A Dynamic Risk Assessment System for Expressway Lane-Changing: Integrating Bayesian Networks and Markov Chains Under High-Density Traffic

Abstract

In high-density expressway environments, lane-changing (LC) maneuvers act as stochastic perturbations that compromise the hydrodynamic stability of traffic flow, leading to safety hazards and operational delays. While existing literature has extensively modeled crash severity in static complex environments (e.g., tunnels and mountainous terrains), there remains a critical deficiency in quantifying the dynamic, systemic risks induced by LC maneuvers under saturation conditions. To address this gap, this study proposes a novel Systemic Risk Assessment Framework. First, a Hidden Markov Model (HMM) is employed to decode the latent state transitions of following vehicles, quantifying the systemic consequence of LC maneuvers as “operational delay” based on traffic wave theory. Second, a Bayesian Network (BN) is constructed to infer the causal probability of risk, integrating geometric proxies such as insertion angle with kinematic variables. Validated with real-world trajectory data, the model achieves high accuracy in identifying risk accumulation precursors. This research contributes to the field of transportation systems by shifting the risk paradigm from static collision prediction to dynamic system reliability analysis, offering theoretical support for Connected and Autonomous Vehicle (CAV) decision logic.

1. Introduction

Expressway systems serve as the critical arteries of modern urbanization, designed to maximize mobility and logistical efficiency. However, the operational reliability of these systems is critically tested under high-density flow conditions. When traffic saturation exceeds critical thresholds (0.8 ≤ V/C ≤ 0.9), the traffic stream transitions from a stable laminar flow to a metastable state, where vehicles are no longer isolated entities but coupled components of a complex system. In this delicate state, lane-changing (LC) maneuvers introduce stochastic lateral interference that can destabilize the entire traffic stream [1]. Unlike the relatively predictable nature of car-following behaviors governed by longitudinal kinematics, lane changing involves active, discretionary decision-making and complex negotiations with surrounding vehicles. A single ill-timed maneuver can trigger a chain reaction, generating shockwaves that propagate upstream, resulting in flow breakdown, safety hazards, and significant operational delays [2].

The complexity of assessing these risks is initially framed by the physical driving environment. Extensive research has established that road geometry and environmental factors set the “baseline” risk of the system. A substantial body of literature has characterized crash severity in specific static environments, such as mountainous freeways, long tunnel groups, and spiral tunnels, where visual load oscillations (the “black hole” and “white hole” effects) and spatial constraints significantly degrade driver reaction times [3,4,5,6,7]. Similarly, external factors like real-time weather conditions have been shown to alter incident clearance times and recovery rates [8]. While these studies provide a foundational understanding of static risk factors, they often treat traffic flow as a continuum affected by the environment, failing to capture the dynamic and stochastic risks generated by vehicle-to-vehicle interactions in open, high-density sections.

To quantify these dynamic risks, methodologies have evolved from traditional statistical regression to advanced Artificial Intelligence. Recent advancements in deep learning have enabled the unified recognition of driver speed and lateral intentions, improving the precision of trajectory prediction [9]. Advanced architectures, such as multi-task learning frameworks and spatio-temporal feature fusion networks, have been developed to capture the non-linear dependencies in driving behavior [10,11]. However, despite the high accuracy of these data-driven models, a critical “black box” dilemma remains. As noted in recent systematic reviews, deep learning models often lack the interpretability required for safety-critical applications in traffic management, making it difficult to trace the causal link between a specific maneuver and its risk outcome [12].

Furthermore, a fundamental gap exists in the definition of risk itself. Most existing frameworks rely heavily on microscopic surrogate safety measures (SSM) such as Time-to-Collision (TTC) or collision risk indices based on trajectory prediction [13]. These metrics focus solely on the probability of a metal-to-metal contact, neglecting the systemic consequence of the maneuver. In high-density flow, a lane change that does not result in a crash but forces a platoon of following vehicles to brake heavily represents a significant “Operational Risk,” causing efficiency loss and potential secondary conflicts [14]. Current models rarely quantify this “invisible” consequence or couple it with the probability of occurrence in a unified system.

To address these limitations, this study proposes a Systemic Risk Assessment Framework that couples probabilistic reasoning with traffic wave theory. By integrating Hidden Markov Models (HMM) to decode the latent state transitions of following vehicles and Bayesian Networks (BN) to infer causal probabilities, this research bridges the gap between microscopic behavior and macroscopic system stability.

The main contributions of this study are organized as follows:

• System-Theoretic Risk Definition: We redefine risk as the product of LC Probability and Operational Consequence. Unlike traditional collision-based metrics, we utilize Hidden Markov Models (HMM) to quantify the systemic consequence by calculating the operational delay propagated through the following vehicle platoon.
• Explainable Probabilistic Modeling: We construct a Bayesian Network (BN) that integrates the geometric feature of “Insertion Angle” with kinematic variables. This structure allows for causal reasoning and the dynamic updating of risk beliefs under uncertainty, addressing the “black box” limitation of pure deep learning approaches.
• Dynamic Risk Zoning and Validation: Based on the coupled risk values, we establish a dynamic clustering model to categorize risk into four distinct levels. This provides a quantifiable and actionable standard for real-time traffic monitoring and future Connected and Autonomous Vehicle (CAV) decision logic.

To bridge this gap, this study views the traffic stream as a complex system. By integrating Hidden Markov Models (HMM) to quantify the propagation of delay (consequence) [15] and Bayesian Networks (BN) to infer causal dependencies (probability) [16], this research moves beyond static severity modeling. This approach aligns with recent advancements in system-theoretic process analysis [17] and provides a quantifiable basis for the cooperative control of mixed traffic flows in the era of Connected and Autonomous Vehicles (CAVs).

2. Related Work

The evolution of traffic risk assessment represents a paradigm shift from post hoc accident reconstruction to real-time, predictive system monitoring. The academic discourse has progressively moved from analyzing static environmental constraints to decoding the dynamic behavioral heterogeneity of road users, and finally, to developing cooperative control strategies for future mobility systems.

Initial research efforts were heavily concentrated on understanding how complex geometric environments distort driver behavior and amplify risk. Beyond the tunnel and mountainous environments mentioned in the introduction, urban expressway weaving segments and ramp areas have been identified as critical bottlenecks where mandatory lane changes create high-turbulence zones. Investigations into these segments have developed enhanced risk indices, demonstrating that conflict rates are highly sensitive to the length of the weaving section and the traffic volume ratio [15,16]. Similarly, studies on freeway bottlenecks have highlighted how rapid queue formation at these choke points creates a feedback loop of collision risk, necessitating dynamic speed control interventions [17]. Furthermore, empirical calculations of lane-change maneuver duration have been revised to reflect these constrained environments, arguing that traditional kinematic models often underestimate the time required for safe insertion [18].

As research moved from the environment to the agent, the focus shifted to vehicle heterogeneity and behavioral dynamics. Traffic is not composed of homogenous particles; it is a collection of heterogeneous agents with varying capabilities and driving styles. Significant disparities exist between different vehicle types. Research focusing on truck drivers near highway ramps has revealed that heavy vehicles exhibit distinct lane-changing intention mechanisms, requiring significantly larger gaps and longer negotiation times compared to passenger cars [19]. Similarly, assessments of regular passenger buses using multi-source data have highlighted that professional drivers, while generally safer, are subject to specific fatigue-related risk patterns that differ from private motorists [20]. A comprehensive investigation into multi-vehicle type risks confirmed that the interaction between small cars and large trucks generates the highest volatility and severity in conflict scenarios [21]. The nature of the maneuver itself is also a key determinant of risk. “Cut-in” maneuvers, where a vehicle aggressively merges into a small gap, have been extensively modeled using various machine learning algorithms, revealing that these actions drastically reduce the safety margin of the following platoon [22]. Further studies have quantified the impact of these risky maneuvers on platoon stability, demonstrating that a single aggressive cut-in can trigger an amplification of braking waves downstream [23]. More proactive frameworks have been developed to predict risk by differentiating between compliant and aggressive lane-changing patterns [24]. Additionally, detecting “failed lane-changing” attempts—scenarios where a driver initiates but aborts a maneuver—has emerged as a crucial indicator of high-risk conflict precursors [25].

To quantify these complex behaviors, methodological frameworks have undergone significant refinement. Traditional statistical and probabilistic approaches remain valuable for their interpretability. For instance, random parameter models and Bayesian frameworks incorporating individual driving styles have demonstrated that knowing a driver’s historical “style” significantly improves real-time prediction accuracy [26,27]. Recent efforts to infer the hierarchy of traffic conflicts using probabilistic methods have enabled researchers to distinguish between minor disturbances and critical near-miss events [28]. Lane-changing risk indices based on these probabilistic approaches provide a scalar metric for evaluating unsafe behaviors [29]. However, to handle high-dimensional trajectory data, Deep Learning (DL) has become the dominant paradigm. Unified recognition models and spatio-temporal feature fusion networks (combining mechanisms like Graph Attention Networks and Transformers) have outperformed traditional baselines in trajectory prediction accuracy [30,31]. Techniques integrating surrounding vehicle information have improved the detection of abnormal behaviors by weighting the importance of neighboring vehicles [32]. Other studies have employed large-scale pre-collision trajectories to identify collision risks under heterogeneous braking patterns [33] and used explainable machine learning to capture short-term traffic states [34]. Furthermore, asymmetric behavior models combined with explainable AI have proven that variables like speed difference and time headway are the critical determinants of conflict risk [35]. Reinforcement learning approaches based on semantic segmentation represent the cutting edge, allowing models to learn decision-making policies directly from complex visual scenes [36].

Finally, the literature increasingly views lane changing not just as a safety issue, but as a systemic control problem, particularly for Connected and Autonomous Vehicles (CAVs). Research has introduced the concept of “Safety Envelopes” to provide theoretical boundaries for AV decision-making in hazardous situations [37]. Dynamic zoning cooperative control methods have been proposed to optimize urban road traffic flow, demonstrating that coordinating lane changes can reduce system-wide delays [38]. Game-theoretic decision control models simulate the negotiation process between vehicles, balancing safety, efficiency, and comfort [39]. Analyses of discretionary lane-changing behaviors of AVs in real-world data suggest that while AVs are generally safer, their conservative behavior can sometimes disrupt human traffic flow [40]. Unified risk field-based models and comprehensive reviews of collision avoidance techniques emphasize the need for robust communication protocols [41,42]. In adverse conditions, such as changing road surfaces, driver assistance systems play a pivotal role in stabilizing maneuvers [43]. Early research into cooperative and competitive characteristics of urban expressways laid the foundation for these modern control strategies [44].

Despite these extensive advancements, three critical deficiencies remain in the current body of knowledge. First, most studies decouple probability from consequence, focusing either on predicting a crash (via TTC) or analyzing post hoc severity, without quantifying the real-time operational delay (consequence) imposed on the traffic stream. Second, while Deep Learning models achieve high accuracy, they often suffer from a lack of interpretability, acting as “black boxes” that fail to explain the causal geometry (e.g., insertion angle) driving the risk. Third, existing risk indices are largely microscopic, often neglecting the systemic “ripple effect” of a lane change on the stability of the entire following platoon in high-density saturation. This study aims to bridge these gaps.

3. Materials and Methods

To overcome the limitations of existing microscopic risk indicators that decouple probability from systemic consequence, this study proposes a novel, integrated methodological framework for quantifying the operational risk of LC maneuvers in high-density traffic. The approach considers the traffic stream as a complex, coupled system where individual maneuvers act as perturbations leading to macroscopic state changes.

The overall research methodology is structured into four logical phases, as illustrated in Figure 1.

Phase I (Data Preprocessing) focuses on transforming raw, noisy roadside perception data into a structured trajectory dataset, with a particular emphasis on extracting novel geometric features like the “insertion angle” alongside traditional kinematic variables.

Phase II (Dual-Pillar Modeling) is the theoretical core, constructing two parallel models: a macroscopic model using Hidden Markov Models (HMM) and traffic wave theory to quantify the systemic consequence (delay), and a microscopic model using Bayesian Networks (BN) to infer the causal probability of risk based on behavioral features.

Phase III (System Coupling) integrates the outputs of the dual pillars into a unified Risk Value (R) and employs unsupervised learning (K-means) to establish a dynamic risk stratification standard.

Phase IV (Validation & Application) validates the proposed framework against real-world data and outlines its application in connected autonomous vehicle (CAV) decision support.

3.1. Section Selection and Data Investigation

An expressway section of Xi’an’s Second Ring Road and Tangyan Road with a degree of saturation of 0.8–0.9 was selected as the research object (Figure 2), considering its high traffic volume and small vehicle spacing. When selecting the survey section, the following criteria were strictly followed:

• A wide field of vision free from tree obstruction should be maintained to facilitate continuous aerial video recording of the traffic flow via drones;
• It should be far away from on-ramps and off-ramps, as vehicles merging into or exiting the main road at these ramps will interfere with vehicles operating normally on the expressway;
• Priority should be given to sections separated by white dashed lines, since lane changing is permitted here—whereas drivers would violate traffic rules if lane changing is conducted across white solid dividing lines;
• The section length should be as long as possible, ensuring that the observed vehicles can travel forward as a continuous traffic flow.

The trajectories of the surveyed vehicles are tracked using Tracker software (Version 6.1.6, available at: https://www.vicon.com/software/tracker/ (accessed on 12 March 2026)). During data extraction, a Cartesian coordinate system is established by taking the lane dividing line as the X-axis and the direction perpendicular to the lane dividing line as the Y-axis, based on which the trajectories of lane-changing vehicles are tracked.

Prior to model training, the raw trajectory data underwent a rigorous preprocessing pipeline to address sudden jumps, outliers, and missing values inherent in video extraction. Since physical vehicle movement is continuous, a five-point cubic smoothing algorithm and locally weighted scatterplot smoothing, known as LOWESS, were applied to the coordinate data. To ensure these techniques did not distort the true kinematic characteristics, residual and relative error validations were conducted. The residual analysis verified the elimination of noise while maintaining data reliability, and the relative error confirmed the high credibility of the smoothed trajectories, ensuring that the 400 curated sets provide high-fidelity inputs for robust model generalization.

3.2. Estimation of the Occurrence Probability of Vehicle Lane-Changing Risks

The estimation of the occurrence probability of vehicle lane-changing risks involves statistically analyzing the probability of vehicle lane changes. The factors influencing vehicle lane changes include: target vehicle speed $v_c$, target vehicle insertion angle $\alpha$, first following vehicle speed $v_b$, preceding vehicle speed in the target lane $v_a$, and spacing between the preceding and following vehicles in the target lane $l_{ab}$. The occurrence probability P of vehicle lane-changing risks is related to the above five factors.

$$P=G\left(X\right)=G(v_c,v_a,v_b,\alpha ,l_{\mathit{ab}})$$

(1)

$$P=p\left(v_c\right)·p\left(\alpha \right)·p\left(v_b)·p{(v}_a)·p\right(l_{\mathit{ab}})$$

(2)

Because of the limited sample size of extracted lane-changing trajectories, calculating the joint probability P using Formula (1) leads to severe data sparsity, where most specific variable combinations lack corresponding empirical probability values. During the lane-changing process, the angle between the vehicle’s traveling direction and the road centerline changes; that is, whether the lane change is successful is related to the insertion angle of the target vehicle into the target lane.

Table 1. Occurrence Probability of Risks for Successfully Lane-Changing Vehicles under Different Insertion Angles.

Insertion Angle	0–3.0°	3.0–6.0°	6.0–9.0°	9.0–12.0°	12.0–15.0°
Lane-Change Percentage	3.90%	13.03%	13.43%	12.19%	10.91%
Insertion Angle	15.0–18.0°	18.0–21.0°	21.0–24.0°	24.0–27.0°	>27°
Lane-Change Percentage	10.73%	10.21%	9.66%	8.90%	7.05%

lists the proportion of successfully lane-changing vehicles under different insertion angles. When the change rate of the vehicle’s initial insertion angle per unit time exceeds 3.0°, it indicates a high probability that the vehicle will make a lane change. To ensure that each set of surveyed lane-changing data has a uniquely corresponding operational delay value and simplify the large amount of data required for Formula (2), the vehicle lane-changing insertion angle is adopted as the probability calculation index for vehicle lane changes. The lane-changing percentage can be used as the occurrence probability of successful lane-changing risks under different insertion angles.

3.3. Estimation of Vehicle Lane-Changing Consequences

Vehicle lane changes by the target vehicle will cause different degrees of impact on the following vehicles in the target lane, reducing their operating speed and resulting in operational delays. Based on classical traffic flow fluctuation theory, the consequences of these maneuvers can be converted into vehicle delay time.

When a lane-changing maneuver causes a disruption or slowdown, it generates accumulation and dissipation wave fronts. Instead of detailing the fundamental kinematic wave derivations, we directly apply the shockwave theory to quantify this impact. The total duration of vehicle congestion, denoted as $t_g$, is fundamentally determined by the propagation speeds of these shockwaves relative to the traffic volume and density changes between the normal and congested states.

Given the low-speed travel distance $L_d$ caused by the maneuver and the initial velocity $V_1$, the final operational delay time $t_{y1}$ for the following vehicles can be quantified as follows:

$$t_{y1} = t_g-{\displaystyle \frac{L_d}{v_1}}$$

(3)

Figure 3 depicts the scenario where a traffic accident caused by the target vehicle’s lane change blocks road traffic. Specifically, State 1 represents the road condition without traffic accidents, where $Q_1$ denotes the traffic volume before the accident (unit: pcu/h, passenger vehicle units per hour); $V_1$ denotes the average vehicle speed before the accident (unit: km/h, kilometers per hour); and $K_1$ denotes the traffic flow density on the road before the accident (unit: pcu/km/ln, passenger vehicle units per kilometer per lane).

When a major traffic accident occurs due to vehicle lane changing, it results in traffic blockage, forming a “traffic accumulation wave front” between State 1 and State 2. The existence time of this “accumulation wave front” is related to the accident dissipation time. In State 2, the traffic volume $Q_2$ = 0, vehicle speed $V_2$ = 0, and traffic flow density $K_2$ = 0 on the road. After the accident dissipates, road traffic returns to normal State 3, where the traffic volume is $Q_3$, vehicle operating speed is $V_3$, and traffic flow density is $K_3$. A “traffic dissipation wave front” is formed between State 2 and State 3.

Figure 4 depicts the scenario of blockage in partial road sections caused by a collision during vehicle lane changing. Vehicles are forced to change lanes to unobstructed ones for passage; at this time, the vehicle delays mainly consist of deceleration delays and acceleration delays.

On expressway sections with a traffic load degree of 0.80–0.90, it is assumed that operating vehicles follow the vehicle-following characteristics, and the operating state of a following vehicle can only be determined based on the operating state of the preceding vehicle. During the lane-changing process of the target vehicle, it will exert an impact on the 1st vehicle behind it in the target lane; meanwhile, the 2nd following vehicle is affected by the 1st following vehicle, and this impact is transmitted sequentially—the operating characteristics of the n th following vehicle are affected by the (n − 1) th following vehicle.

3.4. Overall Model Framework

When analyzing the impact of the target vehicle’s lane change on the speed of following vehicles, the analysis process is divided into two stages: the first stage explores the speed relationship between the target vehicle and the 1st following vehicle, and the second stage investigates the speed transmission relationships—including the relationship between the 1st and 2nd following vehicles, as well as the relationship between the (n − 1) th following vehicle and the n th following vehicle. Based on Markov theory, it is assumed that during the target vehicle’s lane change, the operating state of the 2nd following vehicle in the target lane is only related to that of the 1st following vehicle, and the operating state of the n th following vehicle is only related to that of the (n − 1) th following vehicle.

Markov decision-making can only model discrete states. According to the influence of the target vehicle’s lane change on the first following vehicle, the running state of the first following vehicle is divided into three categories: State I—accelerating forward, State II—maintaining current speed and moving forward, and State III—decelerating forward. These three states correspond to a decrease, no change, and an increase in the running time of the first following vehicle, respectively. The speed change in each following vehicle is compared with its speed at the previous moment. To explore the transmissibility of the influence exerted by the target vehicle on following vehicles during lane changes, a Markov transition model is established. When analyzing the factors influencing the target vehicle’s lane change on following vehicles, the study focuses on the operation process of a series of subsequent vehicles. The n th following vehicle is affected by the (n − 1) th following vehicle. When investigating the influence transmission characteristics between each pair of vehicles, the transmission process is divided into n sub-processes, with each pair of adjacent vehicles taken as one research object and one analytical process, as illustrated in Figure 5.

A schematic diagram (Figure 6) illustrating the “state” transition process of vehicles during lane changing is constructed. The symbols in the figure are defined as follows: TLB1V denotes the 1st vehicle behind the target vehicle in the target lane (marked as $x_1$), TLB2V denotes the 2nd vehicle behind the target vehicle in the target lane (marked as $x_2$), and so on for other corresponding symbols.

A Hidden Markov Model (HMM) can be represented by the parameter $\lambda$, which is generally expressed as $\lambda =\left[N,M,A,B,\prod \right]$. The meanings of each parameter are as follows:

(1)

$N$ denotes the set of all possible values of hidden states, where $N=\left\{q_1,q_2,\dots ,q_n\right\}$, and n is the number of possible values of hidden states. Specifically, this study defines three discrete hidden states for the following vehicle’s operational status: State I for accelerating, State II for constant speed, and State III for decelerating. The hidden state at time t can be denoted as $i_t$, with $i_t\in N$. In general, hidden states can transition arbitrarily between each other; the state at time t + 1 is only affected by the state at time t, not by the states at any other times.

(2)

M denotes the set of all possible values of observation states, where $M=\left\{v_1,v_2,\dots ,v_m\right\}$ and m is the number of possible values of observation states. The observation state at time t can be denoted as $o_t$, with $o_t\in M$.

(3)

∏ denotes the initial probability distribution of hidden states, where $\prod ={\left[{\pi }_i\right]}_{N\times 1}$ and ${\pi }_i=P\left(i_1=q_i\right)$.

(4)

A denotes the state transition matrix, where $A={\left[a_{ij}\right]}_{N\times N}$ and $a_{ij}=P(i_{t+1}=q_j|i_t=q_i)$. It represents the probability that the hidden state at time t + 1 is $q_j$ given that the hidden state at time t is $q_i$.

(5)

B denotes the observation state generation matrix, where $B={\left[b_j\left(k\right)\right]}_{N\times M}$ and $b_j\left(k\right)=P(o_t=v_k|i_t=q_j)$. It represents the probability that the observation state at time t is $v_k$ given that the hidden state at time t is $q_j$.

Given the model $\lambda =\left[N,M,A,B,\prod \right]$ and the observation sequence $O=\left\{o_1,o_2,\dots ,o_T\right\}$, calculate the probability $P\left(O|\lambda \right)$ of the observation sequence occurring under this model. To optimize the model parameters $\lambda$ given the observation sequence, the Baum–Welch algorithm is applied. As a specific application of the Expectation-Maximization algorithm for Hidden Markov Models, it iteratively approaches the optimal model by maximizing the probability $P\left(O|\lambda \right)$ until convergence requirements are satisfied. This type of problem is applicable when multiple models exist: the model with the maximum output probability (i.e., the model that best matches the observation sequence) is selected.

400 sets of lane-changing data were selected, and the Gaussian Mixture Hidden Markov Model, abbreviated as GM-HMM, was used to calculate the cumulative total operational delay propagated through the affected following platoon in the target lane, rather than the average per-vehicle delay. This cumulative metric accurately captures the systemic time loss absorbed by the traffic stream until the localized shockwave fully dissipates. These delay values were sorted in ascending order, resulting in Figure 6: Cumulative Probability Distribution of Following Vehicle Operation Delays. As shown in Figure 7, the cumulative distribution of following vehicle delays is the highest in the range of 5.0–10.0 s, accounting for approximately 50.0% of the total sample size. The sample size of following vehicle delays below 5.0 s accounts for about 22.0% of the total; delays in the range of 10.0–15.0 s account for roughly 20.0%; and delays exceeding 15.0 s make up approximately 8.0%. After determining the cumulative distribution of following vehicle operation delays, it is necessary to define the lane-changing delay distribution levels. Referring to the classification of traffic conflicts or traffic accidents, vehicle lane-changing operation delays can be divided into four categories: Class I (Major Delay), Class II (Significant Delay), Class III (Moderate Delay), and Class IV (Minor Delay). The value range for each delay category is presented in

Table 2. Delay Categories and Their Value Ranges.

Delay Categories	Value Range (s)
Class IV Delay	0.0 s ≤ -- < 5.0 s
Class III Delay	5.0 s ≤ -- < 10.0 s
Class II Delay	10.0 s ≤ -- < 15.0 s
Class I Delay	≥15.0 s

Note: The delay thresholds established in Table 2 are context-specific. They are calibrated exclusively for high-density, near-saturation traffic conditions with a volume-to-capacity ratio between 0.8 and 0.9 based on the empirical cumulative distribution. These fixed values are not intended to be universally applied to free-flow or fully congested regimes.

.

3.5. Model Construction and Analysis

The Bayesian Network (BN) evaluation model is mainly used for learning and evaluating lane-changing risks. It is adopted to predict and assess the risk values of following vehicles in the target lane caused by the target vehicle’s lane changes. Since the BN algorithm can obtain objective evaluation results under incomplete data conditions, it outputs different lane-changing risk values through machine learning by analyzing the lane-changing conditions of vehicles in the initial state and combining with the operational delays of following vehicles in the target lane caused by lane changes.

During the BN risk assessment learning process, referring to the learning steps of the BN algorithm, the following three parameters are used as training samples for learning: the occurrence probability P of the target vehicle’s lane-changing risks, the consequence H of operational delays of following vehicles in the target lane caused by lane changes, and the risk value R imposed on following vehicles in the target lane by the target vehicle’s lane changes.

3.5.1. Construction of the BN Model

The BN model is mainly applied to risk analysis of complex systems, capable of accurately predicting the probability of event occurrence, as well as diagnosing and forecasting event states.

(1)

Discretization of Model Parameters

During the extraction of vehicle lane-changing data, all variable data are continuous and uninterrupted, while the construction of the BN model requires discretized data. The criteria for defining these discrete intervals are based on domain-informed empirical data to systematically balance computational efficiency and model precision. Specifically, the speed variable boundaries were determined by referencing the 2019 Xi’an Urban Traffic Development Annual Report, where peak-hour average speeds across different ring zones range from 21.18 km/h to 27.45 km/h. This local empirical range directly informs the core speed bins. Additionally, the discretization standards for vehicle spacing and kinematic variations were strictly adapted from the established traffic behavior methodologies detailed in Reference [9].

The target vehicle insertion angle is divided into 10 categories: [0, 3), [3, 6), [6, 9), [9, 12), [12, 15), [15, 18), [18, 21), [21, 24), [24, 27), [27, 90), corresponding to [0, 1, 2, 3, 4, 5, 6, 7, 8, 9] respectively.

Vehicle speed v (m/s) is discretized into 9 groups of data: [0, 1), [1, 2), [2, 3), [3, 4), [4, 5), [5, 6), [6, 7), [7, 8), [8, +∞), corresponding to [0, 1, 2, 3, 4, 5, 6, 7, 8] respectively.

Vehicle speed change Δv is discretized into 12 groups of data: [−∞, −5), [−5, −4), [−4, −3), [−3, −2), [−2, −1), [−1, 0), [0, 1), [1, 2), [2, 3), [3, 4), [4, 5), [5, +∞), corresponding to [0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11] respectively.

Vehicle spacing (distance between the front ends of consecutive vehicles) lab is discretized into 9 groups of data: [3, 6), [6, 9), [9, 12), [12, 15), [15, 18), [18, 21), [21, 24), [24, 27), [27, +∞), corresponding to [0, 1, 2, 3, 4, 5, 6, 7, 8] respectively.

Vehicle spacing change Δl is discretized into 12 groups of data: [−∞, −5), [−5, −4), [−4, −3), [−3, −2), [−2, −1), [−1, 0), [0, 1), [1, 2), [2, 3), [3, 4), [4, 5), [5, +∞), corresponding to [0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11] respectively.

(2)

Construction of the BN Structure

Based on the influencing factors of vehicle lane changes and the risk consequences arising from lane changes, a structural framework diagram of the BN evaluation model for vehicle lane-changing risks is constructed, as shown in Figure 7.

In Figure 8, the first row represents the factors influencing vehicle lane changes, namely the target vehicle speed $v_c$, target vehicle insertion angle $\alpha$, and the spacing between the front and rear vehicles in the target lane $l_{ab}$. These three factors affect the vehicle lane-changing probability and lane-changing consequences.

(3)

Parameter Learning and Update

After obtaining the parameter posterior probabilities through BN learning, BN learning is conducted. Combined with the number of vehicle lane changes and their impact consequences, the dynamic update of the BN model for vehicle lane-changing risks is realized.

In

Table 3. Parameter Learning Results of Risk Levels.

Delay	Class IV Delay
Angle	$\alpha \left(0\right)$	$\alpha \left(1\right)$	$\alpha \left(2\right)$	$\alpha \left(3\right)$	$\alpha \left(4\right)$	$\alpha \left(5\right)$	$\alpha \left(6\right)$	$\alpha \left(7\right)$	$\alpha \left(8\right)$	$\alpha \left(9\right)$
Low Risk	0.7	0.77	0.67	0.4	0.4	0.63	0.5	0.57	0.5	0.5
Moderate Risk	0.67	0.83	0.57	0.4	0.75	0.57	0.4	0.63	0.63	0.67
Significant Risk	0.67	0.68	0.09	0.3	0.44	0.29	0.5	0.57	0.5	0.54
Major Risk	0.1	0.02	0.14	0.09	0.1	0.07	0.09	0.09	0.1	0.04
Delay	Class III Delay
Angle	$\alpha \left(0\right)$	$\alpha \left(1\right)$	$\alpha \left(2\right)$	$\alpha \left(3\right)$	$\alpha \left(4\right)$	$\alpha \left(5\right)$	$\alpha \left(6\right)$	$\alpha \left(7\right)$	$\alpha \left(8\right)$	$\alpha \left(9\right)$
Low Risk	0.1	0.08	0.11	0.2	0.2	0.13	0.17	0.14	0.17	0.17
Moderate Risk	0.11	0.06	0.14	0.2	0.08	0.14	0.2	0.13	0.13	0.11
Significant Risk	0.11	0.23	0.73	0.5	0.33	0.43	0.17	0.14	0.17	0.31
Major Risk	0.75	0.8	0.29	0.55	0.6	0.64	0.73	0.45	0.7	0.6
Delay	Class II Delay
Angle	$\alpha \left(0\right)$	$\alpha \left(1\right)$	$\alpha \left(2\right)$	$\alpha \left(3\right)$	$\alpha \left(4\right)$	$\alpha \left(5\right)$	$\alpha \left(6\right)$	$\alpha \left(7\right)$	$\alpha \left(8\right)$	$\alpha \left(9\right)$
Low Risk	0.1	0.08	0.11	0.2	0.2	0.13	0.17	0.14	0.17	0.17
Moderate Risk	0.11	0.06	0.14	0.2	0.08	0.14	0.2	0.13	0.13	0.11
Significant Risk	0.11	0.05	0.09	0.1	0.11	0.14	0.17	0.14	0.17	0.08
Major Risk	0.1	0.16	0.29	0.27	0.2	0.21	0.09	0.36	0.1	0.32
Delay	Class I Delay
Angle	$\alpha \left(0\right)$	$\alpha \left(1\right)$	$\alpha \left(2\right)$	$\alpha \left(3\right)$	$\alpha \left(4\right)$	$\alpha \left(5\right)$	$\alpha \left(6\right)$	$\alpha \left(7\right)$	$\alpha \left(8\right)$	$\alpha \left(9\right)$
Low Risk	0.1	0.08	0.11	0.2	0.2	0.13	0.17	0.14	0.17	0.17
Moderate Risk	0.11	0.06	0.14	0.2	0.08	0.14	0.2	0.13	0.13	0.11
Significant Risk	0.11	0.05	0.09	0.1	0.11	0.14	0.17	0.14	0.17	0.08
Major Risk	0.05	0.02	0.29	0.09	0.1	0.07	0.09	0.09	0.1	0.04

, α(0)–α(9) represent the discretization results of the target vehicle’s insertion angle. The data indicate the probability magnitudes of the corresponding risk levels for different insertion angle intervals under various delay category conditions.

As can be seen from Table 3, under Class IV delay, the probability of vehicle lane changing being at major risk is relatively low, while the probability of it being at medium and low risks is significantly higher. This is because the following vehicles’ delays are small, the overall traffic flow is relatively smooth, the lane-changing conditions for vehicles are favorable, and the low lane-changing risk is consistent with the actual situation.

When vehicles change lanes under Class III delay, the probability of major risks occurring rises significantly; therefore, drivers should minimize the number of lane changes as much as possible in such circumstances. Meanwhile, it can be observed that under Class I delay: when the vehicle’s insertion angle falls within the α(2) interval (i.e., the insertion angle ranges from 6.0° to 9.0°), the probability of the lane-changing risk being classified as major risk is higher; when the insertion angle falls within the α(7)–α(8) interval (i.e., the insertion angle ranges from 21.0° to 27.0°), the probability of the lane-changing risk being classified as significant risk is higher.

3.5.2. Validity Test of the BN Model

To verify the accuracy of the model in predicting lane-changing results, 133 sets of test samples were selected for prediction. Among them, 114 sets were correctly predicted, and 19 sets were incorrectly predicted. The model’s accuracy rate is 85.71%, indicating a certain level of reliability.

Table 4. Comparison of Results between Training Samples and Test Samples.

No.	Training Samples		Test Samples
	Risk Value (True Value)	Risk Value (Predicted Value)	Risk Value (True Value)	Risk Value (Predicted Value)
1	1	1	1	1
2	1	1	1	1
3	1	1	1	2
	·	·	·	·
134	2	2	2	2

In the table, “1” represents the true value and “2” represents the false value.

shows the comparison results between the model’s predicted values and the true values.

3.5.3. Accuracy Test of the BN Model

After the construction of the BN model, it is necessary to verify its rationality, which is mainly explained from the perspective of the accuracy of the model’s prediction results.

The Receiver Operating Characteristic Curve (ROC) is based on the binary classification method. The ordinate represents the true positive rate (sensitivity), i.e., the cumulative percentage of actually occurring vehicle lane-changing risks among the four risk levels; the abscissa represents the false positive rate (1-specificity), i.e., the cumulative percentage of predicted vehicle lane-changing risk levels among the four risk levels. The ROC curve uses the Area Under Curve (AUC) as the evaluation index. The closer the AUC is to 1, the higher the probability of true positives and the better the accuracy of the model.

Based on the risk level data obtained from the BN model, the ROC curve was calculated and plotted, with the AUC value determined as 0.946, as shown in Figure 9.

Table 5. Explanation of AUC Grades.

Levels	Meaning
AUC < 0.5	The model does not conform to the actual situation
AUC = 0.5	The model is ineffective
0.5 < AUC ≤ 0.7	The model has low accuracy
0.7 < AUC ≤ 0.9	The model has moderate accuracy
0.9 < AUC	The model has high accuracy

shows that as the risk level increases, the accuracy of the model also gradually increases. It can be observed that the data obtained from the BN model have good precision, and the model exhibits high accuracy.

4. Results and Discussion

Based on the proposed framework, the systemic risk of lane-changing maneuvers on the Xi’an Second Ring Road was quantified. This section presents the model validation metrics, the risk stratification outcomes, and the sensitivity analysis of key risk factors.

4.1. Model Performance Evaluation

After determining the occurrence probability P of vehicle lane-changing risks and the lane-changing consequence H, the vehicle lane-changing risk value R can be calculated. Based on P (occurrence probability of lane-changing risks), H (lane-changing consequence), and R (risk value), a 3D relationship diagram of R, P, and H is constructed, where the X-axis represents the occurrence probability of vehicle lane changes, the Y-axis represents the consequences caused by vehicle lane changes, and the Z-axis represents the vehicle lane-changing risk value R.

Figure 10 shows the 3D spatial distribution diagram of R, P, and H. When the occurrence probability P of vehicle lane-changing risks is constant, the risk value imposed on the following vehicles in the target lane by vehicle lane changes increases continuously as the vehicle delay increases; when the vehicle lane-changing delay is constant, the corresponding vehicle lane-changing risk value also increases as the occurrence probability of vehicle lane-changing risks rises.

4.2. Risk Stratification and Distribution

After calculating the risk values imposed on the following vehicles in the target lane by vehicle lane changes, it is necessary to classify these risk values. Referring to the classification of risk levels specified in the Classification Standard for Casualty Accidents of Enterprise Employees, the safety risk levels are categorized into four classes from highest to lowest: Major Risk, Significant Risk, Moderate Risk, and Low Risk, represented by four colors (red, orange, yellow, and blue) respectively. This method is characterized by simplicity, efficiency, excellent scalability, and high effectiveness. The main steps are as follows:

Divide the data into c clusters denoted as $k_1,k_2$ …… $k_c$ and select a centroid $p_1$, $p_2$……$p_c$ for each cluster, where $n_j$ represents the size of cluster $k_j$.

$$J={\sum }_{i=1}^k{\sum }_{j=1}^{n_j}{d}_{\mathit{ij}}\left(x_j,p_i\right);{ p}_i={\displaystyle \frac{1}{n_j}}{\sum }_{x_j{k}_j}{x}_j$$

(4)

where $d_{ij}\left(x_j,p_i\right)$—the Euclidean distance between $x_j$ and $p_i$ in cluster $k_i$.

To ensure the validity of this four-level stratification, the Silhouette Coefficient was utilized to evaluate the clustering effect. The analysis confirmed that the optimal inflection point aligns perfectly with four clusters, providing a robust mathematical foundation for the selected risk levels. The K-means clustering algorithm is adopted to cluster vehicle lane-changing risks into four levels:

Level 1 corresponds to Major Risk, with a vehicle lane-changing risk value ≥ 2.091. The characteristic of this level is that there is at least one of the following two scenarios: a high occurrence probability of lane-changing risks or significant delays of following vehicles.

Level 2 corresponds to Significant Risk, with a vehicle lane-changing risk value in the interval [1.404, 2.091).

Level 3 corresponds to Moderate Risk, with a vehicle lane-changing risk value in the interval [0.717, 1.404).

Level 4 corresponds to Low Risk, with a vehicle lane-changing risk value in the interval [0.03, 0.717).

Table 6. Classification of Risk Levels.

Risk Levels	Meaning	Range	Level Colors
Level 3	Low Risk	0.03–0.717
Level 3	Moderate Risk	0.717–1.404
Level 2	Significant Risk	1.404–2.091
Level 1	Major Risk	>2.091

lists the output colors corresponding to different risk levels.

4.3. Discussion

This study proposes a “Dual-Pillar” framework for quantifying systemic lane-changing risk. In this section, we interpret the mechanism of risk formation, benchmark our model against existing literature, and discuss the implications for traffic management.

4.3.1. The Critical Role of Geometric Aggressiveness

A key finding of this research is that the Insertion Angle serves as a more discriminative proxy for risk than traditional time-based metrics (e.g., TTC) in saturated flow conditions. Previous studies focused on gap acceptance as the primary determinant of lane-changing feasibility for trucks and cars [14]. While gap size is critical in free-flow conditions, our results suggest that in high-density traffic (V/C > 0.8), gaps are universally small (often <2 s). In this context, the willingness to accept a small gap—manifested physically as a steep Insertion Angle—becomes the distinguishing factor between an aggressive, high-risk driver and a conservative one. Furthermore, an analysis of the Bayesian Network parameters reveals the coupled sensitivity of vehicle speed and spacing. When the longitudinal spacing falls below the critical threshold alongside a high speed differential, the probability of a Major Risk outcome increases exponentially, regardless of a moderate insertion angle. Compared to classic risk indicators such as Time-to-Collision, this proposed coupled framework demonstrates significant advantages. In high-density saturated flows, traditional time-based metrics often lose their discriminative power because vehicles universally operate with minimal gaps, leading to constant false alarms. By integrating geometric aggressiveness with macroscopic operational delay, our model successfully isolates true systemic hazards from normal tight-gap maneuvers.

A large insertion angle implies a high lateral velocity component. High lateral dynamics reduce the stability margin of the vehicle and minimize the reaction time available to the following driver, thereby exponentially increasing the probability of a conflict [43].

We benchmark the performance of our Coupled Bayesian-HMM framework against recent data-driven models in the literature. Recent studies utilized advanced deep learning architectures (e.g., LSTM, Spatio-Temporal Feature Fusion) for trajectory prediction, achieving prediction accuracies in the range of 92–96% [19,31]. While our model’s AUC of 0.946 is comparable to these state-of-the-art “black-box” models, its primary advantage lies in interpretability. Unlike some existing models whose neural network weights are difficult to decipher [9], our Bayesian Network explicitly maps the causal chain. This transparency is crucial for safety-critical systems, as explainability is a prerequisite for AI adoption in transport safety [7].

Traditional methods, such as probabilistic collision risk assessments, primarily focus on the binary outcome of collision [8,33]. Our model advances this by integrating the Consequence Index. By quantifying the “operational delay” using Traffic Wave Theory, we capture the continuous spectrum of risk. This aligns with the “Traffic Flow Crystallization” concept, confirming that the true cost of a lane change in dense traffic is the crystallization of congestion waves, not just the metal-to-metal contact [2].

4.3.2. Systemic Implications for CAVs and Traffic Management

The quantified risk levels offer actionable thresholds for future mobility systems. The derived thresholds (e.g., R < 0.717 for Low Risk) can serve as the boundary conditions for “Safety Envelopes” [37]. An automated vehicle planning a lane change can use our BN model to estimate its potential R value in real-time; if the predicted R exceeds 1.404 (Significant Risk), the CAV should abort the maneuver or negotiate for a larger gap, thereby implementing “Human-Like” decision-making [39].

For traffic control centers, the spatial distribution of High-Risk events (Level 1) can identify dynamic bottlenecks. Similar to dynamic zoning control strategies [38], our risk stratification can trigger variable speed limits or ramp metering upstream to dissipate the shockwaves predicted by our HMM module.

It is crucial to define the temporal boundary of the insertion angle within practical applications. For the decision-making loop of an ego-CAV, the insertion angle is an a priori planned variable generated by the motion planning module. The CAV evaluates the risk of candidate trajectories using the proposed framework before execution, enabling true proactive risk mitigation. Conversely, when monitoring surrounding human-driven vehicles for active traffic management, measuring the exact insertion angle requires a completed trajectory, introducing a temporal lag. To bridge this gap in real-time monitoring, future implementations should integrate early intention prediction algorithms. By analyzing early kinematic signals such as steering rate and initial lateral acceleration during the first 0.3 s of lane departure, an anticipated insertion angle can be estimated to trigger pre-maneuver warnings.

4.3.3. Limitations and Future Directions

While the proposed framework is robust, several limitations should be acknowledged. First, our dataset comes from a specific urban expressway in Xi’an. Environmental factors like weather can significantly alter driving volatility [12]. Future work should incorporate adverse weather datasets to test model robustness. Currently, the model treats traffic as a relatively homogenous stream. However, multi-vehicle type interactions (e.g., Car-Truck conflicts) exhibit different risk patterns [18]. Incorporating vehicle type as a node in the Bayesian Network would be a valuable extension. We currently assess risk at the moment of lane crossing. Future research could employ conflict hierarchy inference methods [26] to model the temporal evolution of risk throughout the entire maneuver duration.

Furthermore, to comprehensively validate the superiority of the proposed framework, future research must conduct systematic quantitative comparisons with classic microscopic risk indicators, namely Time-to-Collision and Deceleration Rate to Avoid a Crash, utilizing unified trajectory datasets. Expanding the current model to evaluate its robustness and applicability in more complex operational scenarios, particularly under extreme weather conditions and within highly heterogeneous mixed traffic flows, also represents a critical direction for our subsequent studies.

5. Conclusions

This study addresses the critical challenge of quantifying vehicle lane-changing (LC) risks in high-density expressway environments, where traditional microscopic indicators often fail to capture the systemic propagation of traffic disturbances. By proposing a Systemic Risk Assessment Framework that couples a macroscopic consequence model (Traffic Wave Theory and Hidden Markov Models) with a microscopic probability model (Bayesian Networks), this research bridges the gap between individual driver behavior and traffic flow stability. The major findings and implications are summarized as follows:

• The proposed framework successfully integrates the stochastic probability of an LC maneuver with its operational consequence. Empirical validation on the Xi’an Second Ring Road dataset demonstrates that the coupled model achieves an Area Under the Curve (AUC) of 0.946, significantly outperforming single-indicator models. This confirms that systemic risk is best represented as the product of “Geometric Aggressiveness” (Probability) and “Flow Vulnerability” (Consequence).
• Among the extracted precursors, the Insertion Angle (θ) was identified as the most critical geometric proxy for risk. Sensitivity analysis reveals a non-linear threshold effect: when θ exceeds 15°, the likelihood of inducing a high-consequence shockwave increases threefold, regardless of the available longitudinal gap.
• Using K-means clustering, the continuous risk values were effectively partitioned into four actionable levels. The results indicate that while 75% of lane changes (Low and Moderate Risk) are benign, the top 5% (Major Risk, R ≥ 2.091) are responsible for the majority of traffic breakdown events, validating the Pareto principle in traffic safety.