Grading of Traffic Interruptions in Highways to Tibet Based on the Entropy Weight-TOPSIS Method and Fuzzy C-Means Clustering Algorithm

Abstract

The interruption of transportation on the way to Tibet has brought great losses to the Tibetan region. The work proposed a model that integrated the entropy weight-TOPSIS method with the fuzzy C-means clustering algorithm to discuss the causes and characteristics of traffic interruptions on the four main highways to Tibet. This approach aimed to quantify and grade traffic interruption states. First, the entropy weight-TOPSIS method was used to mitigate dimensions among various indices and quantitatively evaluate the status values of traffic interruptions. Then, the fuzzy C-means clustering algorithm was employed to grade these values. The proposed model graded traffic interruption states into four levels by evaluating the duration, mileage, and severity of traffic interruptions. Moreover, the four-level classification scheme can reflect the severity of traffic blocking events more precisely while maintaining a lower PE (Partition Entropy) value. In the four-level classification, the Sichuan–Tibet Highway and Xinjiang–Tibet Highway experienced more level-3 and level-4 serious interruptions, while most high-level interruptions on the Qinghai–Tibet Highway were classified as level-2 ordinary interruptions. The Yunnan–Tibet Highway, with limited data and primarily level-1 classification, was not analyzed in detail. These findings provide a reference for highway management departments to formulate targeted maintenance and emergency measures, especially the Sichuan–Tibet highway, which needs more attention and resource investment to improve its disaster resistance and reduce the impact of traffic interruptions.

1. Introduction

Tibet, a land shrouded in mystery atop the world, boasts breathtaking natural landscapes and is a repository of rich cultural and ecological diversity.

Table 1. Basic information of the four highways.

	Highway Number	Highway Mileage (km)	Year of Construction
Qinghai–Tibet	G109	3901	2009
Sichuan–Tibet	G318/G317	5476/2043	1954/1951
Xinjiang–Tibet	G219	10,065	1956
Yunnan–Tibet	G214	2961	1978

, for example, shows the basic information of the four highways into Tibet. A surge in tourism increases traffic volumes in Tibet. Based on the statistical data of each monitoring station, the annual average daily traffic (AADT) of the four highways into Tibet was calculated. Figure 1 shows that the traffic volume of Qinghai–Tibet Highway is the highest, more than twice that of the Sichuan–Tibet Highway, while the traffic volumes of the Yunnan–Tibet Highway and Xinjiang–Tibet Highway are significantly lower than those of the former, posing unprecedented challenges to road management and safety.

In recent years, the highways to Tibet have suffered significant losses due to natural calamities and traffic accidents exacerbated by extreme weather and geological hazards. In 2022, the losses from geological disasters were heavier than usual, mainly concentrated in the western regions such as Qinghai, Sichuan, and Xinjiang. These disasters affected a total of 940,000 people, resulting in 122 deaths and missing persons, and causing direct economic losses of 22.45 billion yuan. The four highways of Qinghai–Tibet, Sichuan–Tibet, Xinjiang–Tibet, and Yunnan–Tibet have an average of 1870 disasters per year, with traffic interruption amounting to 50–150 times per year, making these highways passable for an average of 320 days per year. Wide-scale heavy snow, dense fog, and torrential rain increasingly disrupt the maintenance and safe functioning of the highways [1,2]. Therefore, there is an urgent need to implement a grading method for traffic interruptions. This method can provide guidelines for relevant departments to quickly identify the severity of incidents and take corresponding emergency measures. With limited human and material resources, it will enable the rational allocation of funds and technical support needed for different levels of disasters, thereby creating favorable conditions for achieving year-round, all-weather accessibility.

In this study, we aim to analyze traffic disruptions on all four major highways leading to Tibet. By considering the entire network, we seek to provide a comprehensive understanding of the factors contributing to traffic disruptions, including mudslides, snow accumulation, landslides, traffic accidents, traffic control, and infrastructure damage. This holistic approach enables us to identify common and unique characteristics across the different highways, thereby offering valuable insights for future planning and management.

2. Literature Review

Adverse weather and geological hazards can severely affect road traffic operations, according to research on traffic interruptions [3,4,5,6,7]. For the grading of traffic interruptions, R. Arawal et al. [8] investigated various factors and their relationships with interruption accidents. They first introduced association rules mining, a data mining technique that uncovers potential associations among item-sets in a database. Additionally, a classic Apriori algorithm was proposed. Xi J et al. [9] used the AHP-Apriori algorithm to develop a traffic accident cause analysis model. The AHP algorithm is utilized to sort the factors contributing to accidents based on their degrees of importance. Then, the Apriori algorithm is used for correlation analysis of the main influencing factors selected. However, certain types of accidents are not considered as part of the frequent item-set due to their low frequency of occurrence. Both algorithms fail to reveal their association with other factors. Therefore, integrating additional data mining techniques, such as clustering analysis and anomaly detection, is important for better understanding rare events.

The grading of traffic operation states commonly employs various clustering algorithms, including partition clustering, density clustering, hierarchical clustering, grid-based clustering, model clustering, and the fuzzy method. Wang L [10] proposed an FCM algorithm combining the K-means algorithm and Random Forest to develop a weighted improved FCM algorithm to evaluate the importance of traffic network nodes, which dynamically identifies the critical traffic nodes more accurately by determining the initial clustering centers using the K-means algorithm in order to reduce the number of iterations and to avoid the local optimal solutions. Huang Y [11] proposed a clustering algorithm based on improved Gaussian Mixture Model (GMM) by analyzing the real-time monitoring data, such as road speed and flow rate, introducing the margin discrimination index, and adopting the improved mean-standard deviation algorithm to preprocess the data to determine the clustering centers. The results show that this method can efficiently and stably identify the state of urban road traffic. Xintong Y [12] used the entropy weight-TOPSIS method and K-means algorithm to determine the risk level of the target road and categorized the road into four risk classes according to the risk level. He et al. [13] discovered the potential relationships among the relevant factors of traffic interruptions by establishing a multi-dimensional attribute model of traffic interruption. Fuzzy correlation rules are used to explore the dependencies of the multi-dimensional attributes of interruption factors. Huang Y [14] proposed a fuzzy cluster analysis method of traffic state to solve the problem of ambiguity and multifactorial influence of road traffic state, allowing for more accurate assessments the road traffic state. Cao J [15] proposed an FCM clustering algorithm based on information entropy weighting to solve the problem of urban traffic state identification. The authors determined the weights of evaluation indexes through information entropy theory and optimize the FCM algorithm by using the weighted Euclidean distance to improve clustering performance of the algorithm and the identification rate of the traffic state. Jiayu L [16] used FCM to partition the traffic state of highway network, used the LSTM algorithm to establish a traffic state prediction model, and finally used the K-means algorithm to build a traffic state classification model. The model performs well in evaluating and predicting the traffic state of highway networks and is consistent with the classification results of actual data.

However, existing studies using only the fuzzy clustering method will ignore the effect of the magnitude of different factors during grading. All input data are treated as equally important, regardless of whether their dimensions are consistent or not. Specifically, if the value range of one attribute exceeds that of another, this attribute may dominate the clustering process, causing the clustering result to be biased towards this attribute.

The Qinghai–Tibet Plateau boasts a unique environment, with the climate, topography, and geology along the four main highways to Tibet being notably complex and variable [17]. Consequently, traffic interruptions in this region exhibit distinct characteristics. However, current research falls short in analyzing the causes and characteristics of traffic interruptions specific to the Tibetan highway environment. A clear standard for grading traffic interruption states has yet to be established. As a result, research fails to provide a scientific foundation for subsequent rapid and precise safety precautions and emergency response measures.

To address this situation, the work employed the entropy weight-TOPSIS algorithm [18] to quantify the state parameters of traffic disruptions on the four highways to Tibet and to mitigate the effects of the dimensions on each other. The algorithm considered the relative importance of indices through the entropy weight method. The entropy weight-TOPSIS method was used to assess the proximity of each scheme to the ideal solution. However, traffic interruption data predominantly comprised static historical data due to the limitations of sensing equipment along each highway. Thus, these data were characterized by a lack of systematization and fuzzy randomness. Consequently, the fuzzy C-means clustering algorithm (FCM) [19] was used to cluster quantified data. Then, a grading method was established for traffic interruption states in the extreme environmental conditions of the highways to Tibet.

3. Causes and Characteristics of Traffic Interruptions in Highways to Tibet

3.1. Causes of Traffic Interruptions

The causes and distribution of traffic interruptions across different highways to Tibet are statistically analyzed based on data from traffic interruptions over the past three years (2021, 2022, and January to June 2023) provided by seven highway development and emergency support centers in the Tibet Autonomous Region, specifically in Changdu, Naqu, and Ngari. The number of traffic interruptions on the four highways to Tibet is shown in Figure 2. Compared with Figure 1, it is found that the number of traffic interruptions and the annual average daily traffic (AADT) do not show a significant correlation. For example, the Qinghai–Tibet Highway has the highest AADT, yet it does not have the highest number of traffic interruptions. On the contrary, although the Xinjiang–Tibet Highway has the lowest AADT, it has the second-highest number of traffic interruptions among the four corridors. This implies that traffic interruptions do not depend entirely on traffic volume, but are influenced by a variety of other factors.

Table 2. Cause of the interruption and definition.

Type of Accident	Definition
Debris flow	Debris flows can directly bury highways, destroying roadbeds, bridges, culverts, and other facilities, causing traffic disruptions, resulting in major accidents, and even forcing the rerouting of roads.
Accumulated snow	Snowfall that persists without melting can result in traffic congestion, power and communication disruptions, and other disasters. According to the DB63/T 1565-2017 standard [20], snow depth greater than 2 m and snow duration of more than 21 h qualify as moderate snowstorms. If these conditions worsen, they can evolve into severe snowstorms.
Collapse	Falling rocks and debris can damage highways and bridges, and even cause serious accidents such as car wrecks and deaths. Aggregates can block rivers and cause water level to rise, resulting in water damage to roadbeds and bridges, and leading to traffic accidents.
Traffic accident	Vehicle collisions or other accidents that occur on the roadways can result in injuries, deaths, and property damage. Common causes of traffic accidents include speeding, driving under the influence of alcohol, fatigue, and disobeying traffic rules.
Traffic Control	Traffic control is a variety of measures taken to ensure safe and smooth roads. This may include restricting the speed of vehicles, enforcing one-way rules, banning certain types of vehicles, etc.
Infrastructure damage	subgrade	Damage to the subgrade, reducing the driving experience and even affecting driving safety.
	pavement	Damaged pavement, reduced driving experience and even affecting driving safety.
	Bridge, underpass	Structural damage or disease anomalies that affect the useful life of the structure and pose safety hazards.
	Facilities	The lack of necessary signage, guardrails, and other safety equipment can make it difficult for to judge road conditions and make sound decisions.

presents the cause of the interruption in the four highways to Tibet. As can be seen in Figure 3, there are differences in the causes of traffic interruptions across the highways. On the Sichuan–Tibet Highway, debris flows are the predominant cause of interruptions, with snow and landslides also contributing significantly. On the Yunnan–Tibet Highway, nearly 50% of traffic interruptions are attributed to accumulated snow, while the incidence of interruptions due to debris flows and collapses is similar. Traffic accidents are the primary cause of interruptions on the Qinghai–Tibet Highway, accounting for approximately 65%, followed by snow (accounting for about 26%). The distribution of interruption causes on the Xinjiang–Tibet Highway is similar to those on the Yunnan–Tibet Highway. The main influencing factors of the interruption are snow, followed by collapses and debris flows.

3.2. Characteristics of Traffic Interruptions

3.2.1. Traffic Interruption Duration

The characteristics of traffic interruption duration along different highways to Tibet are compared (Figure 4 and Figure 5). The traffic interruption duration of the Qinghai–Tibet Highway and Xinjiang–Tibet Highway shows a unimodal distribution, while the Qinghai–Tibet Highway and Yunnan-Tibet Highway show a bimodal distribution, with variations in shape and dispersion degree. Specifically, the Sichuan–Tibet Highway and Qinghai–Tibet Highway display broad distribution with high data dispersion. In contrast, the Yunnan–Tibet Highway and Xinjiang–Tibet Highway show more condensed distribution. The Sichuan–Tibet Highway stands out with significantly higher values in mean, median, maximum, and interquartile range compared to the other highways, with the widest data distribution. The Qinghai–Tibet Highway follows with a slightly shorter interruption duration. The Yunnan–Tibet Highway experiences the shortest mean traffic interruption duration. The highways ranked from highest to lowest mean interruption duration are as follows: Qinghai–Tibet Highway (4.51 h), Xinjiang–Tibet Highway (4.50 h), Sichuan–Tibet Highway (3.64 h), and Yunnan–Tibet Highway (2.91 h).

3.2.2. Traffic Interruption Mileage

Figure 6 and Figure 7 show the cumulative distribution and boxplot of traffic interruption mileage for various highways to Tibet, respectively. The Sichuan–Tibet Highway features higher interruption mileage values in terms of mean, median, maximum, and interquartile range compared to the other highways under the same distribution probability. The overall interruption mileage of the Yunnan–Tibet Highway and Xinjiang–Tibet Highway is low. The Xinjiang–Tibet Highway shows the dispersed data distribution of traffic interruption mileage, with a low average despite some high values in the dataset. The highways ranked from highest to lowest average interruption mileage are as follows: Sichuan–Tibet Highway (9.81 km), Qinghai–Tibet Highway (2.38 km), Xinjiang–Tibet Highway (1.59 km), and Yunnan–Tibet Highway (0.09 km).

3.2.3. Traffic Interruption Severity

The severity of traffic interruption refers to the effects of interruptions on road traffic capacity, denoted by [21]

$$s=t\times l$$

(1)

where s is the set of the severity of traffic interruptions, i.e., $s=s\left(i\right),i=\mathrm{1,2},\dots ,n$; $s\left(i\right)$ is the severity of traffic interruption induced by the ith cause; $t$ is the set of traffic interruption durations; $l$ is the set of traffic interruption mileage.

The index values for the severity of traffic interruptions along each highway to Tibet are calculated, and their distribution is compared. The Sichuan–Tibet Highway experiences significantly higher mean traffic interruption severity compared to the other highways, while the Xinjiang–Tibet Highway exhibits the most dispersed data (Figure 8). Compared with the Yunnan–Tibet Highway and Xinjiang–Tibet Highway, the severity of traffic interruptions of the Qinghai–Tibet Highway is higher, and its values are relatively discrete. The highways ranked from highest to lowest mean interruption severity are as follows: Sichuan–Tibet Highway (77.10 km/h), Xinjiang–Tibet Highway (18.81 km/h), Qinghai–Tibet Highway (12.00 km/h), and Yunnan–Tibet Highway (0.33 km/h).

The climate, topography, and geology along the highways to Tibet are notably complex and variable. Consequently, traffic interruptions along these highways exhibit distinct causes and characteristics. On the Qinghai–Tibet Highway, traffic accidents are the primary factor causing interruptions, followed by snow disasters. Occasionally, the Qinghai–Tibet Highway experiences traffic interruptions with extended duration and mileage. The duration of these interruptions can extend up to 29 h, while the distance affected reaches 20 km, indicating a high level of severity. The Qinghai–Tibet Highway, a critical transportation route, handles more than 85% of the materials entering Tibet and over 90% of those leaving. It boasts an average altitude exceeding 4000 m and an average annual temperature below freezing.

Unlike other highways, the Qinghai–Tibet Highway traverses sections with frozen soil areas. The thaw settlement of frozen soil, along with environmental extremes, leads to pavement subsidence, instability, and cracking, which deteriorates driving conditions. In the case of low-temperature hypoxia and single-lane traffic, the dynamic performance of the truck is reduced. At the same time, drivers who work under such conditions for a long time may feel tired and slow to react, resulting in traffic accidents and blockages. Single-point congestion is easy to form a chain reaction—when a section of the road obstacles or traffic accidents (such as collapse and traffic accidents mentioned in Figure 1), it can quickly lead to serious local congestion. This is especially problematic on road sections where only one lane is available in both directions, blockage in any direction may lead to a significant reduction in the operational efficiency of the entire route.

The Sichuan–Tibet Highway is located in a typical alpine and gorge region, characterized by complex geological conditions along both its northern and southern lines. The terrain is marked by loose geology, sparse vegetation, and a high susceptibility to collapses. Heavy summer rainfall triggers debris flows, while winter brings significant snow accumulation. Additionally, factors such as low technical standards, great linear changes, limited detour options within sections, and poor disaster resilience contribute to frequent traffic interruptions along the Sichuan–Tibet Highway. This route experiences the highest severity of traffic interruptions. Affected by geological and meteorological disasters, traffic interruptions with extended duration and mileage are common. Although the mean interruption duration of the Sichuan–Tibet Highway is lower than that of the Qinghai–Tibet Highway and Xinjiang–Tibet Highway, its mean interruption mileage is considerable. This phenomenon correlates with its traffic volume.

The main causes of traffic interruptions along the Yunnan–Tibet Highway and Xinjiang–Tibet Highway are geological and meteorological disasters, with accumulated snow being a significant factor. The Yunnan–Tibet Highway traverses mountains and gorges with steep cross-slopes, severely weathered geology, and a high susceptibility to collapses. Debris flows tend to occur in rainy seasons. However, significant temperature differences between day and night at high altitudes facilitate winter snow accumulation to freeze, which makes snow the predominant cause of traffic interruptions on this route. The Xinjiang–Tibet Highway is mostly paved with asphalt and meets second-level technical standards. It traverses depopulated zones with low temperatures and oxygen depletion at high altitudes and stretches through vast Gobi deserts characterized by extreme cold. Snow disasters in winter are the main cause of traffic interruptions on the Xinjiang–Tibet Highway. The Xinjiang–Tibet Highway exhibits a longer mean interruption duration compared to the Yunnan–Tibet Highway, from the perspective of traffic interruption characteristics. However, the traffic interruption mileage for both highways is relatively low due to their small traffic volumes.

4. Grading Model of Traffic Interruption States Based on the Entropy Weight-TOPSIS Method and FCM

4.1. Entropy Weight-TOPSIS Method

The entropy weight-TOPSIS method, an objective weighting multi-factor evaluation technique, integrates the advantages of the entropy weight and TOPSIS methods. Its evaluation procedure is as follows.

First, multi-factor data are organized into a matrix denoted as $X_{(m\times n)}$.

$$X_{(m\times n)}=\left[\begin{array}{ccc}{x}_{11}& \cdots & x_{1j}\\ ⋮& \ddots & ⋮\\ x_{i1}& \cdots & x_{ij}\end{array}\right]$$

(2)

where $i$ is the traffic interruption ($i=\mathrm{1,2},\cdots ,n$); $j$ is the index parameter of the interruption ($j=\mathrm{1,2},\cdots ,m$).

Data are normalized and standardized to eliminate the dimensions among different factors. The normalized index is adopted in the work.

$$Y_{ij}=\left\{\begin{array}{c}{\displaystyle \frac{x_{ij}-{\left(x_{ij}\right)}_{min}}{{\left(x_{ij}\right)}_{max}-{\left(x_{ij}\right)}_{min}}},Normalizedindex\\ \\ {\displaystyle \frac{{\left(x_{ij}\right)}_{max}-x_{ij}}{{\left(x_{ij}\right)}_{max}-{\left(x_{ij}\right)}_{min}}},Reversedindex\end{array}\right.$$

(3)

Proportion $P_{ij}$ of the jth parameter index in the ith traffic interruption is denoted by

$$P_{ij}={\displaystyle \frac{Y_{ij}}{\sum _{i=1}^m Y_{ij}}}$$

(4)

where m is the number of traffic interruptions; $Y_{ij}$ is the value of the parameter index after normalization and standardization.

Information entropy $E_j$of the jth parameter index is as follows.

$$E_j=-{\displaystyle \frac{1}{\ln m}}({\sum }_{i=1}^m P_{\mathrm{i}\mathrm{j}}\cdot \mathrm{l}\mathrm{n}{P}_{\mathrm{i}\mathrm{j}})$$

(5)

Utility value $D_j$of the jth parameter index is denoted by

$$D_j=1-E_j$$

(6)

Objective weight $W_j$of the jth parameter is calculated. $n$ is the number of indices, i.e., $n=3$.

$$W_j={\displaystyle \frac{1-E_j}{\sum _{j=1}^n D_j}}$$

(7)

Weighting matrix $Z_{ij}$is obtained.

$$Z_{ij}=W_j\cdot Y_{ij}=\left[\begin{array}{ccc}{z}_{11}& \cdots & z_{1j}\\ ⋮& \ddots & ⋮\\ z_{i1}& \cdots & z_{ij}\end{array}\right]$$

(8)

Each parameter index is defined, i.e., $z_{j^{+}}$and $z_{j^{-}}$are the maximum and minimum values of each column, respectively.

$$\begin{array}{c}{z}_j^{+}=max\left(z_{1j},z_{2j},\dots z_{nj}\right)\\ z_j^{-}=min\left(z_{1j},z_{2j},{\dots z}_{nj}\right)\end{array}$$

(9)

The ideal normalized and reversed distances are calculated.

$$\begin{array}{c}{D}_i^{+}=\sqrt{\sum _{j=1}^n {\left(z_j^{+}-z_{ij}\right)}^2}\\ D_i^{-}=\sqrt{\sum _{j=1}^n {\left(z_j^{-}-z_{ij}\right)}^2}\end{array}$$

(10)

Equation (11) shows the score of each traffic interruption in [0, 100].

$$Scor{e}_i={\displaystyle \frac{D_i^{-}}{D_i^{+}+D_i^{-}}}\times 100$$

(11)

The flowchart of the entropy weight-TOPSIS method is shown in Figure 9:

4.2. FCM

Fuzzy clustering operates through the iterative optimization of an objective function. It initiates with a randomly assigned clustering center and iteratively refines the center points and fuzzy membership degrees of each sample by seeking the minimum point that fulfills the objective function. Finally, sample data are classified into corresponding clusters. The objective function for FCM is as follows.

$$min{J}_m(U,V)={\sum }_{i=1}^c {\sum }_{j=1}^n u_{ij}^m{∥x_j-{\nu }_i∥}^2$$

(12)

where $U=\left[u_{ij}\right]$ is a fuzzy partition matrix; $u_{ij}$ is the degree membership of the jth sample ($x_j$) belonging to the ith category in data set $X=\{x_1,x_2,\cdots ,x_n\}$, and its constraints include $0\le u_{ij}\le 1$, $0<\sum _{j=1}^n u_{ij}<n$, and $\sum _{i=1}^c u_{ij}=1,\forall j=\mathrm{1,2},\cdots ,n$; n is the number of objects in dataset X; $V=\{v_1,v_2,\cdots ,v_c\}$ consists of vectors of c clustering centers; the fuzzy index $m>1$ is the weighting coefficient of the membership degree.

A new objective function is formed using the Lagrange multiplier approach and Equation (13).

$$\mathrm{L}(\mu ,\nu ,\lambda )={\displaystyle {\sum }_{i=1}^N} {\displaystyle {\sum }_{j=1}^C} {\mu }_{ij}^m{∥x_i-{\nu }_j∥}^2+{\sum }_{i=1}^N {\sum }_{j=1}^C \left({\lambda }_i{\mu }_{ij}-{\lambda }_i\right)$$

(13)

The partial derivatives of $\mu$ and $\nu$ in the equation are calculated. The iterative equations of the fuzzy membership degree and clustering center are obtained by combining constraint conditions.

$$u_{ij}={\displaystyle \frac{1}{\sum _{k=1}^c {\left(\frac{∥x_i-{\nu }_j∥}{∥{\nu }_i-{\nu }_k∥}\right)}^{\frac{2}{\left(m-1\right)}}}}$$

(14)

$$v_i={\displaystyle \frac{\sum _{j=1}^n u_{ij}^m{x}_j}{\sum _{j=1}^n u_{ij}^m}}$$

(15)

The iterative process of FCM [22] is as follows.

• Step 1: The number of clusters and fuzzy index m are preset to determine the precision conditions and the maximum allowable iterations for algorithm termination.
• Step 2: Relational matrix $U$ is initialized, and distance $d_{ij}$ between samples is calculated.
• Step 3: Membership matrix $U$ is updated based on Equation (14).
• Step 4: Calculated $u_{ij}$ is substituted into Equation (15) to update the matrix of clustering centers ($V$).
• Step 5: The value of the objective function is calculated based on Equation (12) and Step 4.
• Step 6: Steps 3–5 are iterated until $J\left(n\right)-J(n-1)\le b$, or the maximum number of iterations is reached. Then, the optimal function value of FCM is output.

The flowchart of FCM is shown in Figure 10:

4.3. Grading Model of Traffic Interruption States

Data on the parameters of traffic interruptions (i.e., interruption duration, mileage, and severity) are collected. Then these data are normalized and standardized for a comprehensive evaluation. Subsequently, standardized data are comprehensively evaluated using the entropy weight-TOPSIS method to derive a quantified status value for each traffic interruption. Finally, these quantified status values are clustered using the FCM to realize the grading of traffic interruptions. The model outputs different levels of traffic interruption status (Figure 11), which provides decision support for subsequent precautions and emergency responses.

5. Analysis of Examples

5.1. Calculation of the Status Values of Traffic Interruptions

The entropy right-TOPSIS method is used to analyze the status values of traffic interruptions based on data from traffic interruptions over the past three years, provided by seven highway development and emergency support centers in Tibet Autonomous Region, specifically in Changdu, Naqu, and Ngari.

• Data sources

The data used in this study comes from historical records of traffic interruptions on the four main highways into Tibet. The dataset includes the following parameters:

Interruption Time: Duration of each interruption event.

Interruption Distance: The length of the road segment affected by the interruption.

Disruption Duration: The product of interruption time and distance, providing a comprehensive measure of the impact of each interruption event.

2.

Data pre-processing

After obtaining the raw traffic interruption data, the box-and-line diagram method is applied to remove the outliers, i.e., data smaller than QL-1.5IQR or larger than QU+1.5IQR (QL is the lower quartile, IQR is the interquartile range, and QU is the upper quartile). Based on the preprocessed traffic interruption data, the entropy weight-TOPSIS method is further applied to calculate the interruption state values.

3.

Calculation of interruption state values using Entropy Weight-TOPSIS

First, collected data are rendered dimensionless using Equation (3) and the entropy weight-TOPSIS method. Then, objective evaluation weights for interruption duration, mileage, and severity are determined based on Equations (4)–(7) (

Table 3. Weights of evaluation indices.

Evaluation Indices	Interruption Duration	Interruption Mileage	Interruption Severity
Weight ($W_j$)	0.3356	0.3332	0.3312

). Interruption duration is the most influential factor on the status value of traffic interruptions, while interruption severity exerts the minimum impact.

The weight matrix $Z_{ij}$ is derived using Equation (8). Subsequently, the maximum and minimum values of the solutions for each column are computed by Equation (9), as shown in

Table 4. The maximum and minimum values.

Evaluation Indices	Interruption Duration	Interruption Mileage	Interruption Severity
maximum values	0.335946	0.333497	0.331557
minimum values	0.000336	0.000333	0.000331

. Then, the ideal distances between the values of each factor indicator and both the maximum and minimum values are calculated using Equation (10).

Finally, the comprehensive evaluation value of all events is calculated by Formula (11), and the specific results are shown in Figure 12. A higher status value indicates a more severe traffic interruption.

The status values of traffic interruptions on each highway to Tibet are compared (Figure 13). The statistics for the Sichuan–Tibet Highway are significantly higher than those of the other routes. The Qinghai–Tibet Highway exhibits higher values compared to the Yunnan–Tibet Highway and Xinjiang–Tibet Highway. The statistics for the Yunnan–Tibet Highway exhibit minimal variation due to limited interruption data.

5.2. Cluster Grading and Effectiveness Analysis of the Status Values of Traffic Interruptions

5.2.1. Cluster Grading

Some hyperparameters need to be preset before clustering.

Fuzzy index m: James found that m is related to the convergence of the algorithm, and its value is linked to the quantity of sample data (n). m should be greater than $n/(n-2)$, and its empirical range is $1.1\le m\le 5$. Nikhil et al. believed that the optimal value for m falls within [1.5, 2.5], and it is recommended to take a value of 2 [23], based on the experimental verification of clustering algorithm’s effectiveness. The geometric characteristics of clustering vary with m. Clustering exhibits Boolean characteristics when m approaches 1, with most fuzzy membership degrees being either close to 0 or to 1. The fuzzy membership degree of the cluster resembles a Gaussian function when m = 2. The function of fuzzy membership tends to peak as m increases [24]. Considering these insights, m = 2 in the work.

The maximum number of iterations is set to 100 to ensure that the algorithm has enough opportunities to identify an appropriate clustering center.

Iteration precision is set to 10⁻⁵ to ensure the accuracy of clustering results

Status values undergo fuzzy processing using FCM based on data calculated by the entropy weight-TOPSIS method to yield a fuzzy membership matrix.

The relationship matrix $U$ is first initialized using the interruption number and the traffic interruption status value; the distance between the samples $d_{ij}$ is calculated.

Then, its fuzzy affiliation matrix is obtained after 100 iterations by updating the affiliation matrix $U$ and the cluster center matrix V, using Equations (14) and (15). A portion of this matrix, specifically about the attributes of traffic interruption severity, is presented because the following discussion involves the clustering effects of varying number of clusters. This matrix shows the membership degree of each traffic interruption to levels 1–4. The sum of the membership degrees for each traffic interruption equals 1, which signifies the likelihood of the event belonging to different levels (

Table 5. Four-level fuzzy membership matrix.

1	2		641	642
0.7827	0.9612	…	0.9900	0.9796
0.2040	0.03540	…	0.0087	0.0177
0.0020	0.00054	…	0.0002	0.0004
0.0111	0.0027	…	0.0009	0.0021

).

FCM converts quantitative attribute $x_i(i=\mathrm{1,2},\cdots ,t)$ into attribute set ${\mu }_{ij}(i=\mathrm{1,2},\cdots ,n,j=\mathrm{1,2},\cdots ,c)$ represented by fuzzy attributes. Then, the clustering center of each attribute set ($v_{ij}$) is determined to minimize the value function of non-similarity indices. Finally, grading results for four number of clusters are obtained (

Table 6. FCM clustering results.

Number of Clusters	Level	Clustering Center	Interval for the Status Values of Traffic Interruptions
2	Level 1	1.704	[0.0014, 13.1542]
	Level 2	25.1895	[13.5997, 61.2340]
3	Level 1	1.259	[0.0014, 6.0787]
	Level 2	11.2554	[6.5636, 23.9298]
	Level 3	37.4272	[24.8619, 61.2340]
4	Level 1	1.0993	[0.0014, 4.4056]
	Level 2	7.8311	[4.4829, 14.5598]
	Level 3	22.4148	[15.7651, 32.4697]
	Level 4	47.823	[38.6265, 61.2340]
5	Level 1	0.8635	[0.0014, 2.4523]
	Level 2	4.0759	[2.4716, 7.4245]
	Level 3	10.7764	[7.5325, 17.4541]
	Level 4	24.203	[18.0349, 32.4697]
	Level 5	48.8477	[38.6265, 61.2340]

).

The above table shows the grading results for varying number of clusters. The categorization of status values becomes more refined with the higher number of clusters, which facilitates a more precise evaluation of the severity of traffic interruptions.

5.2.2. Validity Analysis

The number of clusters should be preset in FCM clustering analysis, which relies on personal experience. However, this preset number does not guarantee an optimal clustering outcome. Therefore, the optimal number of clusters is determined through alternative methods to ensure the ideal clustering effect.

PE, a validity index specifically designed for evaluating the performance of fuzzy clustering analysis, quantifies the uncertainty or information entropy within the membership matrix [25]. A lower PE value indicates less uncertainty in the clustering outcome and a more distinct classification of each data point’s affinity to a particular cluster. Calculating PE across various number of clusters can identify the optimal option, which helps to achieve the ideal clustering effect (Equation (16)).

$$PE=-{\displaystyle \frac{1}{N}}{\sum }_{i=1}^N\hspace{1em}{\sum }_{j=1}^C u_{ij}{\mathrm{l}\mathrm{o}\mathrm{g}}_2\left(u_{ij}\right)$$

(16)

where $N$ is the number of data points; $C$is the number of clusters; $u_{ij}$is the membership degree of the jth sample ($x_j$) belonging to the ith category.

Table 7. PCE values for varying number of clusters.

Number of Clusters	2	3	4	5
PE	0.043	0.058	0.057	0.073

shows the PCE values for varying number of clusters.

Figure 14, Figure 15, Figure 16 and Figure 17 show the clustering results with varying levels.

When the number of clusters is changed, there is an impact on the results, and this impact can be discussed from three perspectives:

(1)

Lesser number of clusters: Interruptions were categorized as “major interruptions” and “minor interruptions”. While this categorization simplifies the understanding of the data, it may hide some important nuances. For example, some highways were interrupted for the same reasons, but there were significant differences in the duration and mileage of the interruptions. Take the interruptions numbered 160 to 200 on the Sichuan–Tibet and Yunnan–Tibet highways as an example: although most of these events were caused by collapse and debris flow, they were grouped into the same level when n_cluster = 2 and into different levels when n_cluster = 4 and 5. This suggests that using a smaller number of clusters may overlook these specific differences, leading to an incomplete understanding of the actual situation.

Advantages: This simple categorization offers a quick decision-making tool during emergencies, allowing managers to quickly identify which events need immediate attention.

Disadvantages: However, this approach overlooks significant differences between events, potentially leading to inefficient resource allocation. For example, two highways might experience interruptions due to the same cause, but the interruption duration and the affected distance may differ significantly. A smaller number of clusters may lead to underestimating the severity of certain interruptions, affecting timely and appropriate responses.

(2)

Moderate number of clusters: This provides a more detailed categorization, identifying levels of interruptions with similar causes of interruption. This helps to reveal which highways are more susceptible to specific conditions (e.g., severe weather or geologic hazards) and how they are affected differently.

Advantages: Moderate clustering helps distinguish between various types of interruption events, enabling managers to craft more appropriate emergency response plans. For example, some highways may be more vulnerable to weather conditions, while others may experience more frequent geological hazards.

Disadvantages: Although this level of clustering provides more detailed information, it may still have limitations. As the number of clusters increases, the similarities between some events may become diluted, possibly categorizing very similar events into different clusters and slightly increasing the complexity of the analysis.

(3)

Higher number of clusters: The interruption classification can be further subdivided to show more specific features. However, when there are too many levels, the boundaries between different categories may become blurred, resulting in similar samples being assigned to different categories, reducing the validity of the clustering. For example, some events were categorized into level-1 and level-5 when n_cluster = 5.

Advantages: More clusters can help identify specific traffic interruption patterns and reveal more nuanced characteristics of the interruptions. For example, by using a large number of clusters, very rare but highly impactful events can be identified, aiding in the formulation of more precise recovery plans.

Disadvantages: However, with too many clusters, the classifications become overly detailed, leading to blurred boundaries between categories. This can cause very similar events to be inconsistently grouped into different categories, which could confuse decision-makers and make management more complex.

By analyzing the different numbers of clusters, we can observe that the gradual decrease in the PE values except for the two-level classification indicates that the validity of the clustering results has been improved. Specifically, the PE value is 0.043 for the two-level classification and 0.057 for the four-level classification. Although the two-level classification is more valid than the four-level classification in terms of PE value, we recommend the four-level classification scheme rather than the two-level scheme from a practical application point of view. The four-level classification scheme not only has a lower value of PE, but also ensures an accurate classification of the value of the traffic interruption status, contributing to a more comprehensive understanding of the severity and impact of the different highways to Tibet in the face of traffic interruptions. In the four-level classification, it can be found that the interruptions of the Sichuan–Tibet Highway (events 128–186) and Xinjiang–Tibet Highway (events 207–642) belong to level-3 and level-4 serious interruptions more than the other two highways, and most of the high-level interruptions of the Qinghai–Tibet Highway (events 1–127) are level-2 ordinary interruptions. The Yunnan–Tibet Highway, due to the limited data and its classification primarily in level-1, is not analyzed in detail in this paper.

The Sichuan–Tibet Highway was constructed in the 1950s, when lower construction standards and complex geological and climatic conditions made the route more prone to serious traffic disruptions. The Xinjiang–Tibet Highway passes through the world-famous Kunlun Mountains and the Himalayas, with an average altitude of more than 4500 m, making it the world’s highest and most dangerous plateau highway. It is also prone to serious traffic interruptions at levels-3 and level-4. The Qinghai–Tibet Corridor, on the other hand, is relatively less severe overall, despite the fact that there have been disruptions. These findings are important guidance for road management to develop targeted maintenance and emergency response measures. In particular, the Sichuan–Tibet Highway, with a lower construction standard and complex geo-climatic conditions, requires more attention and resource investment to improve its resilience and reduce the impact of traffic interruptions.

6. Conclusions

The work analyzed the operational and traffic interruption characteristics of highways to Tibet in extreme environments using data on actual traffic operations and interruptions. A comprehensive evaluation method was used to assess and quantify the status values of traffic interruptions, which were then graded using a clustering algorithm.

• The climate, topography, and geology along the highway to Tibet were complex and changeable, which resulted in diverse transportation functions and traffic volumes of these Highways. Therefore, the causes and characteristics of traffic interruptions were distinct. Traffic accidents were the primary cause of interruptions along the Qinghai–Tibet Highway, with snow disasters being a secondary factor. In contrast, debris flows were the predominant cause of interruptions along the Sichuan–Tibet Highway, followed by snow accumulation and collapses. Nearly 50% of traffic interruptions were attributed to snow buildup along the Yunnan–Tibet Highway. The Xinjiang–Tibet Highway and Yunnan–Tibet Highway exhibited similar patterns of traffic interruption causes, with accumulated snow being the predominant influencing factor.
• The Sichuan–Tibet Highway recorded the longest mean interruption duration and mileage among the four routes to Tibet, with its traffic interruption severity being the most significant. Each statistical value for the traffic interruption duration of the Qinghai–Tibet Highway was merely lower than that of the Sichuan–Tibet Highway. However, the Qinghai–Tibet Highway had a low mean interruption mileage, indicating mild traffic interruption severity. The Xinjiang–Tibet Highway showed greater mean interruption duration and mileage compared to the Yunnan–Tibet Highway.
• The status values of the Sichuan–Tibet Highway were significantly higher than those of the other highways based on evaluation results. The Qinghai–Tibet Highway exhibited higher statistical values compared to the Yunnan–Tibet Highway and Xinjiang–Tibet Highway. The parameters ranked from highest to lowest weight in the comprehensive evaluation model corresponded to traffic interruption severity, mileage, and duration.
• The model integrating the entropy weight-TOPSIS method and FCM could grade the traffic interruption states of the highways to Tibet. The four-level classification had a lower PE value in all schemes except for the two-level classification. The work analyzed the operational and traffic interruption characteristics of highways to Tibet in extreme environments using data on actual traffic operations and interruptions. A comprehensive evaluation method was used to assess and quantify the status values of traffic interruptions, which were then graded using a clustering algorithm. The key findings are summarized as follows.
• Practical Applications and Contributions

  (1)

  Real-time decision making

Through clustering algorithms, events can be categorized into different classes based on the interruption status values calculated using the interruption duration and impact range. Different categories of disruptions may correspond to different emergency response needs. The system can provide hierarchical decision support to managers based on the clustering results. Example:

High-risk category (e.g., long-term road closure triggered by snowstorm): more resources (e.g., emergency rescue teams, heavy equipment) need to be deployed immediately for handling.

Medium category (e.g., short-term weather-triggered interruptions): traffic warnings and recommended detours may be all that is needed.

Low-risk category (e.g., minor landslides): only routine maintenance needs to be scheduled.

(2)

Development and Optimization of Traffic Recovery Plans

With the clustering results, the system can help transportation managers develop more effective recovery plans. Different categories of disruptions may require different recovery strategies. For example, some disruptions (e.g., large-scale landslides) require days or even weeks of recovery time, while some events (e.g., snow cover) can be quickly restored to traffic through brief cleanup efforts.

Combined with the clustering results, the system can generate different recovery schedules and provide specific resource allocation recommendations. In this way, managers can choose the most appropriate recovery plan based on different event categories, improving overall traffic recovery efficiency.

(1)

Enhancing Road Management Decisions

Long-term strategic planning: Cluster analysis results can be used not only for real-time emergency response, but also to provide data support for long-term transportation infrastructure construction and optimization. For example, by identifying which road segments are most frequently affected by disruptions, traffic management authorities can develop long-term infrastructure construction plans that prioritize the retrofitting or stabilization of these vulnerable road segments. High-risk areas and areas with frequent traffic interruptions may be prioritized for infrastructure improvements and increased surveillance.

Emergency Preparedness: Understanding seasonal traffic interruptions and the causes of interruptions can help develop more effective emergency preparedness plans. For example, stockpiling necessary equipment and materials in advance for the Sichuan–Tibet and Yunnan–Tibet highways—where debris flow, collapse, and accumulate snow are common—prior to the onset of the rainy season or winter can shorten response times and minimize the impacts of traffic

(2)

Improved Transportation Planning and Operations

Traffic flow optimization: By identifying interruptions with large traffic interruption status values, traffic planners can develop traffic rerouting strategies or implement temporary traffic control measures to alleviate congestion and delays.

Infrastructure Development: Identifying high-risk areas can inform long-term infrastructure development plans, such as building bypasses or reinforcing vulnerable sections of highways.