category: literaturenote citekey: majiadvancedtrafficconflictanalysis2025 title: Advanced traffic conflict analysis for safety evaluation at roundabouts under mixed traffic using extreme value theory authors: "Maji, Abhijnan; Ghosh, Indrajit" year: 2025 date: 2025-00-00 2025 doi: 10.1016/j.aap.2025.108108 publication: "Accident Analysis & Prevention" url: "https://doi.org/10.1016/j.aap.2025.108108" zotero_key: 92HCBURI zotero_storage: 754MUZJP collections: transpordi_planeerimine folder: 001_artiklid firstAuthor: "Maji, Abhijnan"

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Accident Analysis and Prevention

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

Advanced traffic conflict analysis for safety evaluation at roundabouts under mixed traffic using extreme value theory

Abhijnan Maji , Indrajit Ghosh *

Department of Civil Engineering, Indian Institute of Technology (IIT) Roorkee, Roorkee, Uttarakhand 247667, India

ARTICLE INFO

Keywords: Roundabout safety Surrogate safety measures Extreme value theory Peak over threshold Conflict frequency Conflict severity

ABSTRACT

Roundabout safety evaluation in non-lane-based, heterogeneous traffic conditions in low-middle-income countries brings challenges due to unavailable/unreliable crash data, thereby switching to the utilization of safety surrogates. This study employed high-resolution drone videos and advanced image-processing techniques to extract vehicular trajectories. Traffic conflicts were identified using Surrogate Safety Measures (SSMs), namely, Time-to-Collision (TTC) and maximum post-collision (hypothetical) velocity difference (MaxDeltaV). Extreme Value Theory (EVT) was used to determine threshold values for TTC (1.25 s) and MaxDeltaV (4.5 m/s). By employing the determined thresholds in the Surrogate Safety Assessment Model (SSAM) tool developed by the Federal Highway Administration (FHWA), conflicts were classified into lane-change (42 %), rear-end (33 %), and crossing (25 %) types. An AdaBoost regressor model was developed using a negative binomial objective function for conflict frequency prediction. SHAP analysis revealed that increased circular road widths reduced conflict frequency, while higher conflicting and approaching traffic volumes increased the likelihood of conflicts. Based on TTC and MaxDeltaV values, hierarchical and two-step clustering techniques classified the identified conflicts into four severity levels: low (33.8 %), moderate (34.1 %), high (19.3 %), and very high severity (12.8 %). An Ordered Probit model predicted conflict severity based on geometric, traffic, built-environmental factors, and conflict types, with a prediction accuracy of 88.4 %. Larger central island diameters and circulatory road widths reduced severity, while higher average speeds increased conflict severity. This research presents a novel framework that applies EVT to establish SSM thresholds for unsignalized roundabouts under mixed traffic, integrating advanced statistical and machine learning techniques to assess conflict frequency and severity proactively.

1. Introduction

The demand for innovative methods to assess the safety of road users is increasing with the proliferation of smart cities and their corresponding advanced mobility needs. Annually, road traffic crashes (RTCs) result in around 1.19 million deaths globally (World Health Organization, 2023). RTCs are most prevalent in low- and middleincome countries (LMICs), accounting for over 90 % of cases (World Health Organization, 2023). Consequently, the United Nations has established road traffic safety as a specific objective of the 2030 Agenda for Sustainable Development Goals, namely target 3.6 (Sustainable Development Goals, 2020). According to the road traffic crash statistics released by the Ministry of Road Transport and Highways, Government of India, there were 461,312 road accidents in India in 2022 (MoRTH, 2023). These road accidents have resulted in a fatality count of 168,491 individuals and reported injuries to 443,366 people. It is generally agreed that roundabouts are the safest type of intersection among the various types of at-grade intersections. On the contrary, a total of 11,410 accidents took place at Indian roundabouts, resulting in 4,051 fatalities and 10,636 injuries (MoRTH, 2023). Similar crash statistics from several LMICs have shown that roundabouts can present substantial safety challenges. The characteristics of traffic also influence the behavior of drivers at roundabouts (Maji & Ghosh, 2025; Vinayaraj & Perumal, 2023b). Mixed traffic in developing countries such as India encompasses a diverse range of vehicle types, including cars, trucks, bicycles, buses, rickshaws, pedestrians, and others (Maji et al., 2022). The combination of diverse traffic mix and lack of lane discipline presents a greater level of complexity and difficulty in navigating roundabouts (Maji & Ghosh, 2025).

The analysis of historical crash data is an essential component of the

E-mail addresses: a\_maji@ce.iitr.ac.in (A. Maji), indrafce@iitr.ac.in (I. Ghosh).

^* Corresponding author.

conventional approach employed to evaluate and enhance road safety. However, crash data in LMICs often face significant problems concerning their availability, accuracy, and sufficiency (Dandona et al., 2008). Therefore, researchers have chosen to use surrogate safety measures (SSMs) such as the spatial and temporal proximity indicators, namely time to collision (TTC) and post encroachment time (PET) measures, as a reliable and alternative approach to evaluate road safety (Caliendo & Guida, 2012; Osama et al., 2016; Tesoriere et al., 2018). Many studies have demonstrated that traffic conflict analysis is a reliable method for estimating the frequency and severity of crashes (Arun et al., 2022a, 2022b; Fu & Sayed, 2021a, 2021b). The transition of approach from a reactive one, which depends on crash data, to a proactive one, which employs traffic conflict data, has become crucial for improving road safety, especially for the forthcoming generation of Connected and Autonomous Vehicles (CAVs) (Mannering et al., 2020; Virdi et al., 2019). Moreover, the traffic conflict technique is a potent method for examining the factors that impact road safety in situations where crash data reports are unavailable or essential information is lacking. This approach eliminates the necessity of waiting for additional road crashes and fatalities to occur before implementing the necessary actions and countermeasures. The surrogate safety indicators employ different threshold values to categorize the level of risk associated with a conflict and the likelihood of the conflict escalating to a collision. By establishing an appropriate threshold value for a safety indicator in a particular application scenario, it is possible to rapidly determine whether the conflict has the potential to result in an actual crash. The threshold values considered in different existing studies (mostly in developed countries) cannot be directly used in the present study due to dissimilar traffic environments (i.e., non-lane-based highly mixed traffic conditions) prevalent in the case of LMICs (Maji & Ghosh, 2025). Hence, it is imperative to explore techniques such as Extreme Value Theory (EVT) to ascertain the appropriate threshold values for SSMs based on the particular site conditions. To the best of the authors' knowledge, there is no study in which the determination of threshold values for surrogate safety indicators has been investigated in the context of unsignalized roundabouts under non-lane-based highly heterogeneous traffic scenarios.

The application of emerging advanced computer vision and image processing methods enhances the precision of vehicle detection and tracking, as well as the extraction of vehicular trajectory data and traffic conflict measures. The traffic conflict measures can be used to evaluate road safety in real-time (Hu et al., 2022). Therefore, surrogate safety measures (SSMs) are becoming increasingly important for the future of road safety assessment, as they incorporate the utilization of cuttingedge technologies such as image processing, vehicle tracking, and video recording by Unmanned Aerial Vehicles (UAVs) (Xie et al. 2019; Yang et al. 2021). In the context of safety analysis, traffic surveillance video data obtained from street-level cameras are frequently utilized. However, it is important to note that the data captured through these cameras also have certain limitations (Gu et al., 2019). Firstly, analysis can only be conducted in the specific locations where the cameras are deployed. Furthermore, the cameras are generally placed at relatively low heights, thereby limiting the available recording area. Lastly, the videos obtained by these cameras are recorded at an inclined angle, which may lead to inaccuracies in extracting vehicle trajectories and quantifying the resulting SSMs (Gu et al., 2019). Due to its exceptional maneuverability, affordability, flexibility, and capacity to capture a bird's-eye perspective, aerial imagery is an appropriate substitute. Consequently, the present study employs high-resolution aerial videos that have been manually collected as the data source for the extraction of vehicle trajectories and safety performance measures.

The main contributions of this study are (i) the use of UAV-recorded videos to produce high-quality vehicular trajectory data using advanced image processing techniques for safety analysis, (ii) the determination of threshold values for different SSMs using extreme value theory (EVT), (iii) the application of SSM threshold values to identify traffic conflicts (number and type) at roundabouts using the Surrogate Safety Assessment Model (SSAM) of the Federal Highway Administration (FHWA), (iv) the development of a conflict frequency based predictive model to evaluate the relationship among conflict numbers, traffic characteristics, and geometric features, (v) introduction of Hierarchical and Two-step clustering for conflict severity classification, (vi) development of a conflict severity-based safety performance function (SPF) using Ordered Probit model. Overall, a thorough assessment of roundabout safety has been conducted using the traffic conflict technique and video recordings from Unmanned Aerial Vehicles (UAVs).

2. Literature review

Scientific investigations on roundabout safety have mostly concentrated on two main methodologies: crash-based and conflict-based strategies. The Traffic Conflict Technique (TCT) is a proactive method that does not necessitate the use of historical crash data before doing the analysis (Sadeq & Sayed, 2016). Trajectories of vehicles within roundabouts are usually obtained using two approaches. The first procedure involves the extraction of vehicular trajectories from static camera- or UAV-recorded video images by utilizing image processing techniques. The second approach employs microsimulation software such as PTV VISSIM, AIMSUN, and other similar tools to obtain trajectory data. The present study focuses on the extraction of vehicular trajectories from UAV video footage using advanced object detection and tracking algorithms. A limited number of research works have utilized trajectory data from UAV-recorded videos to evaluate the safety of roundabouts by employing SSAM (Hasanvand et al., 2023; Shawky et al., 2023). Nevertheless, these assessments only employed the SSAM approach to identify the number of conflicts, their types, and spatial distribution and did not include the technique for predicting conflict frequency and categorizing conflicts based on their related severity.

In recent times, researchers have been using a platform called DataFromSky (https://datafromsky.com/) for the extraction of vehicular trajectory data from aerial videos. DataFromSky uses advanced image processing techniques to generate accurate vehicle trajectory data (Xie et al. 2019; Yang et al. 2021). The UAV capture videos undergo processing, whereby the trajectories of vehicles are transformed into a '. trj' file format (Hasanvand et al., 2023; Sha et al., 2023). Further, most research studies on roundabout safety using microsimulation have utilized the Surrogate Safety Assessment Model (SSAM) software to detect traffic conflicts from the '.trj' file (Hasanvand et al., 2023; Maji & Ghosh, 2025). Most studies have used the TTC (Time to Collision) and Post-Encroachment Time (PET) as surrogate measures in the context of SSAM (Al-Ghandour et al., 2011; Bulla-Cruz et al., 2021; Gallelli et al., 2019; Ghanim et al., 2020; O. Giuffr[e et al., 2018;](#page-16-0) T. Giuffre et al., 2017; Morando et al., 2018; Shawky et al., 2023; Virdi et al., 2019). In addition to TTC and PET, a number of studies have also investigated safety indicators like MaxDeltaV, Maximum Speed (MaxS), and Deceleration Rate (DR) (Hasanvand et al., 2023; Karwand et al., 2023; Leonardi & Distefano, 2023; Liu et al., 2020; Vasconcelos et al., 2014). According to the results of the previous studies, multivariate models outperformed their corresponding univariate counterparts in identifying potentially dangerous conflicts. The safety analysis in the present study has utilized TTC, PET, MaxD, and MaxDeltaV as surrogate safety indicators. The definitions of these parameters are as follows:

a. TTC, or time to collision, refers to the "minimum collision time between two vehicles that will collide with each other if they do not change their direction of movement." TTC is calculated based on the "current location, speed, and future trajectory of two vehicles at a given instant" (Gettman et al., 2008).
b. PET, or post encroachment time, refers to the time difference between the last occupation of a position by the first vehicle and the subsequent arrival of the second vehicle to that same position (Gettman et al., 2008).
c. MaxD refers to the highest rate of deceleration performed by the second vehicle, which is measured as the lowest instantaneous acceleration rate observed during the conflict event (Gettman et al., 2008).
d. MaxDeltaV refers to the maximum value of change in velocities (conflict velocity and post-collision velocity) of two vehicles involved in a "hypothetical collision" situation (Gettman et al., 2008). The magnitude of this change in velocities can provide insight into the extent of severity of the collision.

In previous studies, extreme value theory (EVT) has been widely employed for the purpose of categorization and modeling of traffic conflicts. EVT offers a systematic approach to examining the likelihood of extreme events using relatively brief periods of observation. Conflictbased Extreme Value Theory (EVT) models allow for the extrapolation of rare crashes from more frequently observed conflicts. Two notable approaches are included in this framework: the generalized extreme-value (GEV) distribution, also referred to as the block-maxima (BM) approach, and the generalized Pareto distribution (GPD), also known as the peakover-threshold (POT) approach. The extreme events are modeled using the GEV distribution in the BM approach, which emphasizes the identification of maximum values within non-overlapping blocks of data. This approach proves to be especially advantageous when there are extreme values that appear in clearly defined and distinct intervals of time or space. This method enables the calculation of extreme event probabilities by considering the highest values encountered within these specified blocks. Conversely, the POT method employs the GPD to evaluate the likelihood of extreme events. The POT method focuses on data points that surpass a pre-established threshold. In this method, only instances that exceed the designated threshold are considered. The GPD is subsequently used to represent these instances of exceedance and calculate the probability of extreme events occurring in the tail. The POT method is particularly beneficial when extreme events are rare and do not follow a monotonic distribution. It demonstrates its utility in situations where the emphasis is on the most extreme values that exceed a specified threshold. Several studies have demonstrated that EVT is a highly promising approach for the modeling of traffic conflicts (Arun et al., 2022b; Fu and Sayed, 2021a,b, 2022, Kumar and Mudgal, 2024a, b; More et al., 2024; Niu et al., 2024; Zheng and Sayed, 2019a; Arun et al., 2022a). Moreover, vehicular conflicts can be distinguished from regular traffic interactions by applying an appropriate threshold value to a specific surrogate safety indicator (Maji & Ghosh, 2025). The choice of an unsuitable threshold would result in an inaccurate estimation of traffic conflicts, hence overrepresentation or underrepresentation of the crash risk (Niu et al., 2024).

The factors influencing the frequency and severity of roundabout crashes have been extensively investigated in several studies. Researchers have used a range of modeling techniques, such as negative binomial (NB) regression (Burdett et al., 2017; Daniels et al., 2010b; Mandavilli et al., 2009), multiple logistic regression (Zheng et al., 2010), zero-inflated Poisson regression (Chen et al., 2013), zero-inflated negative binomial regression (Anjana & Anjaneyulu, 2014), Poisson regression (Bagdade et al., 2011; Dixon and Zheng, 2013), and zeroinflated Poisson regression (Chen et al., 2013). Rodegerdts et al. (2007) devised Safety Performance Functions (SPFs) for roundabouts, taking into account the annual average daily traffic (AADT), number of legs, and number of circulatory lanes as influencing variables. Anjana and Anjaneyulu (2014) examined the safety of roundabouts at the approach level, considering both the geometric as well as traffic characteristics. In developing the NB SPF model, Kim and Choi (2013) took into account several geometric factors, including the number of legs, circulating lane width, entry width, flare length, and flare width. A positive correlation between the frequency of crashes and both the traffic volume and the inscribed circle diameter was observed by Kamla et al. (2016). The study conducted by Al-Marafi et al. (2020) revealed that several factors, including number of entry lanes, entry width, entry radius, traffic volume, circulatory roadway width, weaving width, and speed limit, have an impact on the roundabout safety. Katrakazas et al. (2021) employed zero-inflated NB, conventional NB, and quasi-Poisson models to develop conflict-based SPFs for estimating conflict frequency in lane-based traffic environments. Vinayaraj and Perumal (2023b) developed crash-based SPF models for exit, entry, and circulatory lanes, taking into account mixed traffic scenarios. Moreover, cluster analysis has been employed in many pre-existing studies to investigate problems in transportation systems associated with the perception of risk while driving (Oltedal and Rundmo, 2007), the likelihood of cyclists being injured in road traffic crashes (Vandenbulcke et al., 2009), the attitude of drivers' regarding safety on roads (Thibenda et al., 2022), and roundabout safety perception (Distefano et al., 2018). A classification of the severity of conflicts in terms of the safety indicators was accomplished by Kumar et al. (2019) through the utilization of k-means clustering and silhouette plots. Polders et al. (2015) and Daniels et al. (2010a) employed a logistic regression model to figure out and explain the factors influencing the severity of crashes at roundabouts. Vinayaraj and Perumal (2023a) developed an ordered probit model to investigate the relationship between crash severity and different roundabout geometric features, traffic characteristics, and crash types in mixed traffic conditions. Previous studies have shown that roundabout safety investigations mostly relied on historical crash data and were conducted under homogeneous lane-based traffic conditions. Inadequate research has been performed on the SPF modeling for evaluating roundabout safety, particularly in non-lane-based mixed traffic scenarios. One of the objectives of this study is to develop a conflict-based SPF to evaluate the safety situation and estimate the frequency and severity of conflicts at roundabouts operating under highly heterogeneous non-lane-based traffic scenarios.

3. Methodology

This study presents a comprehensive methodology for the assessment of roundabout safety (following a proactive approach) under non-lanebased highly mixed traffic conditions prevailing in the case of LMICs like India. In the present study, the UAV-captured videos over busy unsignalized roundabout sites were processed using advanced image processing techniques to extract the trajectory data. Subsequently, the trajectory data is imported to SSAM 3.0 to identify the traffic conflicts and their types and obtain the corresponding safety measures, i.e., TTC, PET, MaxS, DeltaS, MaxD, DR, and MaxDeltaV. SSAM categorizes conflicts into three types based on their angles: rear-end conflicts (0–30 degrees), lane-change conflicts (30–80 degrees), and crossing conflicts (80–180 degrees) (Fig. 1) (Gettman et al., 2008). Next, EVT was employed to select suitable threshold values for the SSMs. The number of conflicts obtained after applying the appropriate threshold values was utilized for the development of the conflict frequency prediction model.

Fig. 1. Ranges of conflict angles for different conflict types.

Further, the SSMs were used to define different severity levels of the conflicts utilizing the clustering techniques. Finally, a conflict severity prediction model was constructed. Fig. 2 represents the schematic diagram of the overall structure of the present study.

3.1. Data collection and extraction

Data collection for the current study was conducted at roundabouts located in several cities across different regions of India. A selection of 14 unsignalized roundabouts was made from various cities in northern and eastern India. During the peak hours of traffic flow, the study roundabouts were videotaped in 4K-30 frames per second resolution using a UAV called DJI Mini 3 Pro from a height of 120 m. A thumbnail image of each roundabout site has been presented in Fig. 3. Also, the locations of the selected roundabouts are presented in Table 1.

The extraction of vehicular trajectory data was performed using the DataFromSky platform. Each vehicle is allocated a unique ID and classified into passenger car, medium vehicle, heavy vehicle, bus, motorcycle, and tuk-tuk (i.e., auto-rickshaws and e-rickshaws). Following the input of the video data into the DataFromSky Viewer platform, the recorded video underwent an initial calibration process. The calibration parameters included considerations of speed, particularly at the approaches and circular section of the roundabout, as well as the positions of vehicles traversing the roundabout. In order to calibrate these measurements, Google Maps was used to acquire the coordinates of the reference points (in terms of latitudes and longitudes). The manual georegistration process in the DataFromSky Viewer software involves specifying the region of interest (RoI) and strategically positioning the reference points (usually more than 4 points) together with their corresponding geographic coordinates. The calibrating error value of the points was determined to be nearly zero. The calibration enabled the precision measurement of the speed and acceleration of the identified vehicles. Fig. 4 illustrates the process of defining the RoI, positioning reference points for calibration, and the trajectories of the vehicles. With the help of the DataFromSky Viewer software, a number of entry and exit gates were built to acquire information regarding the classified traffic volume, the circulating and approaching traffic volume, occupancy time, and other relevant traffic data. Following the guidelines provided by the Indian Highway Capacity Manual (2017) (Indo-HCM),

various traffic volumes were converted into passenger car units (PCUs). The percentage of passenger cars was found to be the highest (45.88 %), followed by 2.26 % for medium vehicles (such as pick-up trucks), 0.60 % for heavy vehicles (e.g., trucks, multi-axle vehicles, tractor-trolleys), 0.36 % for buses, 41.16 % for motorcycles, 2.76 % for bicycles, 1.26 % for pedestrians, and 5.72 % for tuk-tuks. Following a comprehensive examination of the videos, the trajectory data of the vehicles was compiled and stored in the '.trj' file format.

3.2. Safety diagnosis using SSAM

The actual field data in the form of vehicular trajectories (i.e., '.trj' files) were imported to the SSAM software to identify traffic conflicts based on the filter of SSMs set by the investigator. Depending on the values of the conflict angle (shown in Fig. 1), the ensuing conflict can materialize into a rear-end, lane change, or crossing collision. After importing the '.trj' files, suitable values of TTC and PET need to be set in order to identify potential conflicts from undisturbed passages. In the present study, the authors had set the maximum value of TTC and PET at 5 s simply to extract all the SSMs associated with all the interactions having TTC and PET values ≤ 5 s (Gettman et al., 2008; Souleyrette & Hochstein, 2012). For the current investigation, we selected four SSMs, namely minimum Time to collision (TTC), Post-Encroachment-Time (PET), Maximum Deceleration rate (MaxD), and Maximum postcollision change in Velocity between conflict and post-collision state (MaxDeltaV), after checking the distribution of the data. Once TTC, PET, MaxD, and MaxDeltaV data were extracted, these data were analyzed using EVT models to determine the suitable and appropriate threshold values of the SSMs corresponding to the collected data. Again, the determined threshold values of the SSMs from the EVT technique were re-entered in SSAM to identify and visualize the conflicts from normal interactions. The descriptive statistics of the surrogate safety indicators, the overall conflict count, and the frequency of each conflict type (i.e., rear-end, lane change, and crossing) were then extracted from the SSAM software.

3.3. Peak over threshold (POT)

In this method, data exceeding a predetermined threshold are

Fig. 2. Overall framework of the study.

Fig. 3. Thumbnail image of each of the roundabouts.

Table 1 List of selected roundabout sites for the study.

Site	Site name	City	Latitude	Longitude	Data collection period
1	ATS	Greater	28.5742	77.4266	1 h (5–6 p.m.)
	Roundabout	Noida
2	ITBP Aiccher	Greater	28.4666	77.5326	1 h (10–11 a.
	Roundabout	Noida			m.)
3	Alpha Circle	Greater	28.4682	77.5086	1 h (9–10 a.
	Roundabout	Noida			m.)
4	Durga Talkies	Greater	28.5091	77.4749	1 h
	Roundabout	Noida			(9:30–10:30 a.
					m.)
5	Surajpur-Kasna	Greater	28.4581	77.5205	1 h (10–11 a.
	Roundabout	Noida			m.)
6	Migsun Ultimo	Greater	28.4620	77.5558	1 h (10–11 a.
	Roundabout	Noida			m.)
7	Labour Chowk	Greater	28.4837	77.5201	1 h
	Roundabout	Noida			(9:30–10:30 a.
					m.)
8	Rayan School	Greater	28.4790	77.5120	1 h (9–10 a.
	Roundabout	Noida			m.)
9	Gautam Buddha	Kolkata	22.5917	88.4200	1 h (4:30–5:30
	Circle				p.m.)
10	Vivekananda	Kolkata	22.5848	88.4120	1 h (10–11 a.
	Circle				m.)
11	Kathgola	Kolkata	22.5934	88.4266	1 h (10–11 a.
	Roundabout				m.)
12	Laal Kuthi	Kolkata	22.5927	88.4147	1 h (5–6 p.m.)
	Island
13	Sukhna-Shanti	Chandigarh	30.7077	76.7673	1 h (9–10 a.
	Path Circle				m.)
14	Chandi Path	Chandigarh	30.7020	76.7725	1 h
	Roundabout				(9:30–10:30 a.
					m.)

identified as extreme occurrences. Previous research indicates that bivariate EVT models more accurately estimate crash risk compared to univariate models (Kumar & Mudgal, 2024a, 2024c, 2024b; Niu et al., 2024; Zheng & Sayed, 2019b). The present study also utilized extreme occurrences of traffic conflicts to fit a bivariate GPD model employing the POT strategy.

For univariate data, the GPD models the conditional excess y = X − u over a threshold u, where X is a random variable of interest (Coles, 2001). The univariate GPD is given by (Eq. 1):

$$G(y)=1-\left(1+\xi\frac{y}{\sigma_u}\right)^{\frac{1}{\xi}},y>0 \tag{1}$$

where ξ is the shape parameter, σ^u = σ +ξ(u − μ) is the scale parameter, and μ is the location parameter. This formulation captures the exceedance behavior by modeling the distribution tail, thereby allowing them to focus on extreme traffic conflicts that surpass critical threshold values.

The bivariate GPD allows to simultaneously model the behavior of two SSMs that exhibit extreme values, thereby capturing the joint distribution of exceedances in higher dimensions. Let (*X1, X*2) represent two independent and identically distributed random variables, each with a generalized Pareto distribution. The joint distribution for exceedances over thresholds *u*1 and *u*2 are modeled using a bivariate GPD, with each variable having its own marginal GPD. For large enough thresholds *u*1 and *u*2, the conditional excess y¹ = X¹ − *u*1|X¹ *> u*1 and y² = X² − *u*2|X² *> u*2 follows a GPD (Coles, 2001) (given in Eq. 2):

$$G_i(y_i) = 1 - \left(1 + \xi_i \frac{yi}{\sigma{u_i}}\right)^{-\frac{1}{\xi_i}}, y_i > 0$$ (2)

where Gi yi ) is the marginal GPD for the i-th variable, *ξi*is the shape parameter, and σui is the scale parameter for the variable Xi [i ∈ {1*,*2}]. In the bivariate setting, it is common to transform each variable to unit Fr´echet margins to facilitate joint modeling. The transformation for each variable Xi is given by Eq. (3). This transformation standardizes the margins of each variable, making it easier to model their joint distribution. The transformed variables (*X̃1,X*̃2) after transformation follow a

Fig. 4. Instances of the (a) setting of the RoI, (b) reference points for calibration, (c) vehicular trajectories.

common distribution, thereby describing their joint behavior.

$$\widetilde{X}{i} = -\frac{1}{log\left(1 - \frac{G{i}(y{i})}{G{i}(u_{i})}\right)}, i = 1, 2$$ (3)

The joint distribution of the transformed variables (*X̃1,X*̃2) is modeled by the bivariate GPD. The bivariate GPD is expressed as Eq. (4), where V ( *X̃1, X*̃² ) is a homogeneous function of degree 1, defining the dependence structure between the variables. One common choice for V(.) is given in Eq. (5).

$$G\left(\widetilde{X}{1},\widetilde{X}{2}\right) = \exp\left{-V\left(\widetilde{X}{1},\widetilde{X}{2}\right)\right}$$ (4)

$$V\left(\widetilde{X}{1},\widetilde{X}{2}\right) = 2\int{0}^{1} max\left(\frac{w\widetilde{X}{2}}{\widetilde{X}{1} + \widetilde{X}{2}}, \frac{(1-w)\widetilde{X}{1}}{\widetilde{X}{1} + \widetilde{X}_{2}}\right) dH(w)$$ (5)

Where w represents the weight that distributes the extreme behavior between the two variables, and H(w) is the distribution of these weights on the unit interval.

The mean residual life (MRL) plot and threshold stability (TS) plot were utilized for determining the threshold values of TTC and MaxDeltaV. In the case of the MRL plot, an appropriate threshold value was found by closely observing the lowest point in the graph after which the plot becomes almost linear (Niu et al., 2024). Similar to the MRL plot, a threshold was also determined from the TS plot, where the scale and shape parameters remain nearly constant, and the graph becomes linear (Niu et al., 2024). If the exceedances of a random variable X = (*X1, X2,* ⋯ , Xn) adhere to the GPD for a specified threshold *u*0, then for any higher threshold value u (*> u*0), the exceedances will similarly conform to the GPD with shape parameter ξ and scale parameter σu(Coles, 2001).

$$\sigmau = \sigma{u_0} + \xi(u - u_0) \tag{6}$$

Eq. (6) indicates that σ^u − ξu = σ^u⁰ − ξu⁰ = σ* is invariant with respect to u. This signifies that the parameters σ* and ξ will be invariant, barring sampling fluctuations. The TS plot illustrates the variation in parameters σ* and ξ across different threshold values (u). The threshold value at which both parameters remain constant, i.e., the plot becomes linear, is designated as the final threshold value (*u*0).

3.4. Conflict frequency prediction

To choose appropriate variables for the traffic conflict frequency prediction model development and explore the relationships between independent and dependent variables, a Spearman correlation analysis was performed in IBM SPSS version 27. Various traffic and geometric variables were considered as independent variables. The number of traffic conflicts obtained from the joint exceedances was considered dependent variable. In developing the model, only variables with a correlation coefficient > 0.3 and < 0.8 and a significance level less than 0.05 were considered.

An AdaBoost framework with a Negative Binomial (NB) objective function was utilized for the model development. The authors employed the NB distribution because of the count and overdispersed (i.e., variance exceeds the mean) characteristic of the dependent variable (Pande et al., 2017; Vinayaraj & Perumal, 2023b). The amalgamation of weak learners was employed to modify the training sample to derive a robust algorithm that achieves high accuracy with the dependent variable (Onan, 2020). This research employed 50 estimators to forecast the frequency of conflicts at roundabouts. The dataset was sampled randomly and divided into training and testing subsets, with 80 % of the data used for training and 20 % for testing. The discrepancy between the standard deviation of the actual conflict count and the predicted conflict count variance was quantified using Root Mean Squared Error (RMSE). The mean prediction error was measured using Mean Absolute Error (MAE) and Mean Absolute Percentage Error (MAPE). Additionally, RMSE, MAE, and MAPE were employed to assess the predictive accuracy of the developed model by quantifying the errors related to the test dataset.

3.5. Conflict severity prediction

The SSMs were extracted as '.csv' files from the SSAM software after filtering the conflicts based on the determined threshold values. The TTC and MaxDeltaV values associated with every conflict were employed to categorize the conflicts based on their severity levels through clustering techniques. Two clustering methods, namely (a) hierarchical clustering and (b) two-step clustering, were used to distinguish between levels of conflict severity. The hierarchical clustering facilitates the identification of the optimal number of clusters through the analysis of the dendrogram. This study employed Ward's method and squared Euclidean distance to generate compact and distinct clusters (Hair et al., 2014). Twostep clustering uses a pre-clustering step where the data is grouped into small sub-clusters using a distance measure (such as log-likelihood) and then applies hierarchical clustering to merge these sub-clusters into the final clusters. It automatically determines the optimal number of clusters by balancing the fit of the model with complexity, using criteria like Schwarz's Bayesian Criterion (SPSS, 2011).

Following the cluster analysis, an Ordered Probit (OP) model was developed to predict conflict severity, considering the severity categories as the dependent variable and geometric features of the roundabouts, traffic characteristics, built-environmental features, and conflict types as the independent variables. The OP model uses a continuous latent variable y* ⁱ = α +βxi +*εi*—where, xi is the set of independent

variables for observation i, , α and β are coefficient vectors, and *εi*is the error term—to predict the observed severity yi, which falls into one of m ordered categories based on thresholds applied to y* ⁱ . In the present study, m has 4 values, as 4 severity levels were determined from the cluster analysis, as mentioned in section 4.5. yi can be calculated using a stepwise function of latent measures (y* ⁱ ). Therefore, for m = 0, 1, 2, and 3, the values of y* *ⁱ*are mentioned in Eq. (7).

$$y{i} = \begin{cases} 0, if y{i}^{} \leq \mu{0} \ 1, if \mu{0} \leq y_{i}^{} \leq \mu{1} \ 2, if \mu{1} \leq y{i}^{*} \leq \mu{2} \ 3, if y{i}^{*} \geq \mu{2} \end{cases}$$

$$(7)$$

where μ is the threshold value of the unobserved variable in an ordered manner (i.e. *μ0< μ1< μ*2). The probability that the traffic conflicts were of a severity level of m (where m = 0, 1, 2, and 3) is calculated as follows (Eq. 8):

$$P(y_i = 0) = P(y_i^* \le \mu_0) = \Phi(\mu_0 - \alpha x_i)$$ (8a)

$$P(\mathbf{y}_i = 1) = P\big(\mu_0 \leq \mathbf{y}_i^* \leq \mu_1\big) = \Phi(\mu_1 - \alpha \mathbf{x}_i) - \Phi(\mu_0 - \alpha \mathbf{x}_i) \tag{8b}$$

$$P(y_i = 2) = P\big(\mu_1 \leq y_i^* \leq \mu_2\big) = \Phi(\mu_2 - \alpha x_i) - \Phi(\mu_1 - \alpha x_i) \tag{8c} \label{eq:8c}$$

$$P(y_i=3) = P(y_i^* \ge \mu_2) = 1 - \Phi(\mu_2 - \alpha x_i)$$ (8d)

where Φ(.) is the standard normal distribution of any variable t (say), which can be expressed as (Eq. 9):

$$\Phi(t) = \frac{1}{\sqrt{2\pi}} \int_{-\infty}^{t} e^{-\frac{1}{2}t^2} dt$$ (9)

The complete dataset with the severity levels and the various independent variables was randomly sampled in 80 (train):20 (test) ratio. The OP model was trained in IBM SPSS.

4. Results and discussion

This section presents the results of the application of the POT model for determining the appropriate threshold values of the selected SSMs. Also, this section showcases the outcomes of the developed conflict frequency and severity prediction models, as mentioned in Section 3.

4.1. Dependence among the SSMs

The four SSMs, i.e., TTC, PET, MaxD, and MaxDeltaV, were selected for this analysis because these four variables fitted the GPD better than the other SSMs. Before illustrating the results of the process of threshold selection, the correlations among the four selected SSMs were checked using Pearson's, Kendall's, and Spearman's correlation tests. Correlation among the SSMs was examined because the usage of independent indicators in bivariate EVT modeling produces better estimates (Kumar & Mudgal, 2024a). It was found that TTC and PET had a significant positive correlation (ρ = 0.86, p-value < 0.001) between them. Also, MaxD and MaxDeltaV had a significant but very weak negative correlation (ρ = − 0.15, p-value < 0.001) between them. All other correlations were not statistically significant. Therefore, TTC and MaxDeltaV were finally selected to carry out the bivariate POT analysis.

4.2. Determination of threshold values

Thresholds for a marginal distribution were determined utilizing the MRL and TS plots (Niu et al., 2024; Arun et al., 2022a, 2022b; Kumar & Mudgal, 2024c, 2024a). Spectral measure plot was also used in multiple studies to choose threshold values in the case of bivariate POT models (Kumar & Mudgal, 2024a, 2024b). In the present study, the TTC values were negated to convert the problem from a minimization to a maximization estimation. Consequently, if the negated TTC rises to zero, a

Fig. 5. MRL and TS plots of negated TTC (top row) and MaxDeltaV (bottom row) for the joint-site model.

Fig. 6. Spectral measure plot.

collision is expected to occur. The MaxDeltaV indicator, by its inherent characteristics, remains unchanged, and a collision's severity increases if the MaxDeltaV value increases.

Fig. 5 illustrates the MRL and TS plots for the joint-site model employed in the current study. From Fig. 5, we have obtained the threshold values for TTC and MaxDeltaV as 1.25 s and 4.5 m/s by observing the approximately linear trend in the MRL and TS plots. Fig. 6 presents the spectral measure plot for the joint-site model. The plot in Fig. 6 shows that H remains approximately constant around 2 (theoretical threshold) for the first few thousand values of k (the index of the sorted radial coordinates). This stability indicates that the bivariate data shows joint extreme behavior in this range. As indicated in prior research, the final thresholds were determined based on the linear region present on both plots (Kumar & Mudgal, 2024a). The chosen threshold values for all the models are presented in Table 3. Subsequently, to validate the goodness-of-fit of the GPD on the dataset, quantile–quantile and probability-probability plots were utilized (Fig. 7 and Fig. 8). The marginal POT distributions demonstrated a strong fit to the data. Finally, a two-dimensional scatter plot (Fig. 9) was used to visualize the joint exceedances based on the determined threshold

values of TTC and MaxDeltaV from the MRL and TS plots. In Fig. 9, the highlighted area shows the joint exceedances based on negated TTC and MaxDeltaV.

4.3. Conflict frequency prediction model

A total of 35 variables (mentioned in Table 2) were chosen at the start of model development. Only 10 variables were included to develop the conflict frequency predictive model after performing the Spearman correlation check in IBM SPSS. The variables included Central Island Diameter (CID), Circular Road Width (CRW), Entry Width (ENW), Exit Angle (EXA), Lane Demarcation Marking (LDM), Circulating Traffic Volume (CTV), Approaching Traffic Volume (ATV), Occupancy Time (OT), Delineator on Splitter Island (DSI), and Roundabout Sign (RS). A custom wrapper, 'StatsModelsNegativeBinomial,' was subsequently developed to integrate 'statsmodels' Negative Binomial regression with scikit-learn. This custom wrapper served as the base estimator in 'Ada-BoostRegressor.' Subsequently, the AdaBoost model was trained with the training dataset, and its prediction efficacy was assessed by computing the MSE, RMSE, and MAPE on the test dataset. The training data yielded MSE, RMSE, MAPE, and R2 values of 14.97, 3.82, 2.15 %, and 0.97, respectively. The testing data yielded MSE, RMSE, MAPE, and R2 values of 109.53, 10.46, 5.79 %, and 0.92, respectively. Fig. 10 illustrates the comparison between actual and predicted conflict frequency. Smaller values of the model's performance or evaluation metrics signify a remarkable ability of the developed model to predict conflict frequency.

Subsequently, a SHAP (SHapley Additive exPlanations) plot (Fig. 11) was generated to examine the impact and pattern or direction of influence of the different predictor variables on roundabout conflict frequency. The most significant features comprised Circular Road Width (CRW), Circulating Traffic Volume (CTV), Central Island Diameter (CID), Approaching Traffic Volume (ATV), and Occupancy Time (OT). This suggested that alterations in these characteristics could substantially influence the frequency of conflict. Fig. 11 demonstrated that as the values of CTV, CID, ATV, OT, Entry Width (ENW), and Exit Angle (EXA) increased, the frequency of conflict correspondingly escalated. Circulating and approaching traffic volume was positively associated with conflict frequency, suggesting that increased traffic volume naturally elevates conflict frequency because more vehicles interact in a confined space, leading to a higher chance of conflict occurrence.

Fig. 7. (a) Quantile-Quantile and (b) Probability-Probability plots for TTC.

Fig. 8. (a) Quantile-Quantile and (b) Probability-Probability plots for MaxDeltaV.

Fig. 9. Scatter plot indicating joint exceedances.

Similarly, increasing the central island diameter with a constant circulatory road width forces more vehicles to navigate the roundabout within a confined circulating space, thereby increasing the conflict frequency. Past studies also found similar results (Al-Marafi et al., 2020; Maji et al., 2024; Vinayaraj & Perumal, 2023b). The conflict frequency increased with the increase in occupancy time (Maji et al., 2024). Increased occupancy time indicated prolonged exposure to vehicular interactions and conflicts. A wider entry width allows a large number of vehicles to enter at varying speeds following no lane discipline, thus raising the frequency of conflicts. Larger exit angles lead to more abrupt transitions from the circulating lane to the exit. When drivers adjust from one direction to another more sharply, it increases the chances of conflicts. These results were found to comply with the findings in the literature (Anjana & Anjaneyulu, 2014; Vinayaraj & Perumal, 2022, 2023b). Nonetheless, as the values of CRW, Delineator on Splitter Island (DSI), Roundabout Sign (RS), Presence of a Direction sign (DS), and Presence of Lane Demarcation marking (LDM) went up, the frequency of conflict declined. Circulatory road width (CRW) was found to have a negative impact on conflict frequency. When the circulatory roadway is narrow, drivers face constrained lateral clearance and must execute

sharper turns and abrupt braking events. This forces vehicles into tighter trajectories, amplifying steering complexity and sudden decelerations, increasing conflict frequency. Wider widths might be associated with more chances of lane-change conflicts, however, overall conflict frequency will decrease due to better vehicle maneuverability in similar volume contexts (Maji et al., 2024; Vinayaraj & Perumal, 2023b). The presence of delineators on splitter islands offers clear visual cues that help drivers follow their intended paths, mitigating erratic movements. Similarly, clear roundabout signs and directional signs guide drivers effectively, enhancing compliance with traffic protocols. Finally, wellmaintained lane demarcation markings, even in non-lane-based environments, reduce ambiguity in vehicle positioning and promote organized flow. The results of the current study accorded with the findings of Anjana and Anjaneyulu (2014), Maji et al. (2024), Vinayaraj and Perumal (2022, 2023b).

4.4. Safety diagnosis using SSAM

The vehicular trajectory files ('.trj') for the different roundabouts were re-imported to SSAM software. The conflict points were identified by setting the threshold value of TTC and MaxDeltaV as per the values mentioned in Table 3 for the different roundabout sites. Table 4 presents the statistics of the total identified traffic conflicts and their classifications based on types. Lane change conflicts constituted the largest share of identified conflicts, representing nearly 42 % of all conflicts. Rear-end conflicts comprised nearly 33 % of the total conflicts, while crossing conflicts represented 25 % of the overall conflicts. Fig. 12 depicts the spatial distribution of conflict points across the roundabout area in three example roundabouts chosen in the present study. It was observed that rear-end conflicts were scattered all over the roundabout area, especially denser at the approach legs due to stop-and-go situations. However, lane-change conflicts were more concentrated over the weaving area of the roundabouts for the obvious reason of weaving interactions. Evidence of crossing conflicts was found mainly at the exits and entrances of the roundabouts due to interactions between road-crossing pedestrians (and bicyclists) and entering/exiting (even violating) traffic. The distribution of different conflict types corresponds closely with findings from earlier research (Hasanvand et al., 2023; Sadeq & Sayed, 2016; Shawky et al., 2023).

Table 2 Variable descriptions and their respective summary statistics.

| Variable | Description |----------|---------------------------- | ANL | Angle to next leg (in degrees) | AS | Average speed of traffic (in km/h) | ATV | Approaching traffic | CID | Central island diameter (in meters) | CRW | Circular road width (in meters) | CTV | Circulating traffic | DA | Deviation angle (in degrees) | ENA | Entry angle (in degrees) | ENR | Entry radius (in meters) | ENW | Entry width (in meters) | EXA | Exit angle (in degrees) | EXR | Exit radius (in meters) | EXW | Exit width (in meters) | ICD | Inscribed circle diameter (in meters) | OT | Occupancy time (in seconds) | PCR | Percentage of cars (in %) | PHV | Percentage of heavy vehicles (in %) | PMC | Percentage of motorcycles (in %) | RAC | Ratio of ATV and CTV | SFW | Splitter island flare width (in meters) | WL | Weaving length (in meters) | WW | Weaving width (in meters) | Variable | Description | BCT | Is a bicycle crossing track present? | CHS | Presence of Chevron sign? | CSW | Whether crosswalk is present or not? | DS | Presence of a Direction sign? | DSI | Presence of Delineator | EDL | Presence of an Edge Line? | LDM | Presence of Lane Demarcation marking? | LU | Land use type? | NL | Number of circulatory lanes | NLEGS | Number of legs/approaches | RS | Presence of a Roundabout sign? | SB | Presence of Speed Breaker? | STPL | Presence of a Stop line? | Min. | Max. | Mean | Std. Dev. | | ----------------|-----------------------------------------------------------|-----------------------------------------------------------|--------|-----------|--| | 25.00 | 60.00 | 40.80 | 8.66 | | | 11.00 | 26.45 | 19.11 | 3.57 | | volume (in PCU/15 min) | 139.97 | 575.47 | 306.37 | 90.68 | | | 8.00 | 81.00 | 44.28 | 18.61 | | | 8.00 | 16.50 | 11.13 | 3.18 | | volume (in PCU/15 min) | 124.04 | 537.61 | 333.40 | 113.01 | | | 40.00 | 80.00 | 59.70 | 12.10 | | | 25.00 | 58.00 | 37.70 | 9.33 | | | 20.00 | 75.00 | 44.30 | 16.06 | | | 8.25 | 19.70 | 12.20 | 4.19 | | | 22.00 | 47.00 | 35.70 | 7.66 | | | 38.00 | 90.00 | 56.80 | 15.95 | | | 8.50 | 19.70 | 12.73 | 3.96 | | | 26.85 | 115.00 | 66.87 | 21.27 | | | 6.35 | 22.92 | 13.50 | 2.75 | | | 13.31 | 57.00 | 38.75 | 10.19 | | | 1.30 | 6.25 | 3.58 | 1.56 | | | 29.52 | 61.12 | 42.29 | 7.88 | | | 0.68 | 1.81 | 0.97 | 0.29 | | | 3.50 | 33.00 | 11.50 | 8.87 | | | 30.50 | 60.50 | 44.80 | 9.31 | | | 10.50 | 26.00 | 14.77 | 5.53 | | | Categories (Proportion) | | | | | | | 0 - absent (85.7 %), 1 - present (14.3 %) | | | | | | 0 - absent (42.8 %), 1 -present (57.2 %) | | | | | | 0 - absent (42.8 %), 1 - faded (50 %), 2 - proper (7.2 %) | | | | | | 0 - absent (57.2 %), 1 - present (42.8 %) | | | | on Splitter Island? | | 0 - absent (35.7 %), 1 - present (64.3 %) | | | | | | 0 - absent (35.7 %), 1 - present (64.3 %) | | | | | 0 - absent (42.8 %), 1 - faded (50 %), 2 - proper (7.2 %) | | | | | | 0 - semi-urban (28.6 %), 1 - urban (71.4 %) | | | | | | 2 lanes (64.3 %), 3 lanes (35.7 %) | | | | | | 3 - legged (21.4 %), 4 - legged (78.6 %) | | | | | | | 0 - absent (28.5 %), 1 - present (71.5 %) | | | | | | 0 - absent (64.3 %), 1 - present (35.7 %) | | | | | | 0 - absent (14.3 %), 1 - present (85.7 %) | | | |

4.5. Conflict severity categorization

The conflict severity levels were defined following a two-fold clustering methodology on TTC and MaxDeltaV values associated with each identified conflict. The selected SSMs function as an effective proxy for evaluating conflict severity (Gallelli et al. 2021; Hasanvand et al. 2023; Liu et al. 2020; Vasconcelos et al. 2014). Fig. 13 illustrates the

dendrogram obtained from the hierarchical clustering analysis. The yaxis in the figure signifies the sample data or individual data points. The data samples progressively converge to create clusters as we move right across the x-axis. The greater the distance along the x-axis, the greater the dissimilarity among clusters. In the current study, the optimum number of clusters was decided to be four (marked by the blue line) by visual inspection of the rescaled distances. Clustering the data into four

Fig. 10. Actual vs. predicted conflict frequency for (a) training data and (b) testing data.

Fig. 11. SHAP plot based on feature values.

distinct severity levels would yield more granular insights into conflict severity.

Followed by hierarchical clustering, two-step clustering was carried out to categorize the severity associated with each identified traffic conflict based on TTC (≤ 1.25 s) and MaxDeltaV (≥ 4.50 m/s). Highquality clusters of the conflict severity levels were generated as their silhouette measures of cohesion and separation exceeded the recommended threshold of 0.5 specified by SPSS (2011). The average silhouette score was 0.65 (shown in Fig. 14). Further analysis revealed that the data samples displayed a satisfactory size ratio of the largest cluster to the smallest cluster, with a value of 2.66 (Fig. 14).

As shown in Fig. 14 and Table 5, four clusters were identified in the sample dataset of identified traffic conflicts. The conflicts were clustered into "Low severity," "Moderate severity," "High severity," and "Very high severity." Moreover, the distribution of TTC and MaxDeltaV in each cluster can be found in Table 5. The names of the various clusters (in terms of severity levels) were designated according to the relative frequency distribution of the selected SSMs in the corresponding clusters.

Cluster 1, comprising 33.8 % of the data (i.e., 332 conflicts), represents the lowest risk conflicts. The TTC values in this group are relatively high, indicating that vehicles have ample time to avoid a collision. The MaxDeltaV distribution in this cluster is skewed towards lower values, suggesting that even when conflicts occur, the potential for significant impact or harm is minimal. This cluster can be interpreted as representing low-risk, low-severity situations where drivers are able to react

in time, reducing the likelihood of severe crashes. These interactions are most common in scenarios where vehicles maintain adequate distance and speed relative to one another. Cluster 2 accounts for 34.1 % of the data (i.e., 336 conflicts) and is characterized by moderate severity conflicts. The TTC values in this cluster are noticeably lower than those in Cluster 1, implying that vehicles are in closer proximity. Although the MaxDeltaV distribution shows moderate values, there is still a relatively low probability of severe crashes. This group represents situations where drivers have less time to react, increasing the likelihood of a conflict but still maintaining a manageable level of crash severity. These are typically moderate-risk interactions, where slight misjudgments or delays in response can escalate into near-miss situations or property damage only (PDO) crashes.

Comprising 19.3 % of the data (i.e., 199 conflicts), Cluster 3 represents high-risk conflicts. The TTC values in this group are skewed toward the lower end of the distribution, indicating that vehicles are often too close to each other, with very little time to avoid a potential collision. Moreover, the MaxDeltaV distribution reveals significantly higher values compared to the first two clusters, suggesting that these conflicts, if not avoided, could result in severe impacts. This cluster highlights scenarios where driver interventions need to be more immediate and decisive to prevent crashes that might lead to PDO crashes or even crashes causing minor injuries. Cluster 4, representing 12.8 % of the data (i.e., 126 conflicts), contains the most severe conflicts. Vehicles in this group have TTC values all over the considered range, i.e., from 0 s to 1.25 s, meaning there are few vehicles in extremely close proximity with almost no time to avoid a collision, and few vehicles have little time to perform evasive action. Additionally, the MaxDeltaV values in this

Table 4 Statistics of different types of conflicts at the study sites.

Sites	Total conflicts	Rear-end (proportion)	Lane change (proportion)	Crossing (proportion)
Site 1	52	22 (42.3 %)	21(40.4 %)	9 (17.3 %)
Site 2	93	47 (50.5 %)	32 (34.4 %)	14 (15.1 %)
Site 3	145	71 (49.0 %)	52 (35.8 %)	22 (15.2 %)
Site 4	74	40 (54.0 %)	24 (32.4 %)	10 (13.6 %)
Site 5	148	60 (40.5 %)	48 (32.4 %)	40 (27.1 %)
Site 6	54	23 (42.6 %)	20 (37.0 %)	11 (20.4 %)
Site 7	160	62 (38.8 %)	58 (36.3 %)	40 (24.9 %)
Site 8	85	28 (33.2 %)	30 (35.0 %)	27 (31.8 %)
Site 9	76	29 (38.2 %)	27 (35.5 %)	20 (26.3 %)
Site 10	99	38 (38.4 %)	33 (33.3 %)	28 (28.3 %)
Site 11	77	26 (33.7 %)	33 (42.8 %)	19 (23.5 %)
Site 12	104	36 (34.6 %)	36 (34.6 %)	32 (30.8 %)
Site 13	122	48 (39.3 %)	54 (44.3 %)	20 (16.4 %)
Site 14	85	35 (41.1 %)	40 (47.0 %)	10 (11.9 %)
All sites	984	323 (32.8 %)	413 (41.9 %)	248 (25.3 %)

Table 3 Parameter estimates of bivariate POT models.

Models	Threshold values		Estimates		Joint exceedances (proportion)
	TTC (u1)	MaxDeltaV (u2)	σ1	ξ1	σ2	ξ2
Site 1	− 1.50	4.00	2.16	− 1.16	1.28	− 0.28	52 (0.07)
Site 2	− 1.50	4.00	2.59	− 1.46	1.75	− 0.24	93 (0.08)
Site 3	− 1.25	4.50	3.54	− 1.74	2.51	− 0.60	145 (0.11)
Site 4	− 2.00	4.25	3.82	− 1.62	2.08	− 0.37	74 (0.09)
Site 5	− 1.50	5.00	2.63	− 1.22	3.24	− 0.91	148 (0.09)
Site 6	− 1.75	4.75	2.15	− 1.12	3.64	− 1.14	54 (0.10)
Site 7	− 1.50	3.00	2.99	− 1.44	2.59	− 0.77	160 (0.13)
Site 8	− 1.25	4.25	3.15	− 1.56	2.27	− 0.54	85 (0.12)
Site 9	− 1.25	4.25	3.16	− 1.57	2.16	− 0.49	76 (0.10)
Site 10	− 1.25	4.50	3.36	− 1.45	1.45	− 0.38	99 (0.11)
Site 11	− 1.50	4.00	3.53	− 1.61	1.15	− 0.14	77 (0.09)
Site 12	− 1.25	4.25	3.47	− 1.48	1.47	− 0.35	104 (0.11)
Site 13	− 1.25	4.50	3.53	− 1.61	1.43	− 0.21	122 (0.10)
Site 14	− 1.25	4.50	3.35	− 1.46	1.38	− 0.25	85 (0.09)
Joint-site	− 1.25	4.50	3.15	− 1.45	1.34	− 0.25	984 (0.08)

Fig. 12. Conflict points and their types at (a) Site 1, (b) Site 2, and (c) Site 13.

Fig. 13. Dendrogram obtained from hierarchical cluster analysis.

Fig. 14. Cluster quality, proportion of conflict points in each cluster, and cluster size ratio.

cluster are the highest among all clusters, indicating that when these conflicts occur, the resulting impacts are likely to be most severe. This cluster represents the most critical traffic interactions, where the chances of a collision are extremely high, and the consequences are most severe. The severity of these conflicts makes this cluster a key area for traffic safety interventions.

4.6. Conflict severity predictive model

The results of the model estimation are presented in Table 6. Central island diameter (CID) showed a negative and significant relationship with conflict severity (β = − 0.025, p < 0.001), indicating that increasing the island diameter reduces the severity of conflicts. Similarly, the circular road width (CRW) was negatively associated with conflict severity (β = − 0.210, p = 0.027), suggesting that wider circular roadways contribute to a reduction in severe conflicts. In contrast, entry width (ENW) exhibited a positive and significant association with conflict severity (β = 0.060, p = 0.035), implying that wider entry points increase the severity of conflicts. Deviation angle (DA), representing the angle between the entry and circulatory lanes, had a negative effect on conflict severity (β = − 0.040, p = 0.001), meaning that sharper angles reduce the likelihood of severe outcomes. The weaving length (WL)

Table 5 Result of cluster analysis presenting cluster sizes and distribution of input variables in each cluster.

| Clusters | Description | Size (proportion) | Input variables (relative cell distribution) | | | | | |-----------|--------------------|-------------------|----------------------------------------------|-----------|--|--|--| | | | | TTC | MaxDeltaV | | | | | Cluster 1 | Low severity | 332 (33.8 %) | | | | | | | Cluster 2 | Moderate severity | 336 (34.1 %) | | | | | | | Cluster 3 | High severity | 199 (19.3 %) | | | | | | | Cluster 4 | Very high severity | 126 (12.8 %) | | | | | |

Table 6 Parameter estimates of ordered probit model.

Variables	Estimate (β)	Std. Error	Sig. (p value)
Central island diameter in meters (CID)	− 0.025	0.006	<0.001
Circular road width in meters (CRW)	− 0.210	0.095	0.027
Entry width in meters (ENW)	0.060	0.108	0.035
Deviation angle in degrees (DA)	− 0.040	0.013	0.001
Weaving length in meters (WL)	0.032	0.012	0.008
Weaving width in meters (WW)	− 0.011	0.006	0.006
Average speed of traffic in km/h (AS)	0.262	0.059	<0.001
Presence of speed breaker at entry:
0-absent	1.077	0.127	<0.001
1-present	0a
Conflict type:
1-rear-end	− 0.393	0.090	<0.001
2-lane change	− 0.296	0.087	<0.001
3-crossing	0a
Model thresholds
Threshold 1	1.138	0.350	0.029
Threshold 2	2.440	0.353	<0.001
Threshold 3	3.490	0.258	<0.001
Goodness-of-fit and validation
Sample size			787
Akaike's information criterion (AIC)			465.583
Bayesian information criterion (BIC)			626.533
Cox and Snell Pseudo R2			0.453
Nagelkerke Pseudo R2			0.483
McFadden Pseudo R2			0.218

^a The parameter was set to zero because it was redundant.

showed a positive impact on conflict severity (β = 0.032, p = 0.008), while weaving width (WW) negatively influenced severity (β = − 0.011, p = 0.006), highlighting the importance of optimized weaving section dimensions for mitigating conflict severity. Furthermore, the average speed of traffic (AS) had a positive and significant impact on conflict severity (β = 0.262, p < 0.001), underscoring the role of speed management in reducing the risk of severe conflicts at roundabouts. The relationships observed in the present study, among several geometric, traffic characteristics, and conflict severity, were found to be consistent with the findings of past studies (Vinayaraj & Perumal, 2023a).

The presence of speed breakers at the roundabout entry significantly reduced conflict severity (β = 1.077, p < 0.001). This result indicates that speed control measures at entry points are effective in lowering the risk of severe conflicts. When examining the influence of conflict types, rear-end conflicts (β = − 0.393, p < 0.001) and lane-change conflicts (β = − 0.296, p < 0.001) were both found to have a lower probability of resulting in severe outcomes compared to crossing conflicts, which served as the reference category. These results suggest that crossing conflicts, due to the angular nature of vehicle interactions, are more likely to result in higher severity outcomes. Similar results were found in the study by Vinayaraj & Perumal (2023a).

The thresholds for the conflict severity levels were estimated to be 1.138, 2.440, and 3.490 for transitions from low to moderate, moderate to high, and high to very high severity, respectively, all of which were statistically significant. The goodness-of-fit measures indicated that the ordered probit model fits the data reasonably well, with a McFadden Pseudo R2 value of 0.218, a Nagelkerke Pseudo R2 of 0.483, and a Cox and Snell Pseudo R2 of 0.453. The Akaike Information Criterion (AIC) and Bayesian Information Criterion (BIC) values were 465.583 and 626.533, respectively, further validating the model's adequacy.

The model's prediction accuracy was evaluated on the test dataset by comparing the actual versus predicted severity categories, as shown in Table 7. The model correctly predicted the severity level of conflicts with an overall accuracy of 88.4 %. The highest prediction accuracy was observed for 'moderate severity' conflicts, with 92 % of cases correctly classified. The accuracy for 'low severity' conflicts was 87.7 %; for 'high severity' conflicts, it was 86.5 %; and for 'very high severity' conflicts, it was 87.5 %. The percent share of each severity category in the predicted dataset closely matched the actual distribution, with 'low severity' conflicts accounting for 29.4 % of the total, 'moderate severity' conflicts

Table 7 Prediction accuracy table of the ordered probit model.

| | | Predicted | | | | | | | | |------------------------|--------------------|--------------|-------------------|---------------|--------------------|-----|-------------------|--|--| | | | Low severity | Moderate severity | High severity | Very high severity | Sum | Percent share (%) | | | | Actual | Low severity | 45 | 17 | 4 | 0 | 66 | 33.5 | | | | | Moderate severity | 12 | 42 | 12 | 2 | 68 | 34.5 | | | | | High severity | 1 | 10 | 19 | 8 | 38 | 19.3 | | | | | Very high severity | 0 | 4 | 9 | 12 | 25 | 12.7 | | | | | Sum | 58 | 73 | 44 | 22 | 197 | | | | | | Percent share (%) | 29.4 | 37.1 | 22.3 | 11.2 | | | | | | Correct prediction (%) | | 87.7 | 92 | 86.5 | 87.5 | | | | |

Fig. 15. (a)–(g) Variation of SSMs with Circulatory Road Width, (h) Variation of Central Island Diameter, Circulating Traffic Volume, and Approaching Traffic Volume with Circulatory Road Width.

37.1 %, 'high severity' conflicts 22.3 %, and very high severity conflicts 11.2 %. The close alignment between the predicted and actual severity levels further supports the robustness of the developed model in classifying conflict severities accurately across all levels.

In order to shed some light on the practical application and transferability of the findings, the effects of the geometric characteristics on the SSMs have been explored in greater detail. Fig. 15 depicts the variability of several SSMs with respect to one of the key roundabout geometric elements, i.e., Circulatory Road Width (CRW). Fig. 15(h) presents the variation of Central Island Diameter (CID), Circulating Traffic Volume (CTV), and Approaching Traffic Volume (ATV) with respect to CRW. TTC and PET (the temporal proximity measures) appear to hover within comparable ranges across narrower to mid-range CRWs, with modest fluctuations. Narrow CRWs (around 8–9 m) have shown more spread in the data, but no single bin indicates an abrupt collapse or sharp drop in temporal proximity. Maximum speed (MaxS) and difference in vehicle speeds (DeltaS) have shown an upward trend in wider CRWs, reflecting that vehicles pick up higher speeds in a more spacious circulatory roadway. However, the distributions do not show a single sudden spike in speeds or speed differences; rather, they tend to gradually increase, decrease or plateau.

MaxDeltaV and Maximum deceleration rate (MaxD) likewise varied in a relatively moderate band for most CRW bins, suggesting that while wider widths can allow higher speeds, there is no dramatic jump in severity at a single width. Deceleration Rate (DR) remained fairly scattered across all bins. Interestingly, there are a significantly large number of outliers at low to medium CRWs (8–10 m) due to harsh braking (Fig. 15d, Fig. 15f), thereby increasing conflict frequency at low/medium CRWs. Narrower CRWs (≈ < 9 m) tend to keep speeds lower (thus smaller MaxS); however, they also introduce more merging-diverging friction, lowering TTC/PET. In the case of moderate CRWs (≈ 9–12 m), there is enough space to separate conflicting vehicles and maintain smoother flow, but not at high speeds. The box-plot medians show stable or slightly improved TTC/PET in combination with moderate speed metrics (MaxS, DeltaS, MaxDeltaV), suggesting fewer extreme conflicts. Wider CRWs (≈ > 12 or 13 m) allow vehicles to travel faster, evidenced by higher upper whiskers for MaxS, DeltaS, and MaxDeltaV in some CRW bins. The box plots do not pinpoint a single width at which the SSMs rapidly degrade. Instead, the safety indicators shift gradually as CRW grows, modulated by traffic volumes, central island size, and driver behavior. In highly heterogeneous traffic, ensuring that CRW is neither too narrow nor too wide is essential. A moderate CRW range (≈ 9–12 m, as per the dataset of this paper) appears to mitigate both extremes: it helps reduce very tight interactions and curbs excessive speeds. However, the safe value geometric design elements cannot be decided based on analyzing CRW alone. Variations of SSMs with respect to several geometric features combined with traffic volume must be analyzed to get the findings translated into design specifications.

The analyses shown in Fig. 15 reveal that the relationship between circulatory roadway width and the surrogate safety measures is strongly influenced by traffic volumes. The present dataset exhibits more outliers in MaxD and DR at lower CRWs. This suggests that when the circulating roadway is narrow, there is a higher frequency of conflicts, and those conflicts tend to be severe as well (Fig. 15e and g; relatively high MaxDeltaV and DeltaS for 8 m CRW). In contrast, for higher CRWs (e.g., 14–16 m), the circulating and approaching traffic volumes are much lower than expected. In effect, even though wider CRWs might typically be assumed to support higher volumes, at our study sites, they are associated with lower traffic volumes than expected, thereby reducing the frequency of conflicts. Smaller roundabouts were not equipped with speed calming measures, whereas roundabouts with wider CRWs had enhanced design features with speed calming and other safety interventions. Thus, in Fig. 15, the maximum speeds are nearly stable across different CRW levels. However, when examining speed-related measures like MaxDeltaV and DeltaS, an upward trend for CRWs beyond 13.5 m has been observed. This suggests that, on a per-conflict

basis, the severity increases at wider widths. Therefore, because the wider roundabouts have significantly lower traffic volumes than expected, the total number of conflicts remains low. Conversely, the narrow CRWs (around 8–8.2 m) not only have higher volumes, but these roundabouts have substantial MaxD, MaxDeltaV, and DeltaS values, indicating that conflicts here are both frequent and severe. In Indian highly mixed disorder traffic scenarios, the occurrence of severe conflicts is relatively more inclined and attributed to pedestrian and bicyclist activity rather than the size of roundabouts, as conflicts with pedestrians and bicyclists generate high values of severity indicators like MaxDeltaV. In reality, pedestrian and bicyclist activities are more at smaller roundabouts with no (or in a dilapidated state) pedestrian and bicyclist facilities. This is evident by red dots near crosswalks and bicycle tracks at the entrances and exits in Fig. 12.

The present study provides a complete structure for evaluating roundabout safety under non-lane-based, heterogeneous traffic conditions using surrogate SSMs, EVT, and clustering techniques. In a nutshell, this study provides valuable insights into roundabout safety by presenting a methodology for the determination of appropriate SSM thresholds, the development of a conflict frequency prediction model, and the classification of conflict severity using clustering techniques, thereby offering a proactive framework for improving road safety. The findings have practical implications for urban planners and traffic engineers, emphasizing the need for optimized geometric designs, effective speed management, site prioritization, and targeted interventions at high-risk roundabout locations. These results are particularly relevant for LMICs, where traffic conditions are highly mixed and lane discipline is limited. The results allow for the recommendation of a number of mitigating techniques aimed at lessening the frequency and severity of crash like situations at roundabouts. Strategies might involve enforcing strict traffic laws, such as those pertaining to speeding violations, putting up warning signs, making sure that pavement markings and sign boards are placed properly, and putting in place extra safety precautions such as channelization and reflective cat eyes. Additionally, lowering the frequency and severity of safety–critical events can be achieved by implementing driving awareness programs to improve drivers' abilities, especially with regard to safe driving techniques in roundabouts. Implementing Intersection Advanced Driver Assistance Systems (I-ADAS) is one technique that uses intelligent technology in conflict reduction. These systems may notify vehicles approaching a junction about the present conditions and activities occurring there.

5. Conclusions

This study presents a comprehensive framework for appraising roundabout safety in non-lane-based, heterogeneous traffic conditions, specifically in lower-middle-income countries like India. The research employed UAV-recorded videos and advanced image-processing techniques to extract vehicle trajectories. Using surrogate safety measures (SSMs), extreme value theory (EVT), and clustering techniques, traffic conflicts were identified, and their severity was classified. The study determined appropriate threshold values for SSMs following the peakover-threshold (POT) approach of EVT modeling, developed a conflict frequency prediction model using the AdaBoost algorithm with a Negative Binomial objective function to cater to the count and overdispersed nature of conflict data, and employed ordered probit regression to predict conflict severity utilizing the geometric, traffic, builtenvironmental characteristics, along with conflict types. Overall, the study contributes to a proactive approach to improving roundabout safety in complex traffic environments where crash data is limited or unavailable. The critical findings of the present study are as follows:

• A critical aspect of the research involved determining appropriate threshold values for SSMs using EVT. The mean residual life (MRL) plot and threshold stability (TS) plot were used to identify thresholds for Time to Collision (TTC) and MaxDeltaV, with final values set at

1.25 s and 4.5 m/s, respectively. These thresholds were tailored to the specific traffic conditions of lower-middle-income countries, capturing extreme conflict events effectively.
The application of bivariate POT modeling further demonstrated the identification of severe conflicts in terms of joint exceedances based on determined SSMs' threshold values, ensuring that these thresholds reliably identify significant safety risks. Validation through quantile–quantile and probability-probability plots indicated a strong model fit, affirming the robustness of the threshold determination process.
The conflict frequency prediction model, based on the AdaBoost regressor with a Negative Binomial (NB) objective function, exhibited high predictive accuracy. The model achieved R2 values of 0.97 for training data and 0.92 for testing data, indicating its efficacy in predicting conflict frequency.
Key variables influencing conflict frequency included circular road width (CRW), circulating traffic volume (CTV), central island diameter (CID), and approaching traffic volume (ATV).
The SHAP analysis provided additional insights, revealing that increased CRW was associated with reduced conflict frequency, while higher CTV and ATV increased the likelihood of conflicts. These findings highlight the importance of geometric design optimization and traffic management strategies in mitigating conflict risks at roundabouts.
The use of the SSAM software for conflict diagnosis was crucial in categorizing conflict types and identifying critical conflict points. SSAM revealed that lane-change conflicts accounted for 42 % of all identified conflicts, followed by rear-end (33 %) and crossing conflicts (25 %).
The spatial distribution of conflict points indicated that most conflicts occurred in the circulatory section and approaches of the roundabout, emphasizing the need for targeted interventions in these areas. These results align with existing research, confirming the validity of using SSAM for proactive roundabout safety assessments.
Conflict severity was analyzed through a combination of hierarchical and two-step clustering techniques, resulting in four distinct severity levels: low, moderate, high, and very high. The majority of conflicts were classified as low (33.8 %) and moderate (34.1 %) severity, while high and very high severity conflicts accounted for 19.3 % and 12.8 %, respectively.
The two-step clustering approach, with a silhouette score of 0.65, confirmed the high quality of the clusters, ensuring that conflicts were appropriately categorized based on their potential severity. The analysis revealed that the largest cluster size was approximately 2.66 times larger than the smallest, confirming the reliability of the classification process.
The ordered probit model for predicting conflict severity achieved a prediction accuracy of 88.4 %, with moderate severity conflicts showing the highest accuracy. The model identified several key variables influencing severity, including central island diameter (CID), circular road width (CRW), and average traffic speed (AS). Larger CID and CRW were associated with reduced severity, while higher average speeds increased the likelihood of severe conflicts.
The presence of speed breakers at roundabout entries also significantly reduced conflict severity, underscoring the importance of speed management at critical locations.
Additionally, crossing conflicts were found to be the most severe compared to rear-end and lane-change conflicts, consistent with their more direct collision paths.

While this study provides important insights into roundabout safety, several limitations should also be acknowledged. The research was not validated using actual crash data due to the unavailability of such data, especially in the case of roundabouts, which may limit the study's comprehensiveness. Additionally, the focus on a limited number of roundabouts could affect the transferability of the results to other traffic environments. Furthermore, while UAV-based data collection proved effective, it may present scalability challenges and higher operational costs for larger implementations. The conflict identification methodology presented in this study relied on TTC and MaxDeltaV threshold values, which might not be universally applicable. Traffic behavior and driving culture vary significantly across regions and scenarios. Different traffic environments might require higher or lower thresholds due to different speeds, vehicle spacing, and driving characteristics. Therefore, the thresholds should be adapted based on specific traffic environments. Future research should aim to integrate actual crash data to validate the predictive models developed in this study further. Expanding the scope to include a wider variety of roundabout geometries and traffic conditions would provide a broader understanding of roundabout safety. Further, future studies should also explore the influence of environmental factors, such as weather and lighting conditions, on roundabout conflict frequency and severity. In terms of practical implications, this research provides urban planners and traffic engineers with a proactive tool for identifying and mitigating traffic conflicts at roundabouts. The findings suggest that optimizing geometric designs, such as widening circular roads or refining entry configurations, combined with implementing effective speed management strategies, can significantly reduce conflicts. The framework presented in this study offers a valuable approach to improving safety, particularly in developing countries with mixed and disorganized traffic conditions. This research lays the groundwork for future investigations into roundabout safety using surrogate safety measures and advanced statistical models. It offers valuable insights for enhancing road safety and can inform traffic safety policy and roundabout design interventions for safer traffic management.

CRediT authorship contribution statement

Abhijnan Maji: Writing – original draft, Visualization, Validation, Software, Methodology, Formal analysis, Data curation, Conceptualization. Indrajit Ghosh: Writing – review & editing, Supervision, Resources, Project administration, Methodology, Investigation, Conceptualization.

Funding

This research did not receive any specific grant from funding agencies in the public, commercial, or not-for-profit sectors.

Declaration of competing interest

The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.

Acknowledgement

Abhijnan Maji wants to extend his sincere thanks to the Ministry of Education (MoE), Govt. of India, for the Prime Minister Research Fellowship (PMRF) (ID: 2802857), which helped a lot to carry out this study. The authors would also like to acknowledge Mr. Lukas Mozga for providing access to the DataFromSky platform.

Data availability

Data will be made available on request.

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