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category: literaturenote citekey: wangsimulationstudytrafficconflict2025 title: A simulation study on traffic conflict risk under shockwave propagation at signalized intersections authors: "Wang, Junqing; Yang, Hong; Zhu, Yuan; Xie, Kun; Yan, Zizheng; Pu, Qingwen" year: 2025 date: 2025-00-00 2025 doi: 10.1016/j.aap.2025.108081 publication: "Accident Analysis & Prevention" url: "https://doi.org/10.1016/j.aap.2025.108081" zotero_key: 9J7RAMHN zotero_storage: N7QAF7ED collections: transpordi_planeerimine folder: 001_artiklid firstAuthor: "Wang, Junqing"

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Contents lists available at ScienceDirect

Accident Analysis and Prevention

journal homepage: www.elsevier.com/locate/aap

A simulation study on traffic conflict risk under shockwave propagation at signalized intersections☆

Junqing Wang a , Hong Yang a,* , Yuan Zhu b , Kun Xie c , Zizheng Yan a , Qingwen Pu c

  • a Department of Electrical and Computer Engineering, Old Dominion University, Norfolk, VA, USA
  • b Inner Mongolia Center for Transportation Research, Inner Mongolia University, Hohhot, Inner Mongolia, China
  • c Department of Civil and Environmental Engineering, Old Dominion University, Norfolk, VA, USA

ARTICLE INFO

Keywords: Driving risk Surrogate safety measures Shockwave analysis Traffic simulation Unmanned aerial vehicles Signalized intersection

ABSTRACT

Traffic congestion and safety at signalized intersections are critical concerns in urban mobility management. The interaction between shockwaves caused by stop-and-go vehicles and the resultant conflict risk remains inadequately understood, necessitating detailed investigation. This study aims to explore the relationship between traffic conflict risk and shockwave propagation at signalized intersections through simulation, focusing on the dynamic conditions as vehicles queue and dissipate. The vehicle trajectory data extracted from the video captured by unmanned aerial vehicles (UAVs) is utilized in this study. The Simulation of Urban MObility (SUMO) software was selected as the simulation platform for building the simulation model. To ensure accuracy, the trajectories are refined with data smoothing and sampling, providing a reliable benchmark input for the simulation model development. Moreover, surrogate safety measures (SSMs) such as modified time to collision (MTTC) and deceleration rate to avoid a crash (DRAC), along with shockwave analysis (SA) were used to investigate the impact of driving risk when shockwave propagates in the queue. Then, the relationship between shockwaves and driving risk was explored under the calibrated model in a signalized intersection scenario. The study results show that conflicts occurred during the process of vehicles approaching until they stop and join the queue. Subsequently, the risk propagated at the tail of the growing queue. Additionally, the space–time diagram reveals that the risk propagation may be initiated before or along with the shockwave's propagation. The findings provide insights for developing control strategies at signalized intersections through the uncovered correlation between the conflict risk and shockwave, contributing to the comprehensive understanding of traffic flow and safety at intersections.

1. Introduction

The increasing number of vehicles in urban areas presents significant challenges to traffic operations and safety. Congestion occurs frequently, leading to the formation of long queues at signalized intersections. These long queues cause periodic shockwaves generated by stop-and-go vehicles in response to signal changes. As queues accumulate, these shockwaves propagate upstream, with longer queues causing prolonged shockwave propagation and potentially faster wave speeds during the approach-slow down-stop-speed up-leave process. Additionally, the complex interactions among vehicles often result in potential conflicts, increasing the risk of crashes. Therefore, it is crucial to examine the

queuing process and its possible interaction with traffic conflict risk.

Several studies have investigated traffic conflict risk at intersections using different approaches to evaluate safety performance (e.g., conflict analysis models (Essa and Sayed, 2018; Zheng and Sayed, 2020) and proactive safety analysis (Yang et al., 2021; Guo et al., 2020). These studies underscore the importance of signalized intersection safety and contribute to traffic signal control optimization and intersection design. However, existing studies have ignored the dynamic nature of vehicle queues, more specifically, the shockwave propagation and its direct impact on traffic conflict risk. Although many existing research has contributed to shockwaves in traffic flow (Liu et al., 2009; Wang et al., 2020) and signalized intersection safety evaluation (Essa and Sayed,

E-mail addresses: jwang014@odu.edu (J. Wang), hyang@odu.edu (H. Yang), zhuyuan@imu.edu.cn (Y. Zhu), kxie@odu.edu (K. Xie), zyan003@odu.edu (Z. Yan), qpu001@odu.edu (Q. Pu).

☆ This article is part of a special issue entitled: 'RSS 2024' published in Accident Analysis and Prevention.

* Corresponding author.

2018; Zheng and Sayed, 2020; Liu et al., 2009; Chauhan et al., 2021), they were typically analyzed independently. Researchers have not yet integrated the two perspectives to provide a comprehensive understanding of their interaction. This gap in the literature emphasizes the need for a study that combines safety risk assessment with shockwave analysis to investigate the correlation between shockwave propagation and traffic conflict risk.

To shorten this gap, this paper investigates the relationship between shockwave propagation and traffic conflict risk at signalized intersections. A well-calibrated microscopic simulation model, based on unmanned aerial vehicle (UAV) video data, is used to simulate traffic operations at signalized intersections and the associated shockwaves. Surrogate safety measures (SSMs), widely implemented as effective indicators for evaluating potential safety risks at signalized intersections, are derived from the simulation to assess traffic conflict risk. This study aims to reveal the correlation between traffic conflict risk and shockwave propagation, providing valuable insights for developing control strategies to improve vehicle arrival management and enhance road safety at signalized intersections.

The rest of the paper is organized as follows: Section 2 describes the methodology, including the data-collection framework and the research analysis approach. The results are presented in Section 3, including the description of the experimental sites and data, followed by the results analysis. The paper concludes with a discussion of potential applications and future research directions (Section 4), followed by conclusions drawn from the study findings.

2. Methodology

This section describes the methodology used in this paper to investigate the relationship between traffic conflict risk and shockwave propagation at a signalized intersection. The following subsections introduce the approach of extracting the vehicle trajectories from the UAV video, developing a microscopic simulation model based on the UAV data, and using surrogate safety measures to analyze the rear-end conflict risk associated with the shockwave due to vehicle queuing.

2.1. Trajectory detection, tracking, and processing

To obtain detailed vehicle trajectories from the UAV video, a deep learning approach combined with computer vision (CV) techniques is utilized in this study. Initially, a customized YOLOV8 model (Ultralytics, 2023), as referenced in our previous research (Pu et al., 2023), was trained by the research team to detect vehicles successfully. Then, the Hybrid-SORT (Yang et al., 2024) algorithm, including an improved Kalman filter, and Re-ID feature matching algorithm, were integrated into the framework to track each vehicle and to ensure the stability of their trajectories. At last, the coordinates of the bounding box for all vehicles in each video frame were summarized into an information table and exported as a comma-separated values (CSV) file. The details of this work can be found in our previous work (Pu et al., 2023).

Once the trajectories are obtained, the speed and acceleration values are calculated based on the vehicle trajectories. However, noise could be generated due to the instability of the tracker during the frame-by-frame tracking process (Wan et al., 2020). To enhance the reliability of the trajectories, two postprocessing steps, including trajectory smoothing and sampling, were applied in this study based on previous research (Krajewski et al., 2018; Khan et al., 2018; Bock et al., 2020). Similar to the study proposed by (Wan, et al. 2020), to minimize outliers and noise, a simple moving average (SMA) (Johnston et al., 1999) approach with a one-second time window was applied to the trajectory data. To facilitate subsequent calculation and evaluation, a one-second sampling interval was selected for each vehicle's trajectory after smoothing. Also, previous efforts have demonstrated that the one-second interval effectively captures vehicle dynamics (Kaufmann et al., 2018).

In this study, the vehicle speed is defined as the sum of the distances

traveled in adjacent frames, corresponding to one second. As such, acceleration can be calculated based on the speed data. Moreover, the speed limit in the study area and the range of acceleration and deceleration values under normal driving conditions serve as auxiliary parameters to identify the effectiveness of the data processing. In this study, the acceleration and deceleration range is set as [ − 6m*/s2 to 5 m/*s2] as recommended in early studies (Treiber and Kesting, 2013; Thiemann et al., 2008).

2.2. Microscopic simulation model development

Based on the UAV video and the extracted trajectories, a real-world signalized intersection is modeled in the Simulation of Urban MObility (SUMO) software (Lopez et al., 2018) as a testbed. SUMO provides a relatively realistic environment with different traffic models, capable of simulating traffic movement in a microscopic way.

The geometry design of this intersection model, including lanesetting, traffic lights deployment, etc., and traffic flow parameters such as volume and speed were used as inputs based on the field data obtained from the UAV. Besides, in the model development, the Application Programming Interface (API) for SUMO, called the Traffic Control Interface (TraCI) (Wegener, 2008), was applied to simulate the traffic flow and control vehicle movements realistically. In this study, vehicle lane-change behavior control is crucial, especially when vehicles approach the stop line. This is because, at most signalized intersections, solid lines are used instead of dash lines to separate different lanes in the area before the stop line. In this area, vehicles are prohibited from changing lanes. Moreover, TraCI allows users to customize the simulation output data in detail as well (Wegener, 2008).

To measure the goodness-of-fit of the simulation results, the distributions of the simulated safety indicators were compared to the field data. Specifically, the Kullback–Leibler divergence (Kullback and Leibler, 1951) is used to quantify the "distance" between two distributions. The Kullback–Leibler divergence from Q to P is defined in Eq. (1) below. The discrete distributions P and Q, denoting the simulated and observed safety indicator distributions respectively defined on the same probability space ψ.

$$D{KL}(P||Q) = \sum{x \in y} P(x) \log \left(\frac{P(x)}{Q(x)}\right)$$ (1)

2.3. Shockwave at signalized intersections

Shockwave analysis is important and widely applied at signalized intersections because traffic lights generate shockwaves cyclically. During each cycle, vehicles will follow an approach-slow down-stopspeed up-leave process. Moreover, with the increased number of vehicles (U.S. Department of Transportation, 2023), the vehicle queue may become longer, resulting in a longer shockwave duration.

In this study, shockwaves at signalized intersections are analyzed through the following steps, including shockwave identification, shockwave area analysis, and shockwave speed calculation. For shockwave identification, the state of each vehicle is classified into "Moving" or "Stopped" based on the speed criteria in Eq. (2) (Ramezani and Geroliminis, 2015). *St i*and *vt i*represent the state and speed of vehicle i at time t, where vthreshold means the threshold value for changing the vehicle state into this classifier, which is considered to be 3.6 km/h based on previous studies (Ramezani and Geroliminis, 2015; Wan et al., 2019).

$$S{i}^{t} = \begin{cases} \textit{Moving}, \textit{if} v{i}^{t} > v{\textit{threshold}} \ \textit{Stopped}, \textit{if} v{i}^{t} \leq v_{\textit{threshold}} \end{cases}$$ (2)

The shockwave start point for each vehicle can be identified when the vehicle changes its state from "Moving" to "Stopped". The shockwave speed can be estimated using a linear function to fit those identified start points, where the slope of the line represents the shockwave speed (Wan

Fig. 1. Example of Video Data: (a) Studied Intersection Location (. Source: Google Map); (b) Video Captured by UAVs; (c) Detected and Tracked Vehicles in a Frame; and (d) Extracted Vehicles Trajectories

Fig. 2. Scatter Plots of Acceleration / Deceleration Values for Raw Trajectory Data (Left) and Processed Trajectory Data (Right).

Table 1 Data used in the Simulation Model Calibration Process.

Data Type Description
Road
Features		 Road Length Collected through recorded video and Google
Map
Lane Setting Collected through recorded video
Traffic Lights Actual traffic signal timing
Speed Limit Actual speed limit
Intersection Collected through the recorded video and
Connections validated with actual situation
Vehicle Vehicle Type Type of the vehicles in the simulation
Model Vehicle Length Length of vehicles of this type
Min-gap Minimum safety distance of vehicles of this
type
Acceleration The acceleration ability of vehicles of this type
Traffic
Flow		 Traffic Volume Extracted from the video

et al., 2019). Likewise, the shockwave endpoint for each vehicle can be determined when the vehicle state changes from "Stopped" to "Moving". Once the two boundaries for the shockwave start and end are established, the shockwave impact area can be defined.

2.4. Surrogate safety measures

Two types of representative SSMs with different perspectives are utilized as performance metrics to profile how traffic conflict risk changes in the queue along with shockwave propagation. In this study, conflicts are analyzed using time-based SSMs (e.g., time to collision (TTC) and modified time to collision (MTTC) (Ozbay et al., 2008), and deceleration-based SSMs (e.g., deceleration rate to avoid a crash (DRAC) (Almqvist et al., 1991). The risk then be categorized into different levels based on the range of these SSMs.

One of the most common time-based SSMs is TTC, which was pro-

Fig. 3. Compared Caputed Video Data (Left) with the Simulated Model (Right).

Fig. 4. Calibration Results of SSMs's Distribution.

posed in the early study (Hayward, 1972). TTC is defined in Eq. (3).

$$TTC = \begin{cases} \frac{D}{\Delta v}, & \text{if } \Delta v > 0 \ \infty, & \text{otherwise} \end{cases}$$ (3)

here, the D is the relative distance between two vehicles and the Δv is the relative speed. This definition of TTC signifies that only if the speed of the following vehicle is greater than that of the leading vehicle a collision will happen. However, such an assumption ignores many potential conflicts due to acceleration or deceleration discrepancies (Ozbay, 2008; Yang et al., 2012). In shockwave analysis, considering the acceleration and deceleration will be important, MTTC is used in subsequent evaluation. MTTC can be calculated by Eq. (4).

For the deceleration-based SSMs, DRAC is utilized to determine the rear-end conflict risk. DRAC is the minimum braking rate required for a vehicle to avoid collision with another vehicle. The calculation of DRAC assumes that one vehicle takes evasive actions while the other retains its speed and direction. The formula is defined in Eq. (5), with the parameter definitions remaining the same as those in TTC and MTTC calculations.

According to Eq. (3–5), three conflict indicators are calculated for each pair of vehicles in the queue. For both TTC and MTTC, the minimum value represents the highest risk, while DRAC shows the opposite

Fig. 5. Identified Shockwave in Field Trajectory Data.

relationship. Moreover, the threshold for each indicator is necessary to determine the number of conflicts and category of each risk level.

vL(t) : Leadingvehicleʹ sspeed(m/s);

$$MTTC = \begin{cases} \min\left(t{1} = \frac{-\Delta v - \sqrt{(\Delta v)^{2} + 2\Delta aD}}{\Delta a}, t{2} = \frac{-\Delta v + \sqrt{(\Delta v)^{2} + 2\Delta aD}}{\Delta a}\right), & \text{if } t{1} > 0, t{2} > 0, \Delta a \neq 0 \ t{1} = \frac{-\Delta v - \sqrt{(\Delta v)^{2} + 2\Delta aD}}{\Delta a}, & \text{if } t{1} > 0, t{2} \leq 0, \Delta a \neq 0 \ t{2} = \frac{-\Delta v + \sqrt{(\Delta v)^{2} + 2\Delta aD}}{\Delta a}, & \text{if } t{1} \leq 0, t{2} > 0, \Delta a \neq 0 \ \frac{D}{\Delta v}, & \text{if } \Delta a = 0, \Delta v > 0 \end{cases}$$

$$(4)$$

$$DRAC = \begin{cases} \frac{(\Delta \nu)^2}{2D}, & \text{if } \Delta \nu > 0\ 0, & \text{otherwise} \end{cases}$$ (5)

Where,

Δv : Relativespeed(m/s), Δv = vF(t)− vL(t);

vF(t) : Followingvehicleʹ sspeed(m/s);

$$\Delta a = Relative acceleration(m/s^2), \Delta a = a_F(t) - a_L(t);$$

aF(t) : Followingvehicleʹ sacceleration( m/s 2)

aL(t) : Leadingvehicleʹ sacceleration( m/s2) ; and

D = Initialrelativedistance(m), t = Time(s).

Fig. 6. Conflict Risk Results: (a) MTTC Events in Field Trajectory Data; (b) DRAC Events in Field Trajectory Data; (c) MTTC Events in Simulation Data; and (d) DRAC Events in Simulation Data.

3. Analysis and results

3.1. Vehicles detection, tracking and trajectories processed results

In this study, a signalized intersection located at Xing'an Road and N 2ndRing Road in Hohhot, Inner Mongolia, China, was selected as the study site (The coordinates are 40.865818, 111.694046). The location and UAV recorded area of this intersection are shown in Fig. 1(a). The data used in this study were recorded at this intersection at 5 PM, corresponding to the city's typical evening peak hour. A sample video frame and detailed information are presented in Fig. 1(b). The detected and tracked vehicle results from the same frame are shown in Fig. 1(c). For data analysis, the research team selected a five-minute length video, which covers a complete traffic light cycle for the case study. The extracted trajectories from this video are plotted in Fig. 1(d).

Regarding the trajectory analysis, the acceleration and deceleration

values for each frame in both the raw and processed data are summarized in Fig. 2. The analysis shows that part of the raw data exhibits deviations from the rational interval [ − 6m*/s2 to 5 m/s2],* indicating that the percentage of data points outside the restricted range is high. These outlying data points may lead to significant errors in the research. However, after applying smoothing and sampling operations to the raw trajectories, the outliers were eliminated effectively. The proportion of acceleration and deceleration data beyond the acceptable range was reduced to less than 1 %, and all extracted speed values were below the speed limit (60 km/h), which improves the trajectory data reliability for further analysis.

3.2. Simulation model calibration and validation

Based on the UAV video and extracted trajectory data, a microsimulation model was built and calibrated. The calibrated parameters in this model and their description are summarized in Table 1. In the captured video, there are two types of vehicles including passenger vehicles and buses. The length, min-gap, and acceleration parameters of each type were calculated based on the mean of the extracted vehicle data from the video and the recommended value from SUMO's official documentation (SUMO, 2023). The simulation model comparison with the video is presented in Fig. 3, while the calibration results for SSMs' distributions are shown in Fig. 4. The DKL calculated from Eq.1 for MTTC and DRAC are 0.2388 and 0.0474, respectively, indicating acceptable results of the simulation from the conflict perspective (Sha et al., 2023).

3.3. Shockwave identification and conflict risk analysis

The identified shockwave in one through-movement lane was selected for analysis and is presented in Fig. 5. The fitted red solid line shows the shockwave propagating along the queue from beginning to end, and the blue solid line represents its dissipation. On average, the dissipation speed is faster than the propagation speed. For the conflict risk analysis, the results are summarized in Fig. 6. The MTTC threshold is selected as three seconds (Sha et al., 2023; Qu et al., 2014), and each indicator is categorized in 0.5-second interval to distinguish different conflict risk levels. The observed results are shown in Fig. 6(a) and (b) for MTTC and DRAC, respectively, and the simulated results are shown in Fig. 6(c) and (d).

Based on MTTC results, the conflicts occur before the shockwave propagates, specifically when the vehicles approach and join the queue. Both the observed and simulated results show that most MTTC values fall into the range of 1.5 s to 2.5 s during this queueing process. A small proportion of medium-risk MTTC (e.g., MTTC <=1.5 s) may also be generated, and some lower-MTTC events (e.g., MTTC <=1s) occur in the field when vehicles approach the end of the long queue. Similarly, DRAC conflicts also occur before the shockwave starts to propagate. One of the differences between the observed and simulated results is that higherrisk DRAC events occur in the simulation only when vehicles are approaching. Moreover, fewer MTTC conflicts occur in the simulation compared to actual observations. This difference may be attributed to the use of the default car-following model in the simulation, where related parameters may need further adjustment instead of using the default settings Another interesting finding is that both two types of SSMs propagate along with the queue as it increases. This suggests that conflict risk propagates with the queue and there is a "Conflict-wave" during the vehicle's stop-and-go process, especially when vehicles approach the end of the queue.

4. Discussion

Based on the results, several questions deserve further discussion. The results show that conflicts with different risk levels can occur and propagate with an accumulating queue. However, whether this impact still exists when the approaching rate changes has not been explored. Different scenarios with varying parameters (e.g., speed limit, acceleration or deceleration ability, etc.) may generate different conflict situations, warranting additional investigation efforts.

Moreover, some key points need to be elaborated. First, in the study area, the crash report data are not available, bringing challenges to investigating the relationship between SSMs indicators and field crashes. Additionally, for safety purposes, the operation of UAVs at intersections with high-density traffic flow in the downtown area is strictly regulated, making it challenging to maneuver the UAV for continuous video recording over a long period. Also, there are a few limitations in this research that could be overcome and improved in future studies. These include but are not limited to: i) Considering the aggressive and abnormal driving behavior; ii) Adding more different intersections with different geometric and traffic flow characteristics into the simulation, and iii) The data sample in this research is relatively limited. Capturing more sample videos for calibrating and validating the simulation model should be considered in further studies.

5. Conclusions

In summary, this study used a microscopic simulation approach to examine traffic conflict risk when shockwaves propagate during the vehicles' stop-and-go processes at signalized intersections. Vehicle trajectory data extracted from UAV video was utilized as input for the simulation model calibration and validation from both operational and safety perspectives. By simulating traffic flow at the well-modeled signalized intersection and analyzing two types of SSM indicators (i.e., MTTC, and DRAC) with shockwave propagation, the study demonstrated a strong relationship between traffic conflict risk and shockwaves in the queue. Moreover, different levels of risk occur when vehicles approach the end of the queue. With a growing queue, most rear-end risks are presented at the tail and propagate along with shockwave. These findings provide additional insights into traffic safety issues at signalized intersections, supplementing existing studies that have focused on the optimization of signal controls mainly from operational perspectives.

CRediT authorship contribution statement

Junqing Wang: Conceptualization, Data curation, Formal analysis, Methodology, Software, Validation, Visualization, Writing – original draft. Hong Yang: Conceptualization, Data curation, Formal analysis, Methodology, Project administration, Supervision, Writing – original draft. Yuan Zhu: Data curation, Formal analysis, Software, Visualization, Writing – review & editing. Kun Xie: Formal analysis, Writing – original draft. Zizheng Yan: Formal analysis, Methodology, Writing – original draft. Qingwen Pu: Formal analysis, Visualization, Writing – original draft.

Declaration of competing interest

The authors declare the following financial interests/personal relationships which may be considered as potential competing interests: co-author serves in the Editorial Advisory Board for the journal – KX. If there are other authors, they declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.

Acknowledgments

We highly thank the great support for data collection from the Traffic Police Department in Hohhot City. The UAV data collection team including Yiming Pan and Siying Chen in the Inner Mongolia Transportation Data Analysis and Visualization Laboratory are appreciated. The early version of this paper has been presented at the Road Safety and Simulation (RSS2024) Conference in Kentucky and was awarded as the Best Student Paper and invited for the AAP special issue. We appreciate the suggestions and recommendations by RSS2024 scientific review committees and reviewers that helped improve the paper for the special issue. The contents of this paper present the views of the authors who are responsible for the facts and accuracy of the data presented herein. The contents of this research do not necessarily reflect the official views or policies of any agencies.

Data availability

As the data were from field recorded video, some processed data may be shared with reasonable request.

References