscopic and microscopic elements with traditional CA models, demonstrates the effectiveness of combining different modeling scales to capture the complexity of traffic scenarios [206].

Further emphasizing the broad applicability of CA models, Tian et al. highlighted their relevance in studying complex systems, particularly in traffic flow research [207]. Hua et al. expanded on this by addressing the impact of three-dimensional road facilities on driving behavior, proposing a new CA model that considers cell width variations to simulate real-world traffic phenomena [208]. This development further enriched the theoretical and methodological landscape of CA models, demonstrating their capacity to adapt to increasingly complex traffic conditions.

Collectively, these studies illustrate the versatility and effectiveness of CA models in understanding and optimizing traffic flow. By interrelating theoretical advancements with practical applications, they contribute to a robust academic framework that supports both theoretical research and practical implementation in traffic flow modeling.

5.3.2. Agent-Based Models

Agent-Based Models (ABMs) have become a crucial tool in traffic flow modeling, offering a sophisticated means to simulate and analyze the complex behaviors of vehicular traffic and pedestrian movements. These studies are interrelated, collectively contributing to a robust theoretical and methodological framework that advances our understanding of traffic dynamics and informs practical policy decisions.

Gorodnichev’s work underscores the importance of ABMs in simulating vehicle interactions, particularly through the use of distributed computing. This approach provides a foundational methodology for studying traffic dynamics in decentralized systems, enabling more accurate simulations of real-world scenarios [209]. Building on this, Sanz et al. presented a microsimulation model using Modelica language, which combines equation-based and discrete-event models to simulate vehicle dynamics, fuel consumption, and CO₂ emissions. Their work integrates multiple modeling techniques, demonstrating the versatility of ABMs in capturing a wide range of traffic-related factors [210].

Alqurashi and Altman further extended the application of ABMs by proposing a hybrid framework designed for real-time decision making during traffic congestion. Their approach improves traffic flow by suggesting alternative routes, highlighting the practical utility of ABMs in dynamic traffic management and congestion mitigation [211]. This real-time application was complemented by Kuehnel et al., who explored the integration of environmental impacts into land-use and transport models. By highlighting the feedback loop between noise emissions and land use, they demonstrated the capability of ABMs to address broader environmental concerns within traffic simulations [212].

Zhao et al. contributed to the scalability of ABMs by developing a city-scale traffic simulation for San Francisco, addressing challenges related to data availability and computational costs. Their work is essential for applying ABMs to large urban environments, where accurate and efficient simulations are critical for urban planning and policy making [213]. In a related vein, Kim et al. introduced an agent-based network transmission model (ANTM) for estimating network-wide flow dynamics and testing perimeter control policies. This model further refined the application of ABMs by focusing on network-level interactions and control strategies [214].

Mastio et al. tackled the computational challenges associated with ABM traffic simulations, proposing load-balancing algorithms to enhance performance in high-performance computing environments. Their work underscores the importance of computational efficiency in the practical application of ABMs, especially in large-scale simulations [215]. Similarly, Raya-Díaz et al. focused on automating traffic flow management in communication networks using ABMs, illustrating how these models can be applied to optimize network operations and manage traffic flow more effectively [216].

Finally, Bastarianto et al. provide a comprehensive overview of the current state of ABMs in urban transportation, identifying key challenges and future research directions. Their review integrates the findings of previous studies, offering a synthesized perspective on the role of ABMs in traffic modeling and highlighting areas for further development [217].

These studies collectively demonstrate the versatility and effectiveness of ABMs in addressing various aspects of traffic flow, from individual driver behaviors and environmental impacts to large-scale urban traffic management and computational efficiency. The integration of ABMs with other modeling techniques, such as cellular automata and macroscopic fundamental diagrams, enhances their capability to simulate realistic traffic scenarios and inform policy decisions, contributing to a comprehensive theoretical and methodological framework in the field of traffic flow modeling.

6. Simulation Platforms for AV Traffic

Simulation platforms are vital for the advancement of autonomous vehicle (AV) technologies, offering a safe and controlled environment for testing and development. This section presents an overview of key simulation platforms used in AV traffic research, including SUMO (Simulation of Urban Mobility), MATSim (Multi-Agent Transport Simulation), VISSIM (visual simulation system), and AIMSUN (Advanced Interactive Microscopic Simulator for Urban and Non-Urban). Each platform offers unique features and capabilities that contribute to the refinement and validation of AV systems.

6.1. SUMO (Simulation of Urban MObility)

The Simulation of Urban Mobility (SUMO) is a versatile and widely utilized traffic simulation tool, capable of handling a broad spectrum of urban mobility studies. Its flexibility allows it to simulate traffic at various scales, ranging from sub-microscopic to macroscopic levels, making it an essential tool for modeling complex real-world scenarios. This includes capabilities such as sensor-based data processing and the simulation of connected intersections, which are crucial for modern urban planning and traffic management [218,219].

One of SUMO’s strengths lies in its ability to model different modes of transportation, including bicycles and other micro-mobility options. However, it has been noted that while SUMO can simulate these modes, there is room for improvement in accurately differentiating between them [220]. This indicates a growing recognition of the need for more precise modeling as cities increasingly adopt diverse mobility solutions.

The integration of communication networks, such as 4G and 5G, into SUMO scenarios is becoming increasingly relevant. This integration allows for the modeling of cellular coverage and its impact on traffic behavior, thereby providing a more comprehensive simulation of modern urban environments where connectivity plays a significant role [221]. Such advancements are particularly important for studying the effects of emerging technologies on traffic patterns and urban mobility.

SUMO’s utility has been demonstrated in various case studies. For example, in Brazil, SUMO was used to analyze intersection improvements, revealing that a speed bump was more effective than a traffic light in reducing vehicle wait times and costs [222]. This case highlights how SUMO can be applied to assess the effectiveness of different traffic control measures in diverse contexts.

This tool is also instrumental in testing intelligent transportation system (ITS) strategies, which are crucial for managing urban congestion. By simulating different ITS strategies, researchers can evaluate their potential impacts on traffic flow and safety, contributing to more informed decision making in urban planning [223]. Additionally, SUMO supports the simulation of Demand-Responsive Transport (DRT) systems, facilitating the dynamic scheduling and routing of DRT vehicles. This capability is essential for optimizing the efficiency and responsiveness of urban transport services [224].

Recognizing the need for more accurate cyclist modeling, efforts have been made to improve the representation of cyclists in SUMO. These efforts are based on real-world cycling data, aiming to enhance the tool’s accuracy in simulating bicycle traffic, which is becoming increasingly important, as cities promote cycling as a sustainable mode of transport [225].

In the realm of traffic control, SUMO has been used to evaluate different systems at intersections. Findings indicate that adaptive traffic controllers can significantly reduce the potential for collisions, demonstrating the tool’s value in enhancing road safety through improved traffic management strategies [226].

The work of Guastella and Bontempi provides a comprehensive guide for generating and simulating traffic scenarios using SUMO. Their paper details the process of creating synthetic traffic models, importing existing traffic data for accurate simulations and analyzing SUMO outputs, offering valuable insights for researchers and practitioners looking to utilize SUMO effectively in their studies [227].

In a focused study, Soni and Weronek used SUMO to model and analyze traffic with the goal of optimizing emergency vehicle arrival times. Their research, which centered on Mörfelder Landstraße in Frankfurt, Germany, included steps such as vehicular demand calibrations, road traffic simulations, and comparisons of various scenarios to find the most effective solutions [228].

Trautwein et al. defined the requirements for a traffic simulation based on real-world scenarios and evaluated SUMO’s capabilities in meeting these requirements. Their study proposed a technical concept to bridge the gap between current capabilities and future needs, underscoring the ongoing development and adaptation of SUMO to meet emerging challenges in urban mobility [218].

Araújo et al. explored the use of SUMO-generated mobility data in the context of Multi-access Edge Computing (MEC) systems. Their research developed and evaluated MEC simulation scenarios, providing insights into how mobility management strategies can be tested and optimized using SUMO [229].

Chakraborty et al. extended the application of SUMO into the realm of Urban Air Mobility (UAM), presenting an approach that includes modeling passenger demands, vehicle allocations, route planning, and vertidrome scheduling. This work represents a forward-looking application of SUMO, as it adapts to new transportation paradigms such as UAM [230].

In summary, SUMO is a powerful and adaptable tool that has been effectively applied across a wide range of urban mobility studies. The diverse case studies and research applications demonstrate SUMO’s capability to evolve alongside emerging transportation technologies and needs. The relationships between these studies illustrate this tool’s versatility and the continuous efforts to enhance its accuracy and applicability in simulating complex urban environments.

6.2. MATSim (Multi-Agent Transport Simulation)

MATSim (Multi-Agent Transport Simulation Toolkit) is a robust and adaptable open-source platform designed for large-scale agent-based transportation planning and simulation. Its versatility allows for it to be applied across various domains, including road transport, public transport, freight transport, and regional evacuation scenarios [231]. The platform’s ability to simulate diverse transportation systems is further enhanced by the BEAM (Behavior, Energy, Autonomy, and Mobility) framework, which extends MATSim’s capabilities. BEAM integrates ‘mode choice’ behavior through a multinomial logit model, offering a range of eight different transportation modes, such as biking, driving, walking, and ride hailing [232]. This extension underscores MATSim’s adaptability in modeling complex urban transportation systems, where mode choice is a critical factor in understanding travel behavior and system efficiency.

The complexity of calibrating such simulations, particularly when accounting for diverse mode choices, has been addressed through the implementation of a parallel Bayesian optimization method. This method significantly improves both the accuracy and efficiency of simulations by optimizing parameters in a computationally effective manner [232]. The successful application of this optimization approach highlights MATSim’s potential in handling large-scale, data-intensive simulations that require precise calibrations.

MATSim’s modular structure is another key strength, allowing it to leverage high-performance computing resources for extensive simulations. For instance, the use of the GRID’5000 infrastructure demonstrates MATSim’s capability to manage simulations that demand substantial computational power, enabling detailed and expansive transportation studies [233]. This capability is particularly relevant for simulations that encompass large urban areas or complex transportation networks.

Beyond traditional transport applications, MATSim has also been adapted to explore the impact of road characteristics on cyclists’ behaviors. Studies have shown that factors like road gradient and surface type can significantly affect travel time and distance, especially for longer trips [234]. This adaptation underscores MATSim’s flexibility in addressing specific transportation issues, such as those related to non-motorized travel modes.

MATSim’s framework also supports the integration of emerging transport technologies, such as shared automated vehicles. The platform’s iterative design and simulation workflows facilitate the evaluation of new transport technologies and their impacts on urban mobility. For example, Maheshwari et al. [235] explore the intersection of urban design and transport simulation using Sketch MATSim, emphasizing how iterative workflows can optimize the network design and enhance the performance of shared automated vehicles.

Moreover, MATSim’s adaptability extends to the incorporation of optimal control solutions for agents with specific shape and density constraints. The introduction of the MASCOT (Multi-Agent Shape Control with Optimal Transport) method demonstrates how MATSim can be used to minimize collisions and optimize source–destination assignments in complex transportation scenarios [236]. This application of optimal control techniques within the MATSim framework illustrates its potential for managing sophisticated transport systems that require precise spatial and temporal coordination.

The platform’s scalability and flexibility are further exemplified by its application in real-world contexts. Ziemke et al. [237] presented MATSim OpenBerlin, a simulation framework that integrates real-world data for agent-based transport simulations in Berlin. This framework demonstrates MATSim’s ability to simulate a wide range of transport scenarios and evaluate the potential impacts of different policy interventions, providing valuable insights for urban planners and policymakers.

Efforts to enhance MATSim’s computational efficiency have also been a focus of recent research. For instance, Moukir et al. [233] introduced a new approach to designing parallel algorithms within MATSim, leveraging high-performance computing architectures provided by GRID’5000 to meet the demands of microscopic and large-scale traffic simulations. This work reflects ongoing efforts to improve the toolkit’s performance and scalability, ensuring that it remains a relevant and powerful tool for transportation researchers.

Chhatre et al. [232] further contributed to this field by presenting a parallel Bayesian optimization method specifically for calibrating MATSim scenarios within the BEAM framework. Their work demonstrates significant improvements in both convergence speed and simulation accuracy, underscoring the importance of effective calibration in achieving reliable simulation outcomes.

In summary, MATSim is a powerful and adaptable tool that supports a wide range of transportation planning and simulation needs. Its modular structure, ability to integrate new technologies, and capacity for high-performance computing make it an indispensable resource for researchers and planners addressing complex, multi-modal transport scenarios. The relationships between the various studies using MATSim illustrate the toolkit’s evolution and its expanding role in the development of sustainable and efficient transportation systems.

6.3. VISSIM (Visual Simulation System)

VISSIM (Visual Simulation System) is a widely recognized tool in the field of traffic modeling and urban planning, offering detailed microscopic, time-interval, and behavior-based simulations. Its utility spans across various domains, from analyzing urban traffic and public transportation operations to evaluating traffic engineering designs and urban planning solutions. VISSIM’s ability to model complex systems, such as lane settings, traffic signals, and bus stops, makes it an effective tool for both researchers and urban planners [238].

One of the key applications of VISSIM has been in modeling and simulating traffic-light-controlled intersections. Studies have demonstrated that using VISSIM can lead to significant improvements in intersection throughput and a reduction in vehicle queue lengths, which are critical factors in urban traffic management [239]. These findings underscore VISSIM’s role in optimizing intersection designs and traffic flows, contributing to more efficient urban transportation networks.

VISSIM’s versatility extends beyond traditional traffic modeling. For example, in the field of education, visual simulation systems, including VISSIM, are used to simulate memory interleaving processes, helping students understand complex systems through hands-on, independent work. This application highlights this tool’s broader educational value, illustrating how simulation can be leveraged to enhance learning in various disciplines.

In passenger transportation, VISSIM has been utilized to optimize routes and improve the quality of public transport by visualizing passenger flows and employing neural networks for better management [240]. This application demonstrates VISSIM’s capacity to integrate advanced technologies, such as artificial intelligence, into transportation planning, thereby improving the efficiency and reliability of public transport systems.

The development of visual simulation systems like VISSIM involves sophisticated computer graphics and visual communication design principles, which enhance both the aesthetic and functional aspects of simulations. These enhancements are crucial for creating realistic and engaging simulation environments that can effectively support decision making in urban planning and traffic management.

Research has also focused on the calibration and validation of VISSIM simulation models to ensure their accuracy and reliability. For instance, Hafram et al. [241] conducted a study in Makassar, South Sulawesi, Indonesia, comparing field data with simulation data to validate the performance of VISSIM models under actual traffic conditions. This work emphasizes the importance of validating simulation results against real-world data to ensure that the models accurately reflect traffic dynamics.

In a related study, Kamala et al. [242] analyzed the impact of heavy vehicles on traffic flow using VISSIM. This study examined the traffic flow speed and capacity of National Highway 83 in India, utilizing macroscopic fundamental diagrams (MFDs) and a statistical analysis to validate the simulation results. This research highlights the ability of VISSIM to model the specific challenges posed by heavy vehicles in traffic flow, contributing to better traffic management strategies on major roadways.

The use of VISSIM to simulate different types of automated vehicles (AVs) has also been explored. Beza et al. [243] reviewed how PTV VISSIM has been calibrated for AV simulations, comparing calibrated values found in the literature with the default values in recent versions of the software. This research is crucial for understanding the differences in modeling AVs and ensuring that simulations accurately reflect the behavior of these emerging technologies.

Innovative applications of VISSIM include the integration of the Unity game engine to create a co-simulation platform, as presented by Shi and Ye [244]. This platform aims to evaluate driving behavior in an immersive and interactive environment, offering new ways to study the effectiveness of collective intelligence countermeasures in improving traffic systems. The integration of VISSIM with game engines represents a significant advancement in simulation technology, providing more dynamic and realistic environments for traffic studies.

Chen et al. [245] used VISSIM to evaluate different expressway exit designs, comparing conventional designs with alternative approaches such as passenger vehicle and truck separations (PVTSs) and lane separations around interchanges. This study demonstrated how VISSIM can be applied to optimize road designs, reduce congestion, and improve operational performance on expressways.

Additionally, VISSIM has been employed in disaster management scenarios, such as the work by Purnawan and Alfathira [246], who developed a metamodel to predict traffic delays and queue lengths in landslide zones. Their study focused on optimizing traffic control during landslides to enhance travel efficiency and safety, showcasing VISSIM’s versatility in handling emergency situations.

In summary, VISSIM is a powerful and adaptable tool that supports a wide range of applications in traffic modeling and urban planning. This tool’s ability to simulate detailed traffic scenarios, coupled with its capacity for integration with other technologies, makes it an invaluable resource for researchers and practitioners aiming to improve urban mobility and transportation systems. The relationships between these studies illustrate VISSIM’s broad applicability and the continuous efforts to refine and enhance its capabilities in various domains.

6.4. AIMSUN (Advanced Interactive Microscopic Simulator for Urban and Non-Urban Networks)

AIMSUN (Advanced Interactive Microscopic Simulator for Urban and Non-Urban Networks) is a versatile and widely adopted tool in traffic modeling and simulation, offering a comprehensive platform for a variety of transportation research and urban planning applications. Its effectiveness is demonstrated across numerous studies, which collectively underscore its broad applicability and the cohesive role it plays in enhancing traffic simulation outcomes.

In Stockholm, Sweden, AIMSUN’s user-friendly interface and effective parameter settings were highlighted in a comparison with SUMO, illustrating its superior ease of use and adaptability in simulating complex urban traffic conditions [247]. This user-centric design was further validated in studies assessing the impact of side friction factors such as on-road parking and pedestrian movements, where AIMSUN effectively modeled the negative effects on speed and capacity, providing critical insights for traffic performance optimization [248].

In Slovakia, AIMSUN was employed to model traffic rerouting strategies aimed at alleviating congestion in Žilina, showcasing its practical utility in urban traffic management by facilitating the development of efficient rerouting solutions [249]. Similarly, in Zagreb, AIMSUN was utilized for multimodal urban traffic simulations, enabling real-world decision making through the testing and comparison of various scenarios, thus reinforcing its value in comprehensive urban planning [250].

The versatility of AIMSUN was further highlighted by its integration with a fuel consumption model in Lausanne, Switzerland, where it optimized signal controls to improve both travel time and fuel efficiency. This application not only exemplifies AIMSUN’s contribution to sustainable transportation solutions but also demonstrates its capacity to link traffic management with environmental impact assessments [251]. In a comparative study with CORSIM, AIMSUN was found to perform comparably in uncongested conditions, while offering distinct advantages under congestion, particularly through its modular design that allows for detailed behavioral analysis, including vehicle interactions and platooning behaviors [252,253].

Additionally, AIMSUN has been utilized to study phase transitions in urban traffic, revealing hysteresis behavior in flow-density diagrams—a crucial insight for understanding and managing traffic flow dynamics in urban settings [254]. Its ability to integrate satellite-based geographical data has also been explored to automate the creation of detailed route networks, enhancing the precision and efficiency of traffic simulations [255].

In modern urban planning contexts, such as in San Jose, AIMSUN was used to evaluate the impacts of street design changes and tactical urbanism strategies, demonstrating its applicability in planning and executing contemporary urban development initiatives [256]. Furthermore, the combined use of AIMSUN and SYNCHRO has proven effective in improving traffic conditions and supporting sustainable urban transportation by optimizing traffic signal phasing and timing [257].

These interconnected studies illustrate AIMSUN’s extensive applicability in traffic simulations, from optimizing traffic flow and fuel consumption to evaluating urban design changes and managing congestion. This tool’s capacity to integrate various aspects of traffic and urban planning makes it an indispensable resource for transportation research and practical urban planning, supporting a cohesive approach to addressing complex transportation challenges.

7. Applications of AV Traffic Modeling

Autonomous vehicle (AV) traffic modeling plays a crucial role in various aspects of transportation research and development. This section explores the diverse applications of AV traffic modeling, including traffic flow optimizations, infrastructure design and planning, safety analyses, and environmental impact assessments. The following subsections highlight how these applications are interrelated, collectively contributing to the theoretical foundations of AV traffic modeling and offering a comprehensive understanding of how AVs can enhance the efficiency, safety, and sustainability of modern transportation systems.

7.1. Traffic Flow Optimization

The optimization of traffic flow, particularly in the context of autonomous vehicles (AVs), has significantly advanced through various interconnected scientific studies. Goatin et al. presented a multi-scale approach that models the interaction between controlled AVs and surrounding traffic using scalar conservation laws coupled with ordinary differential equations, demonstrating how these interactions can reduce congestion and improve traffic flow [258]. This foundational work was complemented by Lad and Mitra’s extensive review of machine learning techniques for traffic flow predictions in AVs, which emphasizes the importance of large-scale datasets and complex models in accurately capturing traffic dynamics [259]. The integration of these advanced modeling techniques is further illustrated by Wang et al., who explore optimal control strategies for AVs, demonstrating, through simulations, that such strategies can significantly enhance traffic efficiency, reduce travel times, and increase road capacities [260].

Bussa et al. expanded this framework by discussing the role of network softwarization in automating network security, indirectly supporting AV traffic modeling by ensuring secure communication networks—a critical component for reliable AV operations [261]. This interrelationship between network security and traffic modeling was further highlighted by Mushtaq et al., who proposed a novel two-phase approach using deep reinforcement learning (DRL) combined with Smart Rerouting (SR) techniques to optimize traffic flow during congestion periods, demonstrating significant performance improvements [262]. The effectiveness of these optimization strategies was further validated by Jalal et al., who explored discrete-event simulations for traffic flow, simplifying modeling efforts through the validation of exponential distributions for inter-arrival times [263].

The importance of accurate simulation tools was underscored by Vrbanić et al., who analyzed traffic simulators like VISSIM and AIMSUN, emphasizing their crucial role in testing the impacts of AVs and Connected Autonomous Vehicles (CAVs) on various traffic scenarios [264]. Lastly, Luo and Liu contributed to this cohesive framework with their optimization algorithm for traffic flow predictions, employing wavelet neural networks and the beetle antennae search algorithm to enhance the prediction accuracy, further solidifying the theoretical underpinnings of traffic flow optimization in AV contexts [265].

Collectively, these studies form a cohesive body of work that advances traffic flow optimization in AV systems. By integrating various modeling, control, and AI techniques, they establish a robust theoretical foundation for future research and practical applications in traffic management.

7.2. Infrastructure Design and Planning

The deployment of autonomous vehicles (AVs) requires significant advancements in infrastructure design and planning, as demonstrated by various interconnected research studies that collectively contribute to the theoretical framework of this evolving field. Roy et al. proposed a mathematical framework for modeling and deploying multi-lane AV zones in mixed-user traffic networks, comparing designs where lanes are either fully dedicated to AVs or shared with human-driven vehicles (HVs). Their findings highlight improvements in the total system travel time (TSTT) when AV lanes are strategically integrated, providing a foundational basis for optimizing lane utilization in mixed-traffic scenarios [266].

Building on this, Wang et al. emphasized the importance of AV-dedicated lanes, particularly in scenarios with varying market penetration rates and infrastructure construction behaviors. Their research suggests that AV lanes are most beneficial to the network when AV penetration is below 55%, reinforcing the necessity of adaptive infrastructure strategies to accommodate different levels of AV adoption [267]. This aligns with broader infrastructure planning needs identified by other studies, which underscores the role of dedicated AV zones in facilitating vehicle platoons and enhancing the overall network performance [268].

Gauglitz et al. extended the discussion to the integration of electric vehicle (EV) infrastructure, addressing the impact of EV charging stations on power grids. Their use of socio-economic data to predict concentrations of electric mobility and optimize grid planning highlights the interdependence between AV and EV infrastructure, further emphasizing the need for holistic planning approaches [269]. Sanusi et al. added to this framework by advocating for a strategic multiyear infrastructure plan to accommodate Connected Autonomous Vehicles (CAVs), which prioritizes infrastructure investments to maximize long-term benefits and ensure scalability [270].

The adaptability of traffic and transport models is another critical aspect highlighted in this section. Tamminga’s work calls for open-source approaches in infrastructure modeling to prevent knowledge loss and ensure that models can evolve with new applications such as in-car systems and intelligent transportation systems (ITSs) [271]. This adaptability is crucial for sustaining innovation and maintaining relevance in a rapidly changing technological landscape.

Li et al. contributed to the theoretical foundation by introducing multi-resolution simulation frameworks for cooperative vehicle-infrastructure systems, focusing on the intricacies of data transmission and interaction. Their work emphasizes the importance of detailed simulation models in understanding and optimizing the dynamic interactions between AVs and infrastructures [272]. Junior et al. further explored these dynamics through an analytical model based on Stochastic Petri Net theory, which evaluates VANET (Vehicular Ad Hoc Network) infrastructures, considering mobility and network parameters [273]. This approach provides a methodological tool for assessing the complex interactions within AV networks.

These studies collectively underscore the importance of comprehensive infrastructure planning and modeling to support the integration and optimization of AV technologies in modern transportation networks.

7.3. Safety Analysis

The field of safety analysis in autonomous vehicle (AV) traffic modeling is extensively covered in the provided research papers, each contributing unique insights and methodologies.

Abdel-Aty et al. highlighted the pivotal role of Computer Vision (CV) techniques in microscopic traffic safety analysis, particularly through the use of Surrogate Safety Measures (SSMs). These techniques bridge the gap between video processing and traffic safety modeling, providing a methodological foundation for analyzing near-miss events and other safety-critical situations [274]. This work was complemented by Wang et al., who emphasized the importance of robust driver models in the certification and simulation-based testing of AVs. By ensuring that AVs meet safety standards comparable to those of competent human drivers, these models form an essential component of the broader safety analysis framework [275].

Building on these foundational elements, Guo et al. applied the System Theoretic Process Analysis (STPA) method to adaptive cruise control (ACC) systems. This approach identifies unsafe control behaviors and establishes safety requirements across various scenarios, further contributing to the systematic analysis of AV safety [276]. Szűcs and Hézer expanded the scope by exploring various aspects of AV technology, including sensor systems, control algorithms, and communication technologies, and their roles in enhancing road safety. Their comprehensive analysis demonstrates how AVs can mitigate common traffic risks, reduce accident rates, and improve overall traffic efficiency, thus reinforcing the need for integrated safety systems [277].

Li et al. introduced a data-driven framework for analyzing the safety of autonomous driving systems, leveraging model learning techniques to simulate and evaluate AV behavior in diverse traffic scenarios. This approach aligns with the need for robust simulation tools that can predict and mitigate potential safety issues before AVs are deployed in real-world environments [278]. Buerkle et al. contributed a probabilistic model that studies the impact of AV perception system imperfections and safety mechanisms, particularly in the presence of road hazards. This model underscores the importance of accounting for uncertainty and variability in safety analysis, ensuring that AV systems can operate safely even in challenging conditions [279].

Razi et al. focused on the application of deep learning (DL) methods to enhance traffic video analysis, offering a comprehensive processing pipeline that extracts operational safety metrics. These metrics are crucial for improving traffic safety, as they provide real-time insights into the performance and safety of AV systems [280].

These papers collectively highlight the importance of integrating advanced modeling techniques, robust driver models, and cutting-edge CV and DL methods to enhance the safety and reliability of AVs in traffic environments. Each study provides a piece of the puzzle, from theoretical frameworks and practical verification methods to real-world applications and future challenges, forming a comprehensive body of knowledge essential for advancing AV traffic safety analysis.

7.4. Environmental Impact Assessment

The field of Environmental Impact Assessments (EIAs) in the context of autonomous vehicle (AV) traffic modeling is rich with diverse research contributions.

Vasconcelos and Aquino explored the use of Vehicle Sensor Networks (VSNs) embedded in public transportation for air quality tracking, significantly improving data accuracy and coverage. Their work provides a foundational approach to monitoring environmental conditions in real-time, which is critical for assessing the direct impact of AV operations on air quality [281]. This study was complemented by Hardaway et al., who highlighted the often-overlooked energy demands associated with AV data management. Their analysis suggests that the energy use required for processing AV data could result in emissions comparable to millions of additional vehicles by 2030, thereby emphasizing the importance of considering data management in environmental impact assessments [282].

Wang et al. contributed a quantitative framework for evaluating AV intelligence in complex environments using a topology structure and analytic hierarchy process. This framework is essential for understanding how AV decision-making processes impact environmental outcomes, particularly in terms of energy consumption and emissions [283]. Building on this, Morello et al. discussed enhancements in traffic simulation models aimed at assessing vehicle energy consumption and CO₂ emissions. Their focus on the implementation of intelligent transportation systems (ITSs) and Information and Communication Technology (ICT) systems, such as Advanced Driver Assistance Systems (ADASs) and Eco-Driving applications, illustrates the potential for technology to mitigate environmental impacts [284].

Kan et al. further developed this discourse by creating an evaluation framework that incorporates energy, traffic, and air quality impacts using advanced fuzzy evaluation methods. This integrative approach allows for a more nuanced assessment of AV environmental effects, considering multiple factors simultaneously to provide a holistic view of AV impacts [285]. Lastly, Cirianni and Leonardi proposed a neural network approach for traffic noise analysis, demonstrating superior performance over classical statistical models in urban settings. Their work highlights the importance of innovative methodologies in accurately assessing noise pollution, a critical component of environmental impact that is often overlooked [286].

These studies collectively advance the understanding of AV traffic modeling’s environmental impacts, offering innovative methodologies and comprehensive assessments across various dimensions of AV and transportation systems.

8. Challenges and Limitations

The integration of autonomous vehicles (AVs) with human-driven vehicles (HDVs) presents several challenges and limitations, as highlighted in recent research. While these studies provide valuable insights, they often lack a thorough examination of the practical limitations and challenges associated with implementing these methods in real-world scenarios. Chen et al. [287] focused on modeling mixed traffic flows in off-ramp diverging areas, highlighting the deterioration in safety and efficiency at higher proportions of cooperative adaptive cruise control (CACC) vehicles. They suggest that guiding lane changes can improve traffic flow efficiency. However, they did not deeply explore how these lane-change strategies might be affected by factors such as varying traffic densities, driver compliance rates, or the accuracy of vehicle communication systems. Khalil et al. [288] proposed an algorithm using transmissibility operators to detect and mitigate faults in mixed vehicle platoons, emphasizing the challenge of predicting human-driver behaviors and the need for robust control methods. Yet, the practical challenges of accurately modeling human-driver unpredictability and the potential computational overhead of implementing such a robust control system in real time are not fully addressed. Hossain et al. [289] examined cooperative driving between AVs and intelligent human vehicles (IHVs), addressing the stochastic nature of human input and system delays. Their stochastic model predictive control framework aims to optimize vehicle coordination despite these uncertainties. However, these authors could have delved further into the limitations posed by real-world communication delays, sensor inaccuracies, and the computational complexity of their predictive models in dynamically changing traffic conditions. Tang et al. [290] investigated the altruistic behavior of AVs towards HDVs during car-following events, finding that such behavior can significantly reduce disturbances for HDV followers, though it may reduce efficiency for AV passengers. Nevertheless, the potential trade-offs between passenger comfort and overall traffic efficiency, as well as the long-term impacts of such altruistic behavior on traffic patterns, remain underexplored. Collectively, these studies underscore the importance of adaptive control strategies, robust fault detections, and cooperative behaviors in ensuring the seamless integration of AVs and HDVs. However, the limitations and challenges of implementing these methods in real-world scenarios deserve a more detailed exploration to understand the potential barriers to their widespread adoption.

The challenge of uncertainty in autonomous vehicle (AV) behavior has been explored in various recent studies. While these approaches are promising, the practical implications of these uncertainty management strategies require a deeper investigation. Tang et al. [291] proposed an uncertainty-aware decision-making framework utilizing a fully parameterized quantile network (FPQN) and conditional value at risk (CVaR) to improve AV decision making at uncontrolled intersections, highlighting the role of surrounding vehicles and pedestrians in decision making. However, the complexity of real-world interactions at such intersections and the potential computational demands of these methods warrant further analysis. Zhou et al. [292] introduce an uncertainty-bound reinforcement learning (UBRL) framework to estimate and constrain the performance uncertainty of deep reinforcement learning (DRL) models, ensuring safer AV decisions by comparing them against baseline policies. Nonetheless, the limitations of reinforcement learning in dynamically changing environments and the challenge of generalizing learned policies across diverse scenarios need further exploration. Sharma et al. [293] focused on short-term trajectory predictions using convolutional neural networks (CNNs) and long short-term memory (LSTM) networks, emphasizing the importance of accurate trajectory predictions in complex scenarios such as pedestrian crossings. Yet, the authors could have discussed the challenges of scaling these models to handle the variability and unpredictability inherent in pedestrian behavior in diverse urban environments. Yang et al. [294] provided an overview of the uncertainty challenges in autonomous driving, categorizing them into external environmental factors and internal system processing and suggest mitigation techniques to enhance AV safety. However, the effectiveness of these mitigation techniques in diverse and unpredictable real-world conditions remains to be thoroughly examined. Collectively, these studies underscore the importance of robust uncertainty management strategies in ensuring reliable and safe AV operations. To fully understand the applicability and effectiveness of these strategies, further research should delve into the specific limitations and challenges posed by real-world implementations.

The integration of autonomous vehicles (AVs) brings significant benefits but also introduces critical data privacy and security concerns. While innovative solutions are being proposed, a more detailed analysis of their practical feasibility and limitations is needed. Bendiab et al. [295] discussed the vulnerabilities of AVs to malicious attacks and proposed the use of Blockchain and AI to enhance security and privacy, highlighting the mutual benefits of these technologies. However, the scalability of Blockchain solutions and the computational demands of AI-driven security measures in real-time AV operations need further consideration. Sun et al. [296] presented a privacy-preserving data-sharing mechanism called PDSM-FC, which ensures secure communication across AV platoons by converting ciphertexts, thereby protecting against various attacks. Nonetheless, the potential challenges in maintaining low latency and high reliability in data communication within large AV networks are not fully explored. An innovative approach by Li [297] addresses data security through secret image-sharing solutions, ensuring that personal and national security information is protected. Yet, the practicality of implementing such image-sharing techniques on a large scale, particularly in the face of evolving cyber threats, warrants a deeper investigation. In summary, while these studies provide promising approaches to data privacy and security in AV systems, a more comprehensive analysis of the practical challenges and limitations associated with these methods is essential to understand their potential for real-world applications.

9. Future Directions and Emerging Trends

The future directions and emerging trends in cooperative autonomous vehicle (AV) systems emphasize advanced communication technologies and collaborative strategies. The feasibility of using reconfigurable intelligent surfaces (RISs) to enhance cooperative driving was explored by Segata et al. [298], who highlighted the potential of RISs to improve signal reflections in challenging vehicular environments. Similarly, the integration of mmWave communications with RISs to support dependable coordination in AV platoons was discussed by Segata and colleagues in another study, demonstrating the benefits of RISs for wireless coverage extensions [299]. In the realm of unmanned aerial vehicles (UAVs), a comprehensive review by authors in IEEE Transactions on intelligent transportation systems underscores the need for high-speed communication links, flexible control strategies, and efficient collaborative decision-making algorithms to improve the autonomy and reliability of UAV swarms [300]. These studies collectively point to the importance of robust communication frameworks and intelligent surface technologies in the advancement of cooperative AV systems.

The future directions and emerging trends in urban air mobility (UAM) integration emphasize the development of robust infrastructures, advanced communication technologies, and regulatory frameworks. Sengupta [301] discussed the vision and challenges of UAM, highlighting the need for real-time autonomous scheduling, dynamic route planning, and airspace traffic management to support sustainable urban mobility. Fasano et al. [302] focused on the integration of Unmanned Aircraft Systems (UASs) with existing air traffic management frameworks, emphasizing the importance of communications, navigation, and surveillance technologies for safe operations. A comprehensive study by another group of researchers outlined the optimization techniques to achieve environmental, sustainability, or climate change mitigation goals [303]. Biswas et al. [304] discussed the role of the Internet of Things (IoT) in UAM, proposing an IoT-supported network to address control, safety, and communication challenges. These studies collectively underscore the importance of integrating advanced technologies and developing comprehensive regulatory frameworks to ensure the successful implementation of UAM.

The future directions and emerging trends in autonomous freight transport highlight significant transformations driven by advanced technologies and innovative business models. Frias et al. [305] examined the impact of technologies like AI, IoT, and autonomous vehicles on logistics, emphasizing their potential to enhance efficiency but also posing challenges such as job displacements and supply chain vulnerabilities. Daduna [306] discussed the influence of automated and autonomous vehicles on freight transport, highlighting the need for new frameworks to manage these advancements. Dalmeijer and Van Hentenryck [307] introduced the Autonomous Transfer Hub Network (ATHN) model, which optimizes freight operations by integrating autonomous and human-driven trucks. Lastly, Wang and Sarkis [308] discussed digitalization trends in freight transport, categorizing them into connecting, collaborating, and capitalizing technologies, which drive significant changes in logistics systems.

The future directions and emerging trends in policy and regulatory considerations for autonomous vehicles (AVs) are critical for their successful deployment and integration into society. Cole et al. [309] discussed the shift in liability from human drivers to AVs, highlighting the need for states to redefine what constitutes a driver. They emphasized the importance of creating consistent regulatory objectives to manage this transition. Tran and Le [310] analyzed the regulatory frameworks in ASEAN countries, comparing them with those in Europe to suggest effective legal approaches for AV integration. Bin-Nun et al. [311] explored the complexities of defining proper AV behavior and the challenges of translating legal driving rules into formal rules for AV systems. Pillala et al. [312] reviewed the current legislation on AVs in the U.S., finding that most states focus on testing rather than general use, with a call for consistent national policies to avoid a patchwork of state laws. These studies collectively underscore the importance of developing robust regulatory frameworks that address liability, safety, and behavioral standards for AVs.

10. Case Studies and Real-World Implementations

Case studies and real-world implementations of urban autonomous vehicle (AV) shuttles provide valuable insights into the challenges and advancements in this field. Anund et al. [313] shared lessons from setting up automated shuttle operations in Brussels, Linköping, and Turin, emphasizing the need for shuttles to adapt to existing traffic environments without extensive infrastructure modifications. Wille and Trumpold [314] investigated the use of V2X communication to enhance the efficiency of autonomous shuttles in urban traffic, demonstrating the benefits of innovative traffic light control systems. Benyahya et al. [315] focused on the cybersecurity challenges of Automated City Shuttles (ACSs), performing risk assessments and penetration tests to identify vulnerabilities. Finally, Li et al. [316] presented an overall architecture and system design for shuttle unmanned ground vehicles, proposing the integration of a cloud brain system to enhance operational safety and performance.

Case studies and real-world implementations of autonomous delivery vehicles (ADVs) provide insights into their potential and challenges. A study by Shaklab et al. [317] introduced an AI-assisted autonomous delivery robot system designed for small urban communities, emphasizing end-to-end automation and optimization for safe last-mile deliveries. This system was tested in real-world trials on a university campus, showcasing its utility in handling operational uncertainties and client schedules. Gao et al. [318] detailed the design and implementation of an autonomous driving delivery robot equipped with advanced sensor technologies and software frameworks, highlighting its effective path planning and obstacle detection capabilities in various outdoor scenarios. An analysis by Reed et al. [319] explored the impact of autonomous vehicle-assisted deliveries in urban to rural settings, finding that such systems significantly reduce delivery completion times and provide cost-effective solutions, particularly in urban environments. These studies collectively emphasize the importance of robust designs, extensive testing, and the integration of advanced technologies to enhance the efficiency and safety of ADVs.

Case studies and real-world implementations of autonomous vehicle (AV) deployment in smart cities provide valuable insights into the potential and challenges of integrating AVs into urban environments. The Vehicle as a Service (VaaS) paradigm proposed by researchers leverages vehicles equipped with sensing, computing, and communication capabilities to build cost-effective service networks in smart cities, highlighting potential use cases and necessary upgrades for traditional vehicular networks [320]. Another study focuses on the design and optimization of solar-powered shared electric AV systems for smart cities, demonstrating significant improvements in operational range and utility through optimized charging station locations and energy management strategies [321]. A pre-deployment testing study of low-speed urban road autonomous driving in Columbus emphasized the importance of extensive lab and controlled environment testing before public road deployment to ensure safety and reliability [322]. The Living Lab for Autonomous Driving in Modena, Italy, showcased applied research in mobility as a service (MaaS) model, contributing to sustainable urban planning [323]. Lastly, a study on AV adoption in Indian smart cities identified high willingness among residents, particularly young adults, to embrace AV technology, suggesting significant potential for reducing accidents and transforming urban mobility [324].

Case studies and real-world implementations of autonomous vehicle (AV) testing and pilots offer valuable insights into the complexities and advancements in this field. The Sohjoa Baltic project (Bellone et al. [325]) explores the challenges of running AV pilots in the Baltic region, particularly focusing on weather-related issues and proposing state-of-the-art solutions and future implementation ideas. Mahmoodi Nesheli et al. [326] reviewed over 25 driverless shuttle (DS) pilot programs worldwide, identifying critical factors for successful deployments and emphasizing the need for diverse operating environments to evaluate the technology realistically. Ortegon-Sarmiento et al. [327] presented a case study on technological acceptance of AVs, using virtual reality to assess user behavior and acceptance in adverse weather conditions. Ebert and Weyrich [328] discussed AI-based testing for AVs, proposing a method for automatically generating test cases to ensure coverage, efficiency, and transparency. Lastly, Razi [329] detailed a model-based testing framework using simulators to generate and evaluate driving scenarios for AVs, highlighting the efficiency and versatility of simulations over real-world testing.

11. Conclusions

The integration of autonomous vehicles (AVs) into our transportation systems signifies a transformative shift in mobility, promising substantial improvements in safety, efficiency, and environmental sustainability. This comprehensive review delved into the multifaceted realm of AV traffic modeling, shedding light on the varied approaches, methodologies, and findings that currently define this research domain.

Our analysis revealed a spectrum of modeling techniques, ranging from microscopic models that capture individual vehicle behaviors to macroscopic models that examine aggregated traffic flows, with hybrid models offering a blend of both perspectives. Each modeling approach provides unique insights and collectively contributes to a comprehensive understanding of how AVs can alter traffic dynamics. This review underscores that even a modest presence of AVs can lead to significant enhancements in traffic efficiency and safety.

In mixed traffic environments, where AVs and human-driven vehicles coexist, the interactions are intricate and demand sophisticated modeling to predict and manage effectively. Research in this area is vital for understanding the cooperative and competitive behaviors that emerge, as well as for developing strategies to mitigate potential conflicts and inefficiencies.

Furthermore, this review highlights the critical role of supportive infrastructure and policy frameworks in ensuring the smooth integration of AVs. Infrastructure adaptations, such as dedicated lanes and smart traffic signals, coupled with appropriate regulatory measures, are essential to fully leverage AV technology.

Despite the advancements, several challenges persist. There is a need for more accurate and scalable models that can address real-world complexities. Integrating real-world data for model validation, considering human factors and addressing ethical and legal issues remain crucial areas for further research. The future development of advanced modeling techniques, incorporating machine learning, edge computing, and 5G networks, presents a promising direction for continued exploration.

In conclusion, while significant progress has been made in modeling autonomous vehicle traffic, the journey towards full integration is ongoing. Continued interdisciplinary collaboration and innovation are essential to overcoming existing challenges and fully realizing the benefits of autonomous vehicles. By enhancing our understanding and developing robust models, we can pave the way for a safer, more efficient, and sustainable transportation future.