Identification Method of Main Road Traffic Congestion Situation in Cold-Climate Cities Based on Potential Energy Theory and GPS Data

Abstract

Traffic congestion is a global problem. Affected by climate, the issue of congestion in cold-climate cities is more serious. To comprehensively and accurately identify the traffic congestion situation on the main roads of cold-climate cities and to provide a reference for city managers for congestion treatment, this study applies the theory of potential energy to the problem of traffic congestion, draws on the symmetry of potential energy and the function mechanism of artificial potential fields, and establishes a traffic congestion potential energy model for the main roads in cold-climate cities. Taking Global Positioning System (GPS) data as the primary data, the model parameters are calibrated using a combination of subjective and objective empowerment methods, and the investigation into the congestion perception level determines the division threshold of the congestion potential energy level. Test results are encouraging, and the method considers the state and the trends and can avoid problems such as lagging road condition information.

1. Introduction

With the continuous acceleration of urbanization, traffic congestion is becoming more and more serious, which has not only become an important “bottleneck” problem for urban residents but has also become a difficult problem that city managers have to face. The term cold-climate city refers to a city that has adverse effects on urban life due to a long winter and harsh climate [1]. As different countries or regions have different climatic characteristics, the criteria for defining cold-climate cities are also different. In this study, the discriminant conditions of severe cold regions (an average temperature of the coldest month ≤−10 °C or the days with a daily average temperature below 5 °C ≥ 145 days) and cold regions (−10 °C < the average temperature of the coldest month < 0 °C or 90 days< the days with daily average temperature below 5 °C < 145 days) in the “Thermal design code for civil buildings” (GB 50176–2016) promulgated by the National Standardization Management Committee are used as the criteria for defining cold-climate cities. In cold-climate cities, winter temperatures are low and last for a long time, with frequent snowfall accompanied by a bitter cold wind, leading to the phenomenon of wind blowing snow and snow blindness (sunlight reflected by snow), resulting in reduced visibility; moreover, the snow adheres to the road pavement, forming icy and snowy pavement, resulting in a decrease in the friction and adhesion coefficients of the road surface [2,3,4,5,6]. Such severe climatic conditions make the traffic operation characteristics of cold-climate cities in the winter different from non-cold-climate cites or from other seasons in cold-climate cities. Based on the traffic flow data of cold-climate cities, some scholars have determined that snow and ice conditions reduce the travel volume of residents, with a decrease range of 16–47%. The greater the snowfall intensity is, the greater the decrease is, and the travel volume of passenger cars is more reduced than that of trucks [7,8,9]. Under the effects of low temperature and snow, the modes of walking and cycling shift to motor vehicles. Among them, the proportion of walking and cycling will decrease by 45–85%, and the proportion of motor vehicles such as private cars, taxis, and conventional buses will increase by 30–70% [10,11]. In addition, under such severe climatic conditions, not only will resident travel be affected, but talent attraction, investment attraction, and construction costs will also be negatively affected. As a result, the economic level of cold-climate cities is usually backward compared to non-cold-climate cities; the construction of subways, light rail systems, and other rail transit lags behind; and new public transport systems such as BRTs are difficult to develop. Eventually, the main form of public transport travel is conventional buses. In this case, the ground traffic pressure in winter in cold-climate cities is greater than it is in non-cold-climate cities or during other seasons in cold-climate cities, and traffic congestion problems are also more serious [12].

Roads can be divided into expressways, main roads, secondary main roads, and branch roads according to their status and functions [13]. Particularly, main roads are the most important. They are not only the main skeleton of the urban road network, and they also bear most of the city’s travel volume and are the main corridor connecting various urban districts, playing a role in traffic collection and distribution; hence, the traffic flow is concentrated, and congestion is mainly distributed along these main roads [14,15]. Although solving the traffic congestion problems of the various road levels can improve the overall traffic operation level of the city, the resource reserves of cold-climate cities are generally limited, and the ecological environment carrying capacity is insufficient. During urban development and construction, step-by-step promotion according to the priorities of the project is necessary to avoid financial deficits. Therefore, cold-climate cities should give priority to solving traffic congestion on the main roads.

Traffic congestion arises along with the traffic system, which is a complex system that is composed of humans, vehicles, and road. During the operation of the traffic system, each component is coordinated with the others. However, when the dynamic change in each component and when the interaction relationships between each component are unbalanced and the work is not coordinated, congestion will occur. The primary task to solve the problem of traffic congestion is to identify the traffic operation level. International studies on traffic congestion have been performed since the 1950s, and scholars from various countries have conducted many effective explorations, from traditional traffic flow theory to emerging interdisciplinary methods, such as the computer [16]. In the early stages of congestion research, scientific research institutions in various countries proposed nearly a hundred indicators for identifying traffic congestion and determined the threshold of each indicator based on the results of multiple experiments. The congestion level was obtained by comparing the actual operation results with the threshold. These indicators are mainly a series of traffic flow parameters, such as travel time, speed, and traffic flow density. For example, the Highway Capacity Manual (2016) developed in the United States takes the road service level as the identifying indicator. When the road service level reaches F (free flow speed is 55 km/h, the actual driving speed is ≤17 km/h and the volumetric capacity ratio is ≤1), it is considered to be congested [17]. The Japan Highway Public Corporation uses speed as an indicator, and when speed is lower than 40 km/h, congestion is indicated [18]. In the ‘Road traffic information service traffic condition description’ (GB/T 29107-2012) issued by the China Standardisation Administration, average travel speed is proposed as the identification indicator. Main roads are considered to be unblocked when $\overline{v}$ is >30 km/h, slow when traffic is moving at 15 km/h < $\overline{v}$ ≤ 30 km/h, and congested when $\overline{v}$ ≤ 15 km/h [19]. As the urban road traffic system becomes increasingly complex and multidimensional, fully expressing complex traffic conditions becomes increasingly difficult for a single traffic flow parameter. Thus, some comprehensive indicators, which are converted from a single traffic flow parameter and traffic characteristics, have been widely used (e.g., the travel time index (actual travel time/travel time under free flow state) proposed in United States’ ‘Accessibility Report’ [20], the congestion severe index (total delay times per thousand vehicles per peak hour/kilometres per thousand vehicles per peak hour) reported by the Federal Highway Administration [21], and the degree of congestion (the actual traffic volume of a section/the evaluation benchmark of 24 h or 12 h) proposed by the Japan Highway Public Corporation [18]). In addition, the macroscopic fundamental diagram, two-fluid theory, and cellular automata model have also been widely used in the study of traffic congestion problems. By counting the relationship between different traffic flow parameters and by simulating the microscopic characteristics of each vehicle, the macroscopic characteristics of traffic flow are obtained, thereby distinguishing traffic congestion.

In recent years, with the development of big data, cloud computing, satellite positioning, and mobile internet technology, real-time urban road dynamic traffic data can be obtained and identified. For example, Petrovska et al. [22] used web applications to evaluate traffic congestion based on real-time traffic flow and travel time and speed data stored in the historical patterns of Google Map’s traffic layer. D’Andrea et al. [23] established traffic congestion and an accident detection system based on Global Positioning System (GPS) data and evaluated the current traffic state by comparing simulated GPS data with actual GPS data. In addition, map navigation software companies also make extensive use of mobile phone signalling data and vehicle GPS data to identify and rank urban traffic congestion and to release real-time road traffic operation information, which greatly facilitates resident travel and route selection. For example, TomTom, which is based on the congestion index, is used to identify the level of traffic congestion in nearly 400 cities around the world [24]; Baidu Map uses the commuter rush hour congestion index to identify and traffic congestion rank in 136 Chinese cities; and AutoNavi Map distinguishes and ranks the traffic congestion status of 100 cities in China using the congestion delay index [25,26]. On the basis of the above analysis, the identification of traffic congestion has been a research hotspot in the field of transportation for many years, and many theoretical and practical results have emerged. However, research that has been specifically focused on the identification of main road congestion in cold-climate cities is lacking. The existing identification method emphasizes the state and ignores the trends, mainly focusing the detection and identification of the congestion state and does not consider traffic congestion trends. Additionally, the special climate characteristics of cold-climate cities are not taken into account. Some methods are a partial theory and less of an application. Although theoretical research is acceptable, it cannot achieve automatic application. Software programs such as Baidu and AutoNavi Map can realize the function of real-time identification due to the fact that traffic flow data require a certain amount of time for data collection, transmission, and processing. However, problems such as lag and asymmetry in road condition information exist.

Potential energy is one of the most important concepts in physics. It originated from the word “potentiality”, which was proposed by Aristotle, the ancient Greek philosopher. It has three meanings: the origin, root, or power of motion change; the logical possibility; and the potential ability of objects to change their motion [27,28]. The term potential energy was first coined by William Rankine, a Scottish physicist in the 19th century. He believed that all forms of energy could be divided into two categories: real, perceived energy—kinetic energy, and potential energy. Here, potential energy represents the tendency of a substance to move under certain conditions and can be measured by the work conducted by the matter overcoming force [29,30,31]. That is, potential energy is equal to the potential, trend, or energy of the work of the object. The greater the potential energy is, the greater the potential, trend, or energy to do work will be, which is in agreement with conservation law. The artificial potential field (APF) is a virtual force method proposed by Professor Oussama Khatib of Stanford University’s Intelligent Robot Laboratory in the mid-1980s. It simplifies the motion mechanism of robot by abstracting the motion of the robot in a certain environment, such as the attraction of the target point to the robot and the repulsion of the obstacles in the surrounding environment to the robot [32,33]. Considering that vehicles in a certain environment also have the potential to drive at fast speeds or decelerated braking, the level of congestion is also relative to the amount of work conducted by the forces amongst people, vehicles, and roads, and the acceleration or braking of the vehicle is mainly affected by the driver’s perception of the hidden dangers of the road environment [34,35]. Therefore, potential energy theory can be introduced into the study of traffic congestion to reflect potential congestion trends. At the same time, the mechanism between the various components of the traffic system can be simplified by an analogy of the artificial potential field method in order to provide a new perspective and new ideas for the study of congestion identification methods.

Dynamic traffic data are the basis for real-time, fast, and automatic congestion identification [36]. Dynamic traffic data have many types, including vehicle GPS data and traffic data from traditional and fixed traffic flow detectors, such as video, wave frequency, magnetic wave, and other types of detectors. The detector layout is expensive, and maintaining it in the later life stages is difficult. Generally, it cannot cover the entire city, and certain usage restrictions exist. However, vehicle GPS data cover a wide range, mainly through the use of taxis or conventional buses equipped with GPS receivers. The collected vehicle speed, geographical location, driving direction, and other information are transmitted to the traffic information interactive processing platform for storage at the frequency of 1–60 s through GPS satellites. The collected information is used to reflect the level of road operation by means of data conversion and software analysis [37,38]. Vehicle GPS data with low cost, high accuracy, and strong stability are not affected by bad weather; they are the main source of all types of road traffic information used worldwide. Therefore, GPS data should be used as the basis for the detection and identification of the congestion level.

Therefore, the purpose of this study is to take the vehicle GPS data as the primary data, draw lessons from the mechanism of potential energy and artificial potential field, establish a traffic congestion identification method suitable for main roads in cold-climate cities to solve the problem that the existing methods are not comprehensive enough to perceive congestion trends and the lack of consideration for the special climate in winter in cold-climate cities, break the asymmetry of road conditions, improve the accuracy of traffic congestion identification in cold-climate cities, and provide the possibility for the further scientific management of main road congestion problems in cold-climate cities. The remainder of the paper is organized as follows: Section 2 introduces the construction method for the congestion situation identification model. Section 3 introduces the selected case areas and data in this study. Section 4 tests the proposed method. Section 5 discusses the identification results. Finally, Section 6 introduces the research conclusions and future research directions.

2. Methodologies of Identification Model

The process for establishing a model that could be used for identifying the main road traffic congestion situation in cold-climate cities is shown in Figure 1. Firstly, the concept of the potential energy generated by traffic congestion is proposed and defined by analogy with the basic idea of APF in physics. Secondly, considering that the road environment is composed of road conditions, traffic facilities and traffic conditions, a traffic congestion situation identification model, namely the traffic congestion potential energy model, is constructed. Thirdly, considering that the model parameters have an important influence on how scientific and accurate the model that has been established, the parameter calibration method is designed to calibrate the model parameters. Fourthly, given that no obvious boundary exists between different congestion levels and because different people have varying perceptions and tolerances to different congestion levels, and different traffic operation levels are difficult to distinguish. Therefore, from the perspective of travellers, the quantitative relationship between potential energy generated by traffic congestion and the traffic congestion situation is established. Then, the mutation threshold of each level is determined, and the level of the potential energy generated by traffic congestion is divided.

2.1. Concept of Traffic Congestion Potential Energy

Potential energy can be divided into gravitational potential energy and elastic potential energy according to the nature of the interaction force. Potential energy is a relative quantity. The value of potential energy is related to the selection of the zero potential energy point. The exact value of the potential energy can only be obtained after the zero potential energy point is determined [39]. Potential energy can be superimposed in the same space. The artificial potential field (APF) method summarizes the force of the robot in the process of motion as gravitation (attraction) and elastic force (repulsion). The potential energy of the attraction and the potential energy of the repulsion are superimposed to generate an artificial potential field. The robot is subjected to the resultant force in the potential field and travels around the obstacle to the target point. The force of the robot in the APF is shown in Figure 2a, and the functional formulas for the attraction potential energy and repulsion potential energy are shown in Equations (1) and (2).

Attraction potential energy:

$$E_{att}\left(x\right)=\frac{1}{2}{k}_{att}{(x-x_g)}^2$$

(1)

Repulsion potential energy:

$$E_{rep}\left(x\right)=\left\{\begin{array}{c}\frac{1}{2}{k}_{rep}{(\frac{1}{x-x_{obs}}-\frac{1}{{\rho }_0})}^2,x-x_{obs}\le {\rho }_0\\ 0,x-x_{obs}>{\rho }_0\end{array}\right.$$

(2)

where $k_{att}$ is the attraction coefficient, x is the location of the robot, $x_g$ is the location of the target point, $k_{rep}$ is the repulsion coefficient, $x_{obs}$ is the location of the obstacle, and ${\rho }_0$ is the maximum distance affected by the obstacle.

Traffic congestion is caused by an imbalance in the internal components of the transportation system; however, the underlying reason for this is the contradiction between the unlimited demand for human travel and the limited supply of travel conditions. From a micro point of view, traffic demand refers to the demand for the spatial movement of people or objects at a certain time, on a certain road, and for the purpose of travel [40]. Traffic supply refers to the ability to provide moving conditions for people or objects, which is determined by the road environment. The road environment depends on the driver’s understanding and judgment of the environment, which is embodied in driving decisions, such as acceleration or deceleration [41]. Therefore, traffic congestion can be regarded as the effect of traffic demand and the road environment on drivers. A large number of calculations are needed due to the complex mechanism of the road environment on drivers. Therefore, this study compares the phenomenon that robots move due to the attraction and exclusion of obstacles in the APF and converts the process of traffic demand and supply into the driving and exclusion of travel demand and road environment on driver psychology, as shown in Figure 2b.

Specifically, the traffic demand is abstracted as the attraction $F_{att}$ of the desired speed to the driver’s psychology, and the effect of the road environment on the driver is abstracted as the obstruction and repulsion $F_{rep1}, F_{rep2}, \dots , F_{repi}, \dots , F_{repn}$ of the driver’s psychology and is caused by the proximity of the front or side vehicles, the uneven road surface, and the vulnerability of the barrier without isolation to the threat of the opposite vehicle. Given that each driver has the same traffic demand for fast passage, the calculation of attractive potential energy for the traffic demand to drivers is omitted, and only repulsive potential energy is used to judge the traffic supply capacity; that is, whether traffic congestion occurs depends on the road environment. Therefore, this study proposes the concept of traffic congestion potential as a basis for judging road traffic congestion. That is, the energy when a certain road tends to be congested at a certain moment or at a period of time is symmetrical to the ability of the road environment to hinder driving vehicles from passing at the desired speed.

The congestion state can be divided into three levels: unblocked, slow, and congested. Congestion trends can be divided into three types: aggravation, alleviation, and stable [19,24]. Therefore, this study divides the traffic congestion situation into seven levels according to its severity and change trends: aggravating congestion, stabilising congestion, alleviating congestion, aggravating slow, stabilising slow, alleviating slow, and unblocked. A mapping relationship exists between the conversion boundaries of each level and the traffic congestion potential energy value. Thus, the traffic congestion potential energy can also be divided into seven levels. The mapping relationship between traffic congestion potential energy and the traffic congestion situation is shown in Figure 3.

2.2. Construction of Traffic Congestion Potential Energy Model

2.2.1. Constituent Elements

The road environment includes three parts: road conditions, traffic facilities, and traffic conditions. In practice, many environmental elements will hinder the rapid passage of vehicles, and based on intuition, accessibility, sensitivity, and independence, this study selects ten elements to build the traffic congestion potential energy function model.

Road conditions:

1.

Longitudinal slope ($S_i$)

Given that the purpose of this study is to determine the congestion situation of the road section, i is used to represent section i, and $S_i$ is used to represent the longitudinal slope of section i, the same as below. When the vehicle exceeds the low-speed vehicle or parking vehicle in the uphill process and when the driving speed is too fast due to gravity and inertia in the downhill process, the driver will have a sense of tension and vigilance. Although the speed does not necessarily decrease, the acceleration will often continue to decrease [42]. Therefore, the slope size is used to reflect the obstacle effect of the road conditions on the rapid passage of vehicles. The greater the value of $S_i$ is, the greater the obstacle effect will be.

2.

Lane number ($L_i$)

Increasing the lane change frequency of vehicles will cause great interference, with the increase in the lane number and will marginally decrease the average road capacity of each lane in the section [43]. Therefore, the number of lanes is used to reflect the obstructive effect of the road conditions on the rapid passage of vehicles. The greater the value of $L_i$ is, the greater the potential energy of the road conditions will be.

3.

Pavement condition ($PC{I}_i$)

Potholes and grooves on the road will cause some obstacles to driving [44]. In this study, the pavement condition index is used to evaluate pavement quality, which is calculated as follows:

$$\begin{array}{l}PC{I}_i=100-{\alpha }_{0}D{R}_i^{{\alpha }_1}\\ D{R}_i=\frac{A}{A_i,}\end{array}$$

(3)

where $PC{I}_i$ represents the pavement condition index of section i, and ${\alpha }_0,{\alpha }_1$ is the correlation factor. For asphalt pavement, ${\alpha }_0$ is 15 and ${\alpha }_1$ is 0.412. For cement pavement, ${\alpha }_0$ is 10.66 and ${\alpha }_1$ is 0.461. For sand pavement, ${\alpha }_0$ is 10.1 and ${\alpha }_1$ is 0.487. $D{R}_i$ is the road damage rate of section i, which can be obtained from the ratio of the road damage area A to the road surface area $A_i$ of section i. The larger the road damage rate is, the smaller the value of the $PC{I}_i$ and the greater the road condition potential energy will be.

4.

Types of intersection ($I_i$)

It is easy for interleaving and conflict to form at intersections, and different types of intersections have different hindering effects on vehicle traffic. Given that the number of traffic accidents can reflect the degree of compliance and traffic safety of drivers, this study uses the number and proportion of accidents at various intersections in the ‘China Road Traffic Accident Statistics Annual Report 2016′ to express the degree of obstruction of different types of intersections to vehicle traffic [45], as shown in

Table 1. Statistics of different types of intersection accident.

	Three-Way Intersection	Four-Way Intersection	Multiway Intersection	Loop Intersection
Number of accidents (pieces)	17,933	25,303	3,310	515
Proportion (%)	38.11	53.77	7.03	1.09

The data come from ‘China Road Traffic Accident Statistics Annual Report 2016′.

.

5.

Roadside friction ($FRI{C}_i$)

Pedestrians, non-motorised vehicles, parked vehicles, and bus stops on both sides of the main road are all roadside friction factors that harm traffic flow and impair road capacity. $FRI{C}_i$ represents the roadside friction of section i, and the magnitude of roadside friction reflects the obstacle effect of road conditions on the rapid passage of vehicles. The calculation formula of roadside friction is based on the empirical formula for the roadside friction value obtained in Indonesia using a large number of experimental data [46], which is as follows:

$$FRI{C}_i=0.6\times PE{D}_i+0.8\times PS{V}_i+1.0\times EE{V}_i+0.4\times SM{V}_i,$$

(4)

where $PE{D}_i$ is the width of the pedestrian path on the roadside, $PS{V}_i$ is the number of bus stops and parking spaces, $EE{V}_i$ is the number of entrances and exits of buildings on the roadside, and $SM{V}_i$ is the width of the non-motorised vehicle lane. The larger the value of $FRI{C}_i$ is, the greater the potential energy of the road conditions will be.

Traffic facility conditions:

1.

Guardrail setting method (${\eta }_i$)

Drivers may feel nervous, oppressed, and anxious because of fear of collision with the guardrail, resulting in lower speed and lower road capacity [47]. Different guardrail setting methods have different effects on drivers. This study uses the attenuation rate of different guardrail setting methods obtained in the literature [48] to reflect the obstacle effect of traffic facilities on the rapid passage of vehicles. That is, when only the central isolation guardrail is provided, ${\eta }_i$ is 3.08; when only the roadside guardrail is provided, ${\eta }_i$ is 5.40; when both sides are installed simultaneously, ${\eta }_i$ is 5.61; and when no guardrail is provided, ${\eta }_i$ is 0.

2.

Direction sign reaction time ($T_i$)

Given a large amount of information on the layout, the direction sign will increase the driver’s reaction time, especially when the layout information is overloaded, and the driver even needs to slow down to read the information [49]. In this study, the reaction time is used to express the obstacle effect of the direction sign in section i on the rapid passage of vehicles. Reference [50] obtained the fitting function formula between the layout information content of the direction sign and the reaction time through a large number of experiments, which is used as the basis for judgment in this study.

$$T_i=0.002N_i^2+0.139N_i+0.265,$$

(5)

where $N_i$ is the number of routing information in section i, and a road name and its matching symbol are used as a piece of routing information.

3.

Traffic lines setting form ($M_i$)

Whether a traffic line exists and how the traffic line is set will have different restraint effects on drivers. In the literature [51,52], the fitting equation for spatial occupancy and average speed was obtained by simulating the traffic flow operation state under different traffic line forms. The present study defines $M_i$ as the blocking effect of the traffic lines of section i on the rapid passage of vehicles, which is as follows:

$$\begin{array}{c}\mathrm{No} \mathrm{traffic} \mathrm{line}:D=\frac{57.016\pm \sqrt{3250.824+62.588\left(67.782-v\right)}}{-31.294}\hfill \\ \mathrm{Dashed} \mathrm{line} : D=\frac{12.29\pm \sqrt{151.044+241.804\left(64.346-v\right)}}{-120.902}\hfill \\ \mathrm{Dashed} \mathrm{line} \mathrm{and} \mathrm{solid} \mathrm{line} : D=\frac{12.345\pm \sqrt{152.399+243.192\left(64.207-v\right)}}{-121.596}\hfill \\ \mathrm{Solid} \mathrm{line} : D=\frac{5.2006\pm \sqrt{27.046+265.328\left(63.407-v\right)}}{-132.664}\hfill \\ \hfill M_i=\frac{D_i}{0.4},\hfill \end{array}$$

(6)

where v is the average speed of the road section in a certain traffic line form, and $D_i$ is the space occupancy rate of the section i in a certain traffic line form. The maximum space occupancy rate at which the vehicle can basically run at free-flow speed is 0.4. The smaller the value of $M_i$ is, the smaller the potential energy of the traffic facility condition will be.

Traffic conditions:

1.

Traffic state index ($TS{I}_i$)

Many indicators can reflect traffic conditions, among which speed can best reflect the effect of traffic conditions on drivers [53]. Since the road section may contain intersections, if the vehicle speed of the stop light is directly used for representation, then the result may be inaccurate. Therefore, this study chooses the TSI, which takes the actual speed and free-flow speed as the core calculation parameters, as one of the indicators to reflect the potential energy of traffic conditions, and the calculation formula is shown in Equation (7). The greater the value of $TS{I}_i$ is, the greater the potential energy of the traffic conditions will be.

$$TS{I}_i=\frac{v_i^{\prime }-v_i}{v_i^{\prime }}\times 100,$$

(7)

where $v_i^{\prime }$ is the free flow speed of section i, and $v_i$ is the actual driving speed of section i.

2.

Climatic conditions ($C{C}_i^{\left( \right)}$)

Climatic conditions have a considerable effect on cold-climate cities, and icy and snowy pavement is the most important factor. It not only reduces the friction coefficient of the pavement, but it also increases the psychological burden of drivers [54]. Icy and snowy pavement take on various forms. Different forms of icy and snowy pavement have different friction coefficients and effects on traffic [55]. Given that main roads are the main channel of urban travel, cities in cold regions generally adopt the snow-clearing standard of ‘immediately down and clear’. Therefore, the icy and snowy pavement morphology of the main roads in cold-climate cities can be summarised as comprising three types: mild snow pavement, snowmelt pavement after snow removal, and ice film pavement after snow removal [56]. To quantify the effects of different ice and snow forms on traffic operation, this study uses video and Microcom Pty’s MetroCount 5600 vehicle classification statistics system to measure speed and headway under the above three road conditions in Harbin, Changchun, and Shenyang—China’s cold-climate cities that were used as experimental cities. The results are shown in

Table 2. Statistic results of headway and speed under different ice and snow conditions.

Ice and Snow Conditions	Headway (s)				Speed (km/h)
	Minimum Value	Maximum Value	Mean Value	Standard Deviation	Minimum Value	Maximum Value	Mean Value	Standard Deviation
Non-icy and snowy pavement	1.16	1.46	1.26	0.12	26.86	61.60	44.84	14.23
Mild snow pavement	2.46	7.09	5.72	1.55	23.96	30.68	27.32	2.16
Snowmelt pavement after snow removal	5.76	11.38	8.45	1.98	18.43	28.02	22.90	3.62
Ice film pavement after snow removal	2.23	7.00	4.54	1.26	18.96	25.69	23.07	2.09

.

As shown in Table 2, icy and snowy pavement will cause the vehicle speed to decrease and the headway to increase. Regression analysis was conducted to obtain the fitting relationship between the speed and headway under different ice and snow conditions. The optimal regression model was selected by variance analysis and significant regression coefficient tests. Four types of road regression models are shown in

Table 3. Regression models for the headway and speed under different ice and snow conditions.

Ice and Snow Conditions	Regression Model	R2, Adjusted R2
Non-icy and snowy pavement	$C{C}_i^o=13.647/v_i+0.926$	R2 = 0.926, Adjusted R2 = 0.901
Mild snow pavement	$C{C}_i^s=392.156/v_i-8.714$	R2 = 0.554, Adjusted R2 = 0.517
Snowmelt pavement after snow removal	$C{C}_i^r=10.225\ln v_i-23.45$	R2 = 0.658, Adjusted R2 = 0.620
Ice film pavement after snow removal	$C{C}_i^b=0.479v_i-6.505$	R2 = 0.623, Adjusted R2 = 0.585

.

In the models, $C{C}_i^{\left( \right)}$ is the headway of road section i under different conditions, and $v_i$ is the speed of road section i. The congestion potential energy of icy and snowy roads is larger than that of non-icy and snowy roads, and that of ice and snow conditions on different roads is different, which produces different obstacle effects.

2.2.2. Model

On the basis of the principle of potential energy superposition and the potential energy function of the repulsion force, a potential energy model of traffic congestion was established, as shown in Equation (8), and the model has a two-layer weight matrix.

$$P_{Ei}=\left[\begin{array}{ccc}{w}_1& w_2& w_3\end{array}\right]\times \left[\begin{array}{c}{P}_{Ri}\\ P_{Fi}\\ P_{Ti}\end{array}\right]=\left[\begin{array}{ccc}{w}_1& w_2& w_3\end{array}\right]\times \left[\begin{array}{c}\frac{1}{2}{k}_1{\left(\frac{S_i-S^{*}}{\overline{S}}\right)}^2+\frac{1}{2}{k}_2{\left(\frac{L_i-2}{\overline{L}}\right)}^2+\frac{1}{2}{k}_3{\left(\frac{100-PC{I}_i}{\overline{PCI}}\right)}^2+\frac{1}{2}{k}_4{\left(\frac{I_i}{\overline{I}}\right)}^2+\frac{1}{2}{k}_5{\left(\frac{FRI{C}_i}{\overline{FRIC}}\right)}^2\\ \frac{1}{2}{k}_6{\left(\frac{{\eta }_i-3.08}{\overline{\eta }}\right)}^2+\frac{1}{2}{k}_7{\left(\frac{T_i}{\overline{T}}\right)}^2+\frac{1}{2}{k}_8{\left(\frac{1-M_i}{\overline{M}}\right)}^2\\ \frac{1}{2}{k}_9{\left(\frac{TS{I}_i}{\overline{TSI}}\right)}^2+\frac{1}{2}{k}_{10}{\left(\frac{C{C}_i^{\left( \right)}-C{C}_i^o}{\overline{CC}}\right)}^2\end{array}\right],$$

(8)

To make the model more general, it can be deduced as follows:

$$P_{Ei}=\left[\begin{array}{ccc}{w}_1& w_2& w_3\end{array}\right]\times \left[\begin{array}{c}{P}_{Ri}\\ P_{Fi}\\ P_{Ti}\end{array}\right]=\left[\begin{array}{ccc}{w}_1& w_2& w_3\end{array}\right]\times \left[\begin{array}{c}{k}_1{\left(\frac{S_i-S^{*}}{\overline{S}}\right)}^2+k_2{\left(\frac{L_i-2}{\overline{L}}\right)}^2+k_3{\left(\frac{100-PC{I}_i}{\overline{PCI}}\right)}^2+k_4{\left(\frac{I_i}{\overline{I}}\right)}^2+k_5{\left(\frac{FRI{C}_i}{\overline{FRIC}}\right)}^2\\ k_6{\left(\frac{{\eta }_i-3.08}{\overline{\eta }}\right)}^2+k_7{\left(\frac{T_i}{\overline{T}}\right)}^2+k_8{\left(\frac{1-M_i}{\overline{M}}\right)}^2\\ k_9{\left(\frac{TS{I}_i}{\overline{TSI}}\right)}^2+k_{10}{\left(\frac{C{C}_i^{\left( \right)}-C{C}_i^o}{\overline{CC}}\right)}^2\end{array}\right]$$

(9)

where $P_{Ei}$ denotes the traffic congestion potential energy of section i; $P_{Ri}$ is the road condition potential energy; $P_{Fi}$ is the potential energy of the traffic facility condition; $P_{Ti}$ is the traffic condition potential energy; and $w_1, w_2, w_3$ denotes the weight of the road condition potential energy, traffic facility condition potential energy, and traffic condition potential energy. $S_i$ is the longitudinal slope; $L_i$ is the lane number; $PC{I}_i$ is the pavement condition; $I_i$ is the types of intersection; $FRI{C}_i$ is the roadside friction; ${\eta }_i$ is the guardrail setting method; $T_i$ is the direction sign reaction time; $M_i$ is the traffic lines setting form; $TS{I}_i$ is the traffic state index; $C{C}_i^{\left( \right)}$ is the climatic conditions; and $k_1, k_2, \dots , k_{10}$ denotes the weight of each element, which can be seen as the repulsion coefficient. Taking $\left(\frac{S_i-S^{*}}{\overline{S}}\right)$ as an example, this form is the distance of analogy exclusion, and $S^{*}$ is the standard slope, that is, the zero point of potential energy. The ‘Code for design of urban road engineering’ (CJJ 37–2016) indicates that the minimum longitudinal slope of the road should not be less than 0.3% [57]. Thus, $S^{*}=0.3\%$ is taken in this study. $\overline{S}$ is the mean longitudinal slope gradient of all of the sections. Hence, $\frac{1}{2}{k}_1{\left(\frac{S_i-S^{*}}{\overline{S}}\right)}^2$ is the dimensionless relative potential energy function value of the longitudinal slope gradient. The more $S_i$ deviates from the standard value, the greater the value of $\left(S_i-S^{*}\right)$, the greater the potential energy of the road conditions, and the more prone to congestion it will be, which conform to the principles of symmetry of potential energy and minimum potential energy. Similarly, the potential energy functions are constructed for other elements.

2.3. Parameter Calibration of Traffic Congestion Potential Energy Model

At present, many methods can be used to calculate weights. Generally, these methods can be divided into the subjective weighting method, the objective weighting method, and the subjective and objective combination weighting method [58]. Although the decision alternative ratia evaluation system (DARE) method is subjective, it is flexible and simple. As an objective weighting method, the criteria importance though intercrieria correlation (CRITIC) method is relatively perfect, but the discreteness of the data is not considered. The entropy weight method determines the weight based on discreteness. Therefore, this study uses the DARE–CRITIC–entropy weight combination method to determine the subjective and objective weights. In this manner, the advantages and disadvantages of subjective and objective weighting methods can be considered and balanced, such that the method is more scientific and practical.

• DARE method

The basic idea is to determine weights by comparing the importance of indicators [59]. The specific steps are as follows:

Step 1: Arrange the indicators from top to bottom according to the principle of similar type and proportion.

Step 2: Starting from the first indicator, determine the proportion of the contribution of the two adjacent indicators item by item as the tentative contribution coefficient.

Step 3: The contribution coefficient of the last indicator is recorded as 1, and the contribution coefficient of each indicator is revised upward by the contribution ratio of two adjacent indicators to obtain the modified contribution coefficient.

Step 4: Calculate the sum of the modified contribution coefficients and divide the modified contribution coefficients of each indicator by the sum to obtain the weight value of each indicator.

2.

CRITIC method

The basic idea is to use the contrast intensity of the indicators and the proportion of conflict measurement indicators. Particularly, the contrast intensity is measured by the standard deviation of the indicator data, and the conflict is measured by the correlation of the indicator data [60]. The specific steps are as follows:

Step 1: To eliminate the possible influence of dimension on the calculation results, proceess the indicators in a dimensionless manner. Given that the standardisation process will adjust the standard deviation of the indicator to 1, use the forward and reverse processing methods. The calculation formulas are shown in Equations (10) and (11), where $x_{ij}^{\prime }$ is the jth indicator, the dimensionless value of the ith data, i = 1, 2, …, n, j = 1, 2, …, m.

When the indicator value is larger, the following is better:

$$x_{ij}^{\prime }=\frac{x_j-x_{\min }}{x_{\max }-x_{\min }},$$

(10)

When the indicator value is smaller, the following is better:

$$x_{ij}^{\prime }=\frac{x_{\max }-x_j}{x_{\max }-x_{\min }},$$

(11)

Step 2: Calculate the standard deviation and correlation coefficient of each indicator. The calculation equation is shown in Equations (12) and (13), where ${\sigma }_j$ is the standard deviation of the jth indicator, $\overline{x_j^{\prime }}$ is the average value of the jth indicator, $R_j$ is the correlation of the jth index, and $r_{ij}$ is the correlation coefficient of indexes i and j.

$${\sigma }_j=\sqrt{\frac{{\displaystyle \sum _{j=1}^n}{\left(x_{ij}^{\prime }-\overline{x_j^{\prime }}\right)}^2}{n-1}},$$

(12)

$$R_j=\sum _{j=1}^p\left(1-r_{ij}\right),$$

(13)

Step 3: Calculate the objective weight of each indicator. The calculation equation is shown in Equation (14), where $w_j^c$ is the weight of the jth indicator based on the CRITIC method.

$$w_j^c=\frac{{\sigma }_j{R}_j}{{\displaystyle \sum _{j=1}^p}{\sigma }_j{R}_j},$$

(14)

3.

Entropy weight method

The basic idea is to determine the objective weights based on the variability of indicators [61]. The specific steps are as follows:

Step 1: Consistent with the CRITIC method, each indicator is processsed in a non-dimensional manner.

Step 2: Calculate the information entropy of each indicator. The calculation equation is shown in Equation (15), where $p_{ij}=x_{ij}/{\displaystyle \sum _{i=1}^m}{x}_{ij}$.

$$E_j=-\frac{1}{\ln m}\sum _{i=1}^m{p}_{ij}\ln p_{ij},$$

(15)

Step 3: Calculate the objective weight of each indicator. The calculation equation is shown in Equation (16).

$$w_j^s=\frac{1-E_j}{n-{\displaystyle \sum _{j=1}^n}{E}_j},$$

(16)

4.

DARE–CRITIC–entropy weight combination method

Given that the importance of the weights obtained by DARE, CRITIC, and entropy weight methods are the same, the three methods are combined by the multiplicative synthesis method [62,63], as shown as follows:

$$w_j=\frac{{\displaystyle \prod _{k=1}^3}{w}_j^k}{{\displaystyle \sum _{j=1}^p}{\displaystyle \prod _{k=1}^3}{w}_j^k,}$$

(17)

where $w_j^z$ is the combined weight of the jth indictor, k is the number of weight calculation methods, and p represents the number of indicators.

2.4. Classification of Traffic Congestion Potential Energy

No obvious boundary exists between different congestion levels, and different people have varied perceptions and tolerance of different congestion levels. To determine the mutation threshold of traffic congestion potential energy between different levels of the main road in cold-climate cities, this study establishes the quantitative relationship between traffic congestion potential energy and traffic congestion situation from the perspective of travellers and uses scientific methods to divide the variation range of potential energy.

• Perception level of different travellers on traffic congestion potential energy

To obtain the psychological perception level of different travellers on traffic congestion potential energy, the influence of the change in the traffic congestion potential energy on travellers’ psychological feelings is explored via inquiry investigation. Given that the operation environment and operation level of the transportation system in cold-climate cities will change considerably under the influence of ice and snow conditions, people’s psychological perception level of congestion will also be different depending on whether ice and snow are present. Therefore, the perception level of the congestion potential energy is investigated in the absence and presence of snow and ice.

The peak travel period is generally 6:30–9:00 and 16:30–19:30, and the normal peak period of travel is generally 9:00–16:30; thus, an inquiry investigation is conducted in the above time [64]. At the same time, a number of main roads, which are coherent routes and are responsible for the collection and distribution of residents’ long- and short-distance activities, were selected as the survey routes, and several motor vehicle drivers and passengers were selected as the investigators. Each investigator followed the recorder and investigated using the vehicle from the designated starting point and starting time according to the predetermined path. The vehicle was equipped with vehicle speed measurement and positioning devices. The survey information was recorded every 10 s, including real-time vehicle operation information, such as speed, time, geographic coordinates, and weather as well as congestion perception information. The content of the congestion perception inquiry is as follows: ‘1. Do you think the current traffic operation environment has reached the level of congestion without ice and snow? 2. Do you think the current traffic operation environment has reached the level of congestion under ice and snow conditions? Answer and record “Yes” and “No” [65].

After the survey, the survey data were sorted out. On the basis of the traffic congestion potential energy model, the traffic congestion potential energy value of each query site was obtained, and the relationship between the feelings of each surveyor and the traffic congestion potential energy was then obtained [66]. Thus, the psychological perception level of traffic congestion potential energy of each surveyor in the absence and presence of snow and ice was obtained.

2.

Quantification of the relationship between potential energy and traffic congestion situation

The probability distribution function $F\left(X\right)$ and probability density function $f\left(x\right)$ were used to describe the perception level of traffic congestion potential energy. The probability distribution function $F\left(X\right)$ can provide the probability of the perceived level of the congestion potential energy in an interval or neighborhood $P\left({\theta }_a<\theta <{\theta }_b\right)=F\left({\theta }_b\right)-F\left({\theta }_a\right),\left(a<b\right)$, and the probability density function $f\left(x\right)$ can provide the change rate of the probability of the perceived level of the congestion potential energy in an interval or neighborhood $f\left(\theta \right)=F^{\prime }\left(\theta \right)$.

On the basis of the psychological perception level experiment of the traffic congestion potential energy, the statistical data of the perception level of traffic congestion potential energy of investigators in ice and snow conditions and in non-ice and snow conditions can be obtained. On the basis of the data, the scatter plot of congestion potential energy perception level and probability density can be obtained, and the probability density function formula can be obtained by regression analysis. The probability density function was integrated to obtain the probability distribution function formula.

3.

Catastrophe threshold for the potential energy levels of traffic congestion

The traffic congestion potential energy can be divided into seven levels. The traffic congestion potential energy value of the 14.29%, 28.57%, 42.86%, 57.14%, 71.43%, and 85.71% of the cumulative probability distribution curve of the traffic congestion potential energy was taken as the mutation threshold of each level.

3. Data Description

3.1. Research Area

This study selected Harbin, a cold-climate city in China, as the case city. Harbin is located in the northeastern part of China’s Northeast Plain. It is the world’s largest city at the same latitude and is a world-famous ice and snow city. The winter temperature in Harbin is low and long, often accompanied by snowfall, and the road surface is slippery and freezes easily. The annual frost-free period is only 100–140 days, and the icing period is 190 days. Harbin is affected by the geographical climate, economic development is backward, and the scale of rail transit is small. Conventional public transportation is the main mode of public transportation. The problem of ground traffic congestion is highly prominent, and it has the typical transportation characteristics that would be expected under the climatic conditions of a cold-climate city.

The enclosed area of Jiankang Road, Fudan Street, Haxi Street, Qinghua Street, Haping Road, Hexing Road, Xidazhi Street, and Xuefu Road was taken as the research area (126°35′–126°39′, 45°41′–45°44′). This area is Harbin’s science and education center, service center, and business center. The traffic intensity in the area is relatively high. The transportation system has diverse functional characteristics. In addition to transportation functions, it also has multiple functions, such as science, education, and entertainment, which makes the area attract considerable traffic flow. To obtain the perception level of the traffic congestion potential energy of different travellers, the Xidazhi Street–Xuefu Road–Baojian Road–Zhengyi Road–Hexing Road area in Harbin was selected as the survey route. The research scope and the survey route is shown in Figure 4.

3.2. Data Sources

To improve the identification accuracy, the roads in the research area were divided into different directions and main and auxiliary roads according to the standard of 200 m length, and a total of 390 segments were obtained. The data for each road segment were collected on this basis. On the basis of the traffic congestion potential energy model, the data that this study needed to collect included: longitudinal slope, number of lanes, road damage area, types of intersections, the width of the pedestrian paths on the roadside, the number of bus stops, parking spaces, the number of building entrances and exits, the width of non-motorised vehicle lanes, guardrail setting method, the number of road guidance information, traffic line setting form, free flow speed of the road section, actual driving speed, and climate. In these data, the actual driving speed and climate of the road section change dynamically, and their values will not only affect the final values of elements such as traffic lines and the traffic state index (TSI), but will also affect the value of the weights. This study obtains the actual driving speed data for each road section through the GPS data of the Harbin Transportation Bureau. The Harbin Transportation Bureau has installed GPS receivers on buses and taxis. The receiver sends a piece of GPS data to the Harbin Transportation Bureau every 30 s, and the daily collection time is 24 h. Approximately 20 million pieces of GPS data are generated every day. Buses have a fixed route and frequency, stop at night, and need to stop multiple times during operation, whereas taxis operate around the clock, do not have a fixed driving route, and will drive through every corner of the city, which can reflect the real running status in the city. Therefore, this study chooses to use taxi GPS data to calculate the actual driving speed of each road section. The formation of icy and snowy pavement is closely related to climatic conditions. Reference [67] analysed the process of icy and snowy pavement formation from rain, sleet, and snow in the cold-climate cities of Baicheng, Changchun, Baishan, and Yanji during the 30 years from 1986 to 2015 and obtained the formation conditions of icy and snowy pavement, as shown in

Table 4. Judgment standard of icy and snowy pavement.

	No Snowfall	Rain, Sleet	Slight Snow	Moderate Snow, Heavy Snow, Snowstorm
Daytime temperature ≤ −3 °C	Normal	Mild snow pavement	Mild snow pavement	Ice film pavement after snow removal
Daytime temperature > −3 °C	Normal	Normal	Normal	Snowmelt pavement after snow removal
Nighttime temperature ≤ −3 °C	Normal	Mild snow pavement	Mild snow pavement	Ice film pavement after snow removal
−3 °C < Nighttime temperature ≤ 0 °C	Normal	—	Mild snow pavement	Ice film pavement after snow removal
Nighttime temperature > 0 °C	Normal	—	—	Snowmelt pavement after snow removal

. Therefore, in the climate data, this study only collects the temperature and snowfall data and then obtains the real-time road shape.

The temperature in Harbin was still low during the period from 12 (Monday) to 18 (Sunday) April 2021. It experienced rainy and snowy weather, and its road pavement qualities were diverse. Thus, this study selected this period to test the congestion situation. A data analysis period that is extremely short, such as 1 min or 2 min, may cause large fluctuations because the analysis period is smaller than the signal period; conversely, a data analysis period that is too long may not accurately reflect traffic characteristics [68,69]. Therefore, 15 min was selected as the data analysis period, that is, the congestion situation was identified every 15 min. Then, the speed and climate data at 96 times in each section of a day were collected. In order to explore the impact of changes in the traffic congestion potential energy on the psychological feelings of travelers, 10 drivers and 10 passengers were selected as investigators to conduct a survey of the congestion potential energy perception level along the survey route. The vehicle was equipped with a GPSMAP 60CS satellite positioning and navigation system (with 12 parallel receiving channels and update rate of 1/s). The data used for the congestion situation identification test are shown in

Table 5. Data and sample size for the traffic congestion situation identification test.

Data Name	Source	Sample Size
Speed	GPS data of the Harbin Transportation Bureau	304 million pieces, 15.61 GB (one per 30 s, 7 days in total)
Temperature, snowfall	Historical weather query website	672 pieces (one per 15 min, 7 days in total)
Static data	Field investigation, data collection and street view map query	390 pieces
Survey data of congestion potential energy perception level	Inquiry investigation	93600 pieces (one per 10 s, 6:30–19:30)

.

3.3. Data Processing

GPS data collection can be affected by equipment failure, building occlusion, and network errors, amongst others, which cause the GPS receiver to fail to receive data or data errors [70]. To improve the data quality, the GPS data must be checked and processed.

Firstly, data where the taxi positioning coordinate data fell outside the research area are removed because they do not affect this study. Secondly, data with completely consistent information for all of the fields are retained, but only the first item in the data table is kept, and the rest are deleted. Thirdly, data from vehicles that have been out of service for a long time, that is, those that have been parked for more than 30 min, are also removed. Fourthly, the latitude and longitude coordinates may jump due to electromagnetic interference; thus, data where the average speed of two positioning points exceeds the instantaneous speed limit value are deleted. Fifth, given that Harbin’s GPS data sampling cycle is 30 s, if the data are sorted in time series, then the collection time of two adjacent data is longer than 30 s; this condition indicates that data are missing, which requires supplementation and for the data to be repaired. The data processing results are shown in

Table 6. Data processing results of taxi GPS data in the research area.

	Number of Processing (Strip)	Proportion (%)
Total amount of data	303,905,952	—
Data outside the research scope and time	297,827,833	98
Data inside the research scope and time	6,078,119	2
Repeated data in the research area	607,812	1
Failure data in the research area	0	0
Error data in the research area	3039	0.05
Missing date in the research area	175,657	2.89
Data after repair	5,642,925	—

.

After GPS data processing, the data points were matched to the 200 m long road section divided by direction and main and auxiliary roads. On the basis of ArcGIS software, this study used buffer analysis function to judge the proximity and degree of GPS data and road to achieve the purpose of map matching. Moreover, the time stamp transform and GPS latitude and longitude transform were used to calculate the driving direction of the GPS data, and they were then matched to the road in the right direction.

4. Results

On the basis of the identification method introduced in Section 2 and the collected data, the congestion situation in the research area from 12 to 18 April 2021 was identified.

4.1. Model Parameter

On the basis of the decision alternative ratia evaluation system (DARE) method, criteria importance though intercrieria correlation (CRITIC) method, and entropy weight method, the weights of each element for road condition potential energy $P_{Ri}$, the potential energy of the traffic facility condition $P_{Fi}$ and traffic condition potential energy $P_{Ti}$ were obtained. On this basis, the final weights of each element were obtained based on the multiplication synthesis method. Given that the five elements constituting the road condition potential energy are static data, the weight values can be obtained directly based on the above method, as shown in

Table 7. Weight of each element in the potential energy of road condition in the research area.

Constituent Elements		DARE	CRITIC	Entropy Weight	Combination Method
Road condition potential energy $P_{Ri}$	Longitudinal slope $S_i$	0.12500	0.16345	0.13269	0.06739
	Lane number $L_i$	0.25000	0.20402	0.27222	0.34513
	Pavement condition $PC{I}_i$	0.12500	0.30220	0.44918	0.42177
	Types of intersection $I_i$	0.25000	0.20879	0.10239	0.13284
	Roadside friction $FRI{C}_i$	0.25000	0.12152	0.04353	0.03287

.

Given that the potential energy of the traffic facility conditions of traffic lines $P_{Fi}$ and the TSI and that the climatic conditions of traffic condition potential energy $P_{Ti}$ in real time change with speed, the weight values obtained based on the CRITIC and entropy weight methods also change in real time. In view of a large amount of data, only the data points from 0:00–0:15 on 12 April 2021 are taken as an example to show the weight value of each element of the potential energy of traffic facilities $P_{Fi}$ and the potential energy of traffic conditions $P_{Ti}$ during this period, as shown in

Table 8. Weight of each element in the potential energy of traffic facility conditions $P_{Fi}$ and traffic condition $P_{Ti}$ from 0:00 to 0:15 on 12 April 2021.

Constituent Elements		DARE	CRITIC	Entropy Weight	Combination Method
Traffic facility condition potential energy $P_{Fi}$	Guardrail setting method ${\eta }_i$	0.40000	0.44194	0.90632	0.93850
	Direction sign reaction time $T_i$	0.20000	0.23659	0.01905	0.00528
	Traffic lines setting form $M_i$	0.40000	0.32147	0.07463	0.05621
Traffic condition potential energy $P_{Ti}$	Traffic state index $TS{I}_i$	0.67000	1	0.00563	1
	Climatic conditions $C_i^{\left( \right)}$	0.33000	0	0.99437	0

.

On this basis, the weight values of the road condition potential energy $P_{Ri}$, potential energy of the traffic facility condition $P_{Fi}$, and traffic condition potential energy $P_{Ti}$ for the traffic congestion potential energy $P_{Ei}$ from 0:00 to 0:15 on 12 April 2021 were obtained by the above method, as shown in

Table 9. Weight of each element in the traffic congestion potential energy from 0:00–0:15 on 12 April 2021.

Constituent Elements		DARE	CRITIC	Entropy Weight	Combination Method
Traffic congestion potential energy $P_{Ei}$	Road condition potential energy $P_{Ri}$	0.21429	0.28874	0.04528	0.07208
	Traffic facility condition potential energy $P_{Fi}$	0.07143	0.48128	0.92975	0.82237
	Traffic condition potential energy $P_{Ti}$	0.71429	0.22999	0.02497	0.10555

.

4.2. Threshold of Potential Energy Classification

Through the survey of the perception level of the traffic congestion potential energy, the relationship between the feelings of a surveyor and the traffic congestion potential energy is shown in Figure 5. As shown in Figure 5, the investigator has different psychological perception levels of the traffic congestion potential energy depending on whether ice and snow conditions are present.

The statistical data on the perception level of the traffic congestion potential energy of the investigators under non-ice and snow conditions and ice and snow conditions were sorted. The probability density of the congestion potential energy and the congestion perception level was obtained, and regression analysis was performed, as shown in Figure 6. The best regression model that was able to pass the significance test as the probability density function was selected and is shown in Equations (18) and (19).

$$\mathrm{Non-icy} \mathrm{and} \mathrm{snowy} \mathrm{pavement} : f\left(x\right)=-0.000164+\frac{0.381330}{x},R^2=0.603$$

(18)

$$\mathrm{Icy} \mathrm{and} \mathrm{snowy} \mathrm{pavement} : f\left(x\right)=-0.000162+\frac{0.385055}{x},R^2=0.569,$$

(19)

where $f\left(x\right)$ is the probability density function of the investigators’ perception level of the congestion potential energy, and x is the traffic congestion potential energy. By integrating the probability density function, the probability distribution function formula is obtained, as shown in Equations (20) and (21). The probability distribution function figure is shown in Figure 7.

$$\mathrm{Non-icy} \mathrm{and} \mathrm{snowy} \mathrm{pavement} : F\left(X\right)=0.381330\ln X-0.000164X-1.567000$$

(20)

$$\mathrm{Icy} \mathrm{and} \mathrm{snowy} \mathrm{pavement} : F\left(X\right)=0.385055\ln X-0.000162X-1.595890,$$

(21)

The 14.29%, 28.57%, 42.86%, 57.14%, 71.43%, and 85.71% points of the cumulative probability distribution curve of the traffic congestion potential energy were taken to obtain the mutation thresholds of each level, as shown in

Table 10. Level range of the traffic congestion potential energy of the research area with or without ice and snow conditions.

	Aggravating Congestion	Stabilising Congestion	Alleviating Congestion
Non-ice and snow	(820.401, +∞)	(489.183, 820.401]	(311.612, 489.183]
Ice and snow	(836.769, +∞)	(501.44, 836.769]	(320.682, 501.44]
	Aggravating Slow	Stabilising Slow
Non-ice and snow	(204.651, 311.612]	(136.631, 204.651]
Ice and snow	(211.339, 320.682]	(141.6192, 211.339]
	Alleviating Slow	Unblocked
Non-ice and snow	(92.162, 136.631]	(-∞, 92.162]
Ice and snow	(95.862, 141.6192]	(-∞, 95.862]

.

4.3. Identification Result

Taking 15 min as the time granularity, on the basis of the collected traffic data, combined with the weight calibration method of DARE–CRITIC–entropy weight method and the traffic congestion potential energy model of the main road in cold-climate cities, the congestion potential energy values of each section in the research area from 12 to 18 April 2021 are obtained. On the basis of the mutation threshold of each level of traffic congestion potential energy, the traffic congestion situation level of each section is obtained, and the statistical results are shown in Figure 8.

5. Discussion

To discuss the validity of the identification results, the variation in the standard deviation of the traffic congestion potential energy of all of the road sections in the research area on different dates and in different periods of a week (Figure 9) as well as the mean value and standard deviation of traffic congestion potential energy of each road section in a week (Figure 10) were counted.

As shown in Figure 9, the potential energy value of traffic congestion in the study area fluctuates greatly throughout the entire day. Particularly, the fluctuation degree of the traffic congestion potential energy is similar in the whole range of 0:00–5:30, and the change is relatively stable. Between 5:30–9:00m, although the degree of dispersion has decreased, the degree of volatility is intense, which may be due to the congestion in the time related, the current congestion situation, and the subsequent congestion situation having a greater correlation, and the degree of dispersion is smaller. At the same time, the amount of travel in this period is large, and travel increases sharply during the peak commuting period, which then decreases sharply; thus, the fluctuation is large. After that, the traffic congestion potential fluctuations between 17:00–19:00 after experiencing steady changes; however, the fluctuation degree is smaller than the early peak. In addition, the congestion potential on Saturday (April 17) and Sunday (April 18) is significantly different from that on weekdays, and the overall congestion potential on Monday (April 12) and Tuesday (April 13) is higher than that on Wednesday and Friday. Notably, the fluctuation of the congestion potential energy rises sharply at about 13:00 on April 16, which is related to the snowfall. Therefore, the identification results obtained by the proposed method in this study are consistent with the actual situation in time.

As shown in Figure 10, the congestion potential energy of adjacent sections in the study area is highly correlated, and the congestion potential energy between different sections is significantly different. Particularly, the average congestion potential energy of Section 183–198 (Baojian Road (West–East)) is high, and the standard deviation is large, followed by Section 316–328 (Yanxing Road (West–East)). This result may be due to the schools, residential areas, and the Second Affiliated Hospital of Harbin Medical University on the west to east side of the Baojian Road. Particularly, the Second Affiliated Hospital of Harbin Medical University integrates medical treatment, teaching, and rehabilitation and is one of the best hospitals in Heilongjiang Province. The traffic demand is high regardless of weather, holidays, and other factors, but the parking spaces inside the hospital are insufficient. Moreover, vehicles often cannot enter, return, or directly occupy a lane for parking. Since there are four lanes on this side of the road and parking spaces and bus stops are present on the side of the road, the traffic pressure on this side of the road is high, the anti-interference ability is poor, and the possibility of congestion is high. As the main road, Yanxing Road only has two lanes on the west to east side. The land along the road is mainly used by residential communities and schools. To improve the convenience of residents, 17 entrances and exits have been set up on this side of the road with a length of 1.9 km, which is far more than the 2–3 km [71] specified in the ‘Urban Comprehensive Transportation System Planning Standard’ (GB/T51328-2018), which not only affects the normal running of vehicles on trunk roads but also the operation of adjacent lanes when vehicles slow down and change lanes, thereby creating a great possibility of congestion. Particularly, the dispersion degree of the congestion potential energy is the highest during the commuting and school periods.

To make the verification results more convincing, statistics are made on the road sections in a congestion situation. Particularly, there are 38 congestion alleviating roads, namely Xidazhi Street (South–North), Xidazhi Street (North–South), Yanxing Road (East–West), and Qinghua Street (East–West); 96 road stabilising congestion sections, namely Jiankang Road (East–West), Zhongxing Street (East–West), Hexing Road (East–West), Haxi Street (North–South), Qinghua Street (West–East), Zhengyi Road (South–North), and Wenchang Street (South–North); and 109 aggravating congestion road sections, namely Xuefusi Street (West–East), Haping Road (South–North), Baojian Road (West–East), Fudan Street (East–West), Yanxing Road (West–East), Xuefu Road (South–North), and Hexing Road Auxiliary Road (West–East), as shown in Figure 11a. To obtain the real congestion data, a questionnaire about the congestion sections and congestion time in Harbin (according to their own understanding) was distributed to the citizens of Harbin, and the data related to the congestion roads and congestion frequency in the study area were obtained by means of investigation, the traffic management department, and traffic broadcast information collection, as shown in Figure 11b. By comparing the experimental and field survey results, the proposed method is generally consistent with the real situation in space.

6. Conclusions

To solve the problem of existing traffic congestion identification methods not being suitable for the use of main roads in cold-climate cities and the lack consideration of the trends and the problems related to road condition information lagging behind when only the traffic flow parameters are used for evaluation, this study introduces the physical term ‘potential energy’ into the problem of traffic congestion. Referring to the principle that robots operate under the attraction and repulsion in the APF, the traffic congestion mechanism was internalized into the driving and repulsion of traffic travel demand and traffic environment on the driver’s psychology, and the potential energy model of traffic congestion for the main road in cold-climate cities was then established. The model is composed of 10 environmental elements and 13 weight coefficients in road conditions, traffic facilities, and traffic conditions. Each element constructs a function model that can reflect the traffic environment that hinders the rapid passage of vehicles. Particularly, the function models of headway and speed under different ice and snow pavement forms are emphatically established. To calculate the weights more scientifically, the DARE subjective weighting method, CRITIC objective weighting method, and entropy weight objective weighting method were combined with the multiplication synthesis method. To determine the mutation threshold of the traffic congestion potential energy between different levels of the main road in cold-climate cities, the quantitative relationship between traffic congestion potential energy, and the traffic congestion situation was established from the perspective of travellers, and the changes in the potential energy range was divided. Taking Harbin, a typical cold-climate city, as a case city to improve the identification accuracy, this study proposes the division of the roads into 200 m sections, direction, and main and auxiliary roads. On this basis, the environmental elements of each section were collected. Particularly, the speed data were obtained through the GPS data from Harbin taxis. To improve the data quality, repeated data, failure data, error data, and missing data were checked and repaired. Pavement shape was determined by collecting temperature and snowfall. Given that the speed data and climatic conditions change in real time, the weight coefficient of the model also changes in real time. To obtain the perception level of the traffic congestion potential energy of different travellers, the influence of the change of the traffic congestion potential energy on travellers’ psychological feelings was obtained by means of inquiry and investigation, and the conclusion that travellers’ psychological perception level of the traffic congestion potential energy is different depending on whether there are icy and snowy conditions was obtained. At the same time, the probability and distribution functions of the perceived level of congestion potential energy with or without ice and snow conditions were obtained. On this basis, this study took the 14.29%, 28.57%, 42.86%, 57.14%, 71.43%, and 85.71% points of the cumulative probability distribution curve of traffic congestion potential energy to obtain the seven-level classification threshold of the traffic congestion potential energy. Finally, taking 15 min as the time granularity, the congestion potential energy value of each section in the study area during the period of 12–18 April 2021 was obtained. On the basis of the mutation threshold of each level of traffic congestion potential energy, the traffic congestion situation level of each section was obtained. By comparing the experimental and field survey results, the identification results obtained by the proposed method are generally consistent with the real situation, and the effectiveness of the method is proven.

The underlying cause of traffic congestion is the contradiction between the infinite development needs of human beings and the limitation of resources and environment, which is simply the contradiction between the travel demand of vehicles and the supply of travel conditions [72]. To solve the traffic congestion problem of the main road in cold-climate cities, the road supply capacity can be improved based on the existing facilities according to the congestion characteristics of cold-climate cities, thereby ensuring the sustainable development of cold-climate cities. For example, to prevent road frost heave and to improve road friction, pavement materials with an antifreeze function should be used. In addition, strict snow removal standards should be formulated. The United States, Japan, Europe, and other countries have formed detailed legal norms and technical regulations for road maintenance operations in winter. Particularly, Japan proposed the ‘Snow and Cold Law’ as early as 1956, which aims to protect road conditions in winter from the legal level [73]. Germany pays attention to the training of operators and establishes a 24 h duty system, such that snow can be cleared immediately once it falls [74]. Given topography and landform, steep slopes and bumpy sections of a ramp cannot be completely avoided, and to alleviate the difficult problem of the ramp, the following measures can be taken to alleviate and improve it: Firstly, the width of the ramp or the number of lanes should be increased to improve the capacity of the ramp. Secondly, corresponding provisions on the length of uphill and downhill slopes and speed limit should be made, the impact of the slope on road efficiency should be weakened, the frequency of acceleration and braking should be reduced, and driving safety should be improved. Third, the ramp should be taken as a priority during snow removal, and snow should be immediately de-iced, or antiskid should be spread. In addition to traffic demand, the cross-sectional design of the main road in cold-climate cities should also consider the climatic characteristics. For example, the cross-section of the road should be designed in accordance with the width of the snow pile. In the cross-sectional design of roads in Japan, the effects of snow factors are considered in detail. On the basis of the amount of snow, the calculation formulas of the primary snow width (the width required for the temporary accumulation of snow on the side of the road before being compacted by the vehicle) and the secondary snow width (the width required for the transportation of snow outside the road) are established. When designing the cross-sectional form and the number of lanes, the snow width is initially satisfied, and the remaining space of the road is then allocated to the use of motor vehicles, pedestrians, or non-motor vehicles [75].

Given the limitations of technical information and data acquisition, the method proposed in this study still has several problems that need to be further explored. In the future, to further optimise the method for identifying the congestion situation of the main road in cold-climate cities, the amount of data, including the congestion data of other cold-climate cities, and the congestion data of different years, should be increased to improve the accuracy of the identification criteria. At the same time, the elements that can affect the rapid passage of vehicles should be collected as much as possible to enrich the model. In addition, considering congestion not only occurs on the main roads but also on other grade roads and the mutual influence between roads, and how to extend the method proposed in this study to the whole road network and identify the overall operation level of the city is also worthy of further investigation.