Study on the Spatial and Temporal Distribution and Traffic Flow Parameters of Non-Motorized Vehicles on Highway Segments Crossing Small Towns

Abstract

The traffic flow of non-motorized vehicles on the highway segments crossing small towns is disorderly and chaotic. In order to improve the traffic environment and regulate the order of non-motorized operations, this article studies the spatial and temporal distribution and traffic flow parameters of non-motorized traffic on the highway segments crossing small towns. The non-motorized traffic within the section of the National Highway G310 crossing small towns in Henan Province, China, is investigated through various research tools such as questionnaires, interviews, and on-site statistics. The regularity and characteristics of non-motorized traffic in terms of travel purpose, travel distance, travel time, and travel frequency were obtained. Meanwhile, based on the actual collected traffic data, the speed–density relationship, flow rate–density relationship, and speed–distance relationship of non-motorized traffic flow were studied using mathematical and statistical methods. The results show that thresholds exist for both time and distance traveled by non-motorized vehicles on small town road sections. The threshold value of riding time is 30 min, and the threshold value of riding distance is 5 km. Under the free flow state, the speed distribution is near a certain desired speed, and the flow rate–density relationship conforms to the exponential function relationship when the flow rate is greater than the critical flow value. The speed and distance show a cubic function relationship, and the speed gradually increases with the increase in distance between the non-motorized vehicles and towns. Based on the results of the above analysis, it is possible to grasp the travel regularity of non-motorized cyclists on highway segments crossing small towns. This provides a theoretical basis for enhancing the efficiency of non-motorized travel and improving the non-motorized travel environment.

1. Introduction

The highway segments crossing small towns are defined as special road segments with the characteristics of both urban roads and highways. They are formed due to population and various production factors gathering on both sides of the highway. This type of road section is densely populated on both sides, and pedestrians, motor vehicles, and non-motorized vehicles interfere with each other, resulting in complex traffic flow conditions. At present, in small towns in China, the average number of electric bicycles per 100 households is 75.1. Electric bicycles have replaced bicycles as an important mode of travel for residents and become the main choice for short and medium distance travel [1,2]. On the highway segments crossing small towns, electric bicycles overspeed and occupy the motor carriageway, which makes the traffic conditions more diversified and the traffic flow more complicated and has a great impact on the safety and efficiency of traffic operation [3]. At the same time, it also puts forward higher requirements for non-motorized traffic management and control strategies on the highway segments crossing small towns.

Due to the differences in the basic conditions of each country and the influence of the socio-economic level and city size, the population base and non-motorized vehicle ownership in each country are much lower than those in China [4]. At the same time, many countries have legal restrictions on the movement of non-motorized vehicles on highways. For example, the New York Traffic Code prohibits the use of bicycles on highways, expressways, main roads, interstates, and overpasses unless there is a permit sign. In addition, the Canadian Federal Safety Act also prohibits electric bicycles from being allowed on highways, expressways, and other prohibited roads [5]. Therefore, the conflict between motorized and non-motorized vehicles on the road is not as obvious as in China. Therefore, foreign scholars have focused their research on traffic safety, non-motorized riding behavior characteristics, and non-motorized traffic flow parameters. Den analyzed traditional bicycles and electric bicycles in terms of safety and listed the traffic safety hazards of electric bicycles in various aspects [6]. Starting from the perspective of non-motorized vehicle riders, Taylor explored the maximum and optimal speed reduction of non-motorized vehicles under different traffic environments by establishing the individual gap acceptance probability independent decision model between motor vehicles and non-motor vehicles under the condition of mixed driving [7]. Smith observed the riding conditions of conventional bicycles on the road and established the relationship model among the three parameters of traffic flow [8]. Chinese scholars have more extensive research on the characteristics of non-motorized vehicle traffic. In terms of theoretical research on non-motor vehicle speed, flow, and density, Ping analyzed the basic characteristics of non-motorized vehicle traffic in the road section where motor vehicles and non-motorized vehicles drive separately and created the optimal relationship model of speed–density and speed–flow [9]. Zeng studied the speed characteristics and density characteristics of non-motorized vehicles on urban roads. It is proved that the vehicles in the non-motorized lane affect each other, and their speed obeys normal distribution [10]. Mao et al. studied the travel characteristics of electric bicycles using a logit regression model and concluded that the distance and time distribution of electric bicycle travels conformed to a quadratic curve model [11]. Zhu et al. studied the relationship between the speed and density of non-motorized vehicles and proved that speed and density are exponential functions under congestion, and speed decreases with increasing density [12]. Some scholars have modeled the travel distance of residents on the basis of analyzing the land use status. Chen et al. proposed to use the two-stage distribution model of Ireland to simulate the distance and spatial distribution state of total urban non-motorized travel [13]. Qu et al. introduced the electron energy level theory into the non-motorized travel model of residents and used the simulated electron cloud resident travel distribution model as the basis to build a resident travel distribution model [14].

In summary, existing studies focus on non-motorized traffic on urban roads, and few studies have been conducted on the non-motorized traffic characteristics of highway segments crossing small towns, so this area is a blind spot for research. The main feature of the highway crossing small towns in China is mixed non-motorized traffic, and the relevant research results have little significance for the study of the traffic characteristics of mixed non-motorized traffic [15]. The large number of non-motorized traffic flow on highway segments crossing small towns has a great impact on the operation efficiency and safety of highways and puts forward higher requirements on the spatial and temporal planning and management of non-motorized riding [16]. Based on this, the second part of this article studies the spatial and temporal distribution of non-motorized traffic on highway segments crossing small towns in the form of a survey questionnaire. Using this method, the patterns and characteristics of non-motorized traffic in terms of travel purpose, distance, time, and frequency can be obtained. The third part describes the research method of traffic flow parameters in four aspects: conceptual assumptions, sampling method, tool description, and analysis scheme. In the fourth part, based on the actual collected traffic data, the speed–density relationship and flow rate–density relationship of non-motorized traffic flow are studied using mathematical and statistical methods. Meanwhile, the proposed conceptual hypotheses are verified. The fifth part uses SPSS to perform regression analysis of the two variables, speed and distance, as linear, quadratic, and cubic functions. Based on the values of the coefficients of determination, the final chosen functional model is determined, and the correctness of the model is verified using relevant data from other cities.

It is very common to see motor vehicles and non-motorized vehicles mixed driving on highway sections through small towns. Therefore, it is very necessary to set up non-motorized lanes on the highway. However, the length of the non-motorized lane needs to be studied. Too long non-motorized lanes not only have a low road utilization rate but also will occupy too much road slab space and affect the normal movement of motor vehicle flow. The research results of this article can provide a theoretical basis for determining the setting range of non-motorized lanes in the segments of highways crossing small towns.

2. Analysis of Spatial and Temporal Characteristics of Non-Motorized Cycling

The questionnaire (see Appendix A) consisted of three parts: the first part was to collect the personal information of cyclists, including their gender and age; the second part was about the reasons for choosing non-motorized travel, the type of vehicle, and the purpose of travel; and the third part was to count the cycling time, frequency, and distance of cyclists. The statistics were conducted using a combination of online and offline methods, with a sample size of 6219, and 5876 valid questionnaires were collected after removing those that did not meet the requirements. The effective rate of the questionnaire was 94.5%.

2.1. Analysis of Travel Purpose

The travel purpose of residents on highway segments crossing small towns is obtained using the statistics of the actual survey data, as shown in

Table 1. Statistical table of residents’ travel purpose.

Category	School or Work	Transfer	Grocery Shopping	Hospital	Business	Noon Party	After School or after Work	Evening Exercise
Frequency	1439	67	993	511	628	517	1204	505
Proportion	24.5%	1.3%	16.9%	8.7%	10.7%	8.8%	20.5%	8.6%

.

As can be seen from Table 1, the purpose of riding non-motorized vehicles on the highway segments crossing small towns is mostly for school or work, grocery shopping, and after school or after work. These three accounted for as much as 61.9% of the total. As can be seen from Figure 1, non-motorized travel is characterized by morning and evening peaks, and some road sections can become congested within a short period of time due to the gathering of traffic.

2.2. Analysis of Travel Distance

After sorting out the statistical questionnaire, the travel distance of residents on highway segments crossing small towns riding non-motorized vehicles is obtained, as shown in Figure 2.

The non-motorized travel distance on the highway sections crossing small towns has a great correlation with the area of the small towns. As shown in Figure 2, only 1.5% of the cyclists ride non-motorized bikes for more than 10 km, and 79.7% of the cycling distance is within 5 km. This indicates that people’s main activity areas are distributed near residential areas. It can be seen that the cycling non-motorized travel distance is basically within a certain range, and the survey data can provide an important basis for traffic organization, management, and safety facility setting.

2.3. Analysis of Travel Time

The questionnaire was counted to derive the travel time of the residents on highway segments crossing small towns, as shown in Figure 3.

From the data in Figure 3, it can be seen that the majority of residents on highway segments crossing small towns do not ride for more than 60 min. The number of people who ride for 10–30 min is the largest, accounting for 56.1%. When the travel time exceeds 60 min, it means that the travel distance is longer, and the residents are more willing to choose motor vehicle travel at this time.

2.4. Analysis of Travel Frequency

By sorting out the statistical questionnaire, the frequency of residents riding non-motor vehicles on highway segments crossing small towns is concluded, as shown in Figure 4.

From the data in Figure 4, it can be seen that the majority of residents use non-motorized vehicles for less than 12 trips in a day, accounting for 86.7%. Due to the layout characteristics of small towns, a large number of non-motorized vehicles will gather in specific time periods and some road sections. As the road is not physically separated, a large number of non-motorized vehicles will occupy the motor vehicle lane, squeeze the motor vehicle running space, affect the motor vehicle running speed, and lead to traffic accidents and congestion.

In summary: there are limit values for the time and distance of non-motorized travel for the residents of small towns. When a certain travel distance threshold is exceeded, residents will choose to travel by motor vehicle. Travel time of 10–30 min accounts for the most, with a frequency of 56.1%. The frequency decreases significantly as the riding time increases, accounting for only 11.6%. This indicates that 10–30 min of riding time is an acceptable and comfortable riding time for the residents, and the threshold of riding time can be set at 30 min. As small towns are small and people’s activity areas are mainly concentrated near residential areas, the travel distance of less than 5 km accounts for nearly 80.0%, and the percentage of cycling distance beyond 5 km decreases significantly. Therefore, the threshold value for residents’ non-motorized cycling travel distance is defined as 5 km.

3. Traffic Flow Parameter Research Methods

3.1. Conceptual Assumptions

The study of the relationship between flow rate, speed, and density began in 1935 with Greenshields’ study [17]. Since then, studies on the relationship between the three parameters of traffic flow have appeared in Greenberg’s logarithmic model of speed–density relationship [18], Underwood’s exponential model of speed–density relationship [19], and Edie’s segmental exponential model [20], etc. In 1992, Hall conducted a comprehensive review of this study and pointed out the general form of the flow rate–density relationship curve [21].

Based on the above research on the three parameters of urban road traffic flow, this article assumes that there is also a certain functional relationship between the flow rate–density and speed–density of the non-motorized traffic flow of highway segments crossing small towns.

3.2. Sampling Methods

The sampling principles for the survey sites were as follows:

• The area of highway segments crossing small towns;
• Mixed motor vehicles and non-motor vehicles; road cross-section is not physically separated;
• Road terrain gentle; road longitudinal slope is gentle slope section.

Therefore, the section from Xiangyunsi Village to Houwang Village of G310 National Highway in the suburb of Zhengzhou is selected as the survey area, as shown in Figure 5. In order to ensure the validity of the survey data, the survey was conducted under good weather conditions and high visibility. The survey period was selected as 7:00–9:00 in the morning peak and 17:00–20:00 in the evening peak. The survey took into account the peak traffic period and avoided Monday morning and Friday night.

3.3. Tool Description

3.3.1. Data Collection Tool

The traffic survey data acquisition method adopts ‘video shooting + virtual coil method’, and the main equipment includes camera, tripod, stopwatch, range finder, etc. Its working principle is that, after selecting the survey position, two straight lines are delineated on the ground of the non-motorized vehicle driving area. The distance between the two straight lines is 5 m, and the width of the non-motorized vehicle lane is 3.5 m. The two straight lines are used as virtual detection coils, as shown in Figure 6. The area is regarded as a video shooting detection area, and the time that the non-motorized vehicle passes through the two virtual straight lines is recorded to facilitate the calculation of non-motorized vehicle speed, flow, and other traffic parameters.

3.3.2. Data Analysis Tool

The mathematical and statistical software used for the analysis of the survey data is SPSS, which is the world’s first statistical analysis software. This software is capable of automatic statistical plotting and related data analysis.

The basic functions of SPSS cover data management, chart production, statistical analysis, and output production. The statistical analysis can be subdivided into descriptive statistics, correlation analysis, analysis of variance, regression analysis, mean comparison, cluster analysis, time series analysis, and non-parametric tests. Each section will allow users to set the relevant parameters according to their own wishes. The more used functions in this case are descriptive statistics, correlation analysis, and regression analysis.

Fitting the data using the linear fit module of SPSS gives the coefficient of determination, R², which is an important statistic. The coefficient of determination is expressed numerically as regression sum of squares/total sum of squares, and its central role is to reflect the goodness of fit of the model. R² takes values in the range [0, 1] without specific numerical units. R² is the most commonly used metric to evaluate regression models. The closer R² is to 1, the better the fitted regression equation is [22].

3.4. Analysis Scheme

3.4.1. Data Statistical Interval and Sample Size

• Determination of survey statistical interval

Non-motorized vehicle flow has very obvious cluster and discrete characteristics, and vehicle flow will increase or decrease sharply in a short time [23]. Therefore, a reasonable determination of statistical time interval is conducive to improving the accuracy and effectiveness of sample data. Literature [24] research shows that the statistical interval of non-motorized vehicle traffic flow is usually set to 10~60 s, but with the extension of time, the discreteness and volatility of traffic flow and speed data will also be weakened to a certain extent. Taking this into account, the time interval of this survey takes the median value of 30 s.

2.

Determination of statistical sample size

The larger the capacity of the sample, the higher the accuracy. When the number of samples obeys the normal distribution in the ideal state, the minimum sample size formula is as follows:

$$\mathrm{N}\ge {\left(\frac{\mathrm{ST}}{\mathrm{E}}\right)}^2$$

(1)

In Formula (1), N—minimum observed sample size; S—standard deviation of samples; T—t-distribution statistic obeying degrees of freedom n − 1; T = 1.96, when the confidence level is 95% (90%); and E—sample standard deviation size.

When the confidence level is 95 %, T is 1.96, the standard deviation of non-motorized vehicle speed is 4 km/h, the standard error is 1 km/h, and the minimum sample size is 64.

3.4.2. Extraction of Traffic Flow Data

Static data such as road facilities and road width can be obtained through field investigation. The extraction method of non-motorized vehicle flow dynamic data is as follows:

3.

Video processing

In video processing, the video format is set to 25 frames per second, and the accuracy of each frame is 0.04 s. The survey video is played frame by frame to improve the accuracy of the collected data.

4.

Speed

The length of the video detection area is 5 m, and the formula for calculating the average speed of non-motorized vehicles is as follows:

$$\mathrm{v}=\frac{\mathrm{x}}{{\mathrm{t}}_2{-\mathrm{t}}_1}$$

(2)

In the formula, v—the average speed of non-motorized vehicles, and the unit is m/s; x—the length of the detection area, taking the value of 5 m; ${\mathrm{t}}_1$—the time of non-motor vehicle passing through the first test line; and ${\mathrm{t}}_2$—the time of non-motorized vehicles passing through the second detection line.

5.

Flow rate

The vehicle flow rate is defined as the equivalent hourly flow rate through a specified section of a lane or roadway for a given time interval of less than 1 h [25]. The processing of the video data is performed using 30 s as a time span for a set of data, from which the magnitude of the mixed non-motorized flow rate on the non-motorized lane is counted. The specific equation is as follows:

$$\mathrm{q}=\frac{\mathrm{n}}{\mathrm{t}}$$

(3)

In the formula, q—non-motor vehicle flow size, and the unit is veh/h × m; n—the number of non-motor vehicles passing through the detection area within 30 s; and t—statistical time of each group, and the value is 30 s.

6.

Density

There are no lane lines for non-motorized vehicles on highway segments crossing small towns. Therefore, when counting the density of non-motor vehicles, the use of dynamic collection formulas is more in line with the actual state [26]. The dynamic density collection also uses 30 s as the statistical interval and the concept of arithmetic average for statistical calculation. The formula is as follows:

$$\mathrm{k}=\frac{1}{\mathrm{L}·\mathrm{d}}\ast \frac{{{\displaystyle \sum }}_{\mathrm{i}=1}^{30}{\mathrm{n}}_{\mathrm{i}}}{30}$$

(4)

In the formula, k—density of non-motor vehicles, and the unit is veh/m²; L—length of the detection area, and the unit is m; d—width of the detection area, and the unit is m; and ${\mathrm{n}}_{\mathrm{i}}$—number of non-motorized vehicles passing through the detection area within 30 s, and the unit is veh.

According to the Chinese standard for the physical size of non-motor vehicles, the sizes of the two types commonly used in non-motor vehicles are shown in

Table 2. Classification and design size of non-motor vehicles (m).

Vehicle Type	Length Range	85 % Quantile Length	Width Range	85 % Quantile Width	Height Range
Electric bicycle	1.36~2.0	1.88	0.53~0.7	0.68	1.00~1.10
Human bicycle	1.35~1.9	1.78	0.5~0.63	0.60	0.95~1.10

.

The density k takes the maximum value when the coil is filled with bicycles inside. The virtual coil size at the time of traffic survey is 3.5m × 5.0 m, and the safety distance is 0.3~0.5 m. Taking 85% percentile length and width of bicycle as the calculation value, the maximum number of non-motorized vehicles allowed to drive side by side inside the coil is 3, and the maximum number of rows accommodated is 2.29 rows. Therefore, the maximum number of non-motorized bicycles to be accommodated in the virtual coil is 3 × 2.29 = 6.87. At this time, the maximum value of density is 0.4 veh/m².

3.4.3. Sample Data Analysis

The traffic survey started from Xiangfulu Village in Figure 5, and a detection area is set every 500 m. A total of 10 detection areas are set up. The time of shooting morning and evening traffic peaks in each detection area is 30 min, and every 30 s is the statistical time interval. The number of sample groups is 540, and a total of 4674 non-motor vehicle data are obtained, including 4431 electric bicycles and 243 bicycles. In data processing, based on conversion factor 1.2 between bicycles and electric bicycles, the bicycle is converted into an electric bicycle for processing and analysis. In total, 540 sets of data were imported into SPSS for descriptive statistical analysis, as shown in

Table 3. Non-motorized traffic flow data.

Parameters	Unit	Mode	Standard Deviation	Variance	Extreme Value
					Minimum	Maximum
Flow rate	vehicle/h × m	68.00	127.49	16,254.21	23.00	700.00
Speed	m/s	6.90	1.65	2.73	2.76	13.91
Density	vehicle/m2	0.19	0.24	0.058	0.05	1.30

.

As can be seen from Table 3, the extreme values of flow rate, speed, and density of non-motorized vehicles all have a large variation. The two data, flow rate and density, have a large degree of dispersion. This indicates that the flow rates and densities of mixed non-motorized flows have large differences at different locations, and the data produce large fluctuations with distance.

This can be visualized in Figure 7. The speed values of the survey sample conform to a normal distribution, and the variability of the flow and density data is large. This indicates a significant change in the flow and density of mixed non-motorized traffic flows as non-motorized vehicles gradually move away from the town.

4. Test Results

4.1. Flow–Density Relationship Model

After analyzing the survey data, the correlation between mixed non-motorized flow density and flow rate is shown in

Table 4. Correlation description of flow rate and density.

R	R2	Durbin–Watson	Significance
0.981	0.964	1.776	0.001

.

The coefficient of determination R² representing the fitting degree of the model is 0.964, the Durbin–Watson value is 1.776, and the numerical value is close to 2. This indicates that the independence of the two variables is good and meets the prerequisites of linear regression. The significance is less than 0.05, so the linear regression is more significant, and the model is statistically significant. The VIF value of 1 in the regression coefficient result indicates that there will be no multicollinearity between these two variables and the fit was good. The resulting linear regression equation for flow–density is as follows:

$$\mathrm{q}=1714.346\mathrm{k}-7.047$$

(5)

In the formula, q is non-motorized vehicle flow rate, and k is non-motorized vehicle flow density.

From Figure 8, it can be seen that the flow rate and density are in a clear positive correlation–function relationship, and as the density of non-motorized flow increases, its flow rate increases accordingly. Due to the limitation of the width of non-motorized lanes on highways, it makes most of the non-motorized flow travel in a comfortable density interval, and the scatter points are mostly concentrated in the interval of density of 0.05~0.15 vehicles/m². In Figure 8, there are not many scatter points with excessive non-motorized flow density, and the distribution is sparse, which is mostly due to the emergent road conditions or pedestrian crossings, etc., which make the non-motorized flow speed drop and produce delays, resulting in a gradual increase in density.

4.2. Speed–Density Relationship Model

The speed of the mixed non-motorized vehicle flow is affected by the density. In the non-crowded state, both bicycles and electric bicycles can run freely with weak mutual interference. At this time, the influence of density and bicycle mixing rate on the speed can be ignored [27]. In crowded conditions, the mutual interference between traffic flows is intensified, and the vehicle cannot overtake at will and can only follow the vehicle. According to the car-following theory, the speed of the traffic flow is determined by the lower speed. Therefore, the speed of the non-motorized vehicle flow decreases under crowded conditions, and the higher the density, the more significant the speed of the mixed non-motorized vehicle flow decreases.

The statistical survey data are used to draw the speed–density scatter diagram of the mixed non-motorized vehicle flow (Figure 9). From Figure 9, it can be seen that when the density of non-motorized vehicle flow is small, the speed values are more densely distributed in the interval of 6.25 m/s~10 m/s; when the density accumulates to 0.2 vehicles/m², the speed will gradually decrease with the increase in density.

When the non-motorized vehicle flow density exceeds a certain value, the rider will gradually reduce the speed due to the constraints of the road environment and the surrounding vehicles. As the speed decreases, the vehicles behind will gradually accumulate, and the traffic speed will become smaller as the density increases [28]. When the traffic flow density is less than 0.2 veh/m², the speed of non-motorized vehicles is dispersed. When it exceeds this value, the traffic flow speed will decrease significantly with the increase in density. Taking the density k = 0.2 veh/m² as the data demarcation point, the sample data of the density value exceeding the critical point is redrawn. The scatter plot is shown in Figure 10.

From Figure 10, it can be found that the traffic speed has a significant decreasing trend with the increase in vehicle density. The change trend was fitted using primary, quadratic, and exponential functions, respectively, and from

Table 5. Equation curve regression fitting table.

Model Type	R2
Linear function	0.814
Quadratic polynomial	0.893
Exponential function	0.942

, it can be found that the exponential function model was found to have the largest coefficient of determination.

When the density of mixed non-motorized traffic flow is greater than 0.2 veh/m², the data between the two has a significant exponential function relationship. In order to verify the credibility of the exponential equation, the data samples are tested again using t-test, and the t-test significance probability of the function model is less than 0.001. Based on the above analysis, the velocity–density relationship model of the urban section of arterial highways is obtained as follows:

$$\mathrm{v}=\{\begin{array}{c}6.25~10.0\hspace{1em}\hspace{1em}\hspace{1em}\mathrm{k}<0.2\\ 24.071{\mathrm{e}}^{-5.759\mathrm{k}}+2.251\hspace{1em}0.2\le \mathrm{k}<0.4\end{array}$$

(6)

In the formula, v—the speed of non-motorized vehicles, and the unit is m/s; and k—the density of non-motorized vehicles, and the unit is veh/m².

The curve fitting of the data shows that the curve is in good agreement with the actual scatter points; see Figure 11.

According to the speed–density relationship model, it can be seen that when the density is small, non-motorized vehicles mostly travel according to the free-flow state, and the speed is discretely distributed in the interval of 5.0~10.0 m/s. When the density exceeds 0.2 vehicles/m², the number of non-motorized vehicles on the road increases, and cyclists can no longer ride at their desired speed and can only travel according to the traffic flow speed. When the density is greater, the speed of traffic gradually decreases until it stops.

4.3. Limitations of the Relationship Model

As the study site was selected from a section of the G310 national highway road crossing a small town in Henan Province, China, which is located in a plain area, the resulting model is not applicable to other road types in other terrain conditions. At the same time, there is no hard separation facility between motorized and non-motorized vehicles within the section, so this element also needs to be considered when using the model.

5. Analysis of the Relationship between Speed and Distance to Town Center

5.1. Velocity–Scatter Plot

A detection area was set to obtain the velocity values at every 500 m interval, but the velocity variation between each detection area was not known. The velocity–frequency scatter diagrams are plotted at 0.5, 1.0, 1.5, 2.0, 2.5, 3.0, 3.5, 4.0, 4.5, and 5.0 km from the center of the small town using each detection area as the reference point; see Figure 12, Figure 13 and Figure 14. The velocity scatter conditions in the diagrams were analyzed to obtain the characteristic values to characterize the velocity values of the detection area. Ten eigenvalues of velocity variation with distance were obtained.

5.2. Analysis of Velocity Eigenvalue

From the velocity–frequency scatter plot, it can be seen that the smaller the velocity value, the smaller the corresponding frequency value, and the scatter distribution in the middle part of the velocity interval is concentrated and uniform. Therefore, the velocity characteristic values within each detection region can be characterized by calculating the median value of the velocity interval corresponding to the uniformly distributed points; see

Table 6. Distance–speed scatter eigenvalue.

Distance from Town (km)	0.5	1.0	1.5	2.0	2.5	3.0	3.5	4.0	4.5	5.0
Characteristic value of speed (m/s)	2.62	3.84	4.92	6.02	6.72	7.21	7.87	9.00	10.56	12.14

.

From Table 6, it can be seen that the characteristic speed has a significant tendency to increase with the increase in distance. In order to study the specific functional relationship between the two variables, SPSS was used to perform linear, quadratic, and cubic regressions of the two variables, as shown in

Table 7. Summary table of curve fitting.

Abstract	R	R2	Re-R2	Estimated Standard Error
Linear	0.985	0.971	0.968	0.531
Quadratic	0.989	0.978	0.972	0.497
Cubic	0.999	0.997	0.997	0.174

.

As shown in Table 7, the cubic function curve fit is the best with an R² value of 0.997, which is higher than the other functions and means that the cubic function fits the scattered data best compared to the other two types of functions. A functional model of the relationship between the speed of non-motorized vehicles and distance of vehicles from the town center on highway segments crossing small towns is shown below.

$$\mathrm{v}=0.504+4.63\mathrm{x}-{1.32\mathrm{x}}^2+{0.175\mathrm{x}}^3$$

(7)

In the formula, v—non-motorized flow speed (m/s); and x—distance from town center to non-motorized vehicle travel (km).

See Figure 15, as the distance between non-motorized vehicles and the town increases, the number of non-motorized vehicles will gradually decrease. At the same time, the traffic density decreases, the road disturbance and vehicle disturbance when non-motorized vehicles are traveling will be reduced accordingly, and most cyclists will then travel at a faster riding speed. With the change in travel distance, the vehicle speed will have a greater variability, which is more consistent with the actual situation and verifies the traffic survey conclusion.

5.3. Correctness Analysis of Speed–Distance Calculation Model

By fitting the scattered data of speed–distance, we derived the calculation model of the relationship between the speed of non-motorized traffic and the distance from the center point of the town on the segments of the highway through the town. In order to analyze the correctness of the calculation model, we summarized the data related to non-motorized travel on highway segments crossing small town in four cities in Henan Province, namely, Luoyang, Jiaozuo, Hebi, and Puyang, as shown in

Table 8. Distance–speed data table for other cities.

Distance from the Center of Town (km)	Speed (m/s)
	Luoyang	Jiaozuo	Hebi	Puyang
0.5	2.41	2.80	2.21	3.02
1.0	3.42	3.96	4.02	4.51
1.5	5.03	4.39	4.83	5.21
2.0	6.50	6.41	5.74	5.84
2.5	6.85	6.92	6.35	7.01
3.0	7.51	7.51	7.14	7.96
3.5	8.02	8.03	7.79	8.64
4.0	8.78	9.11	8.52	9.08
4.5	9.98	10.55	10.47	10.85
5.0	12.24	11.87	12.09	12.74

.

The applicability of the computational model to the relationship between the speed of non-motorized vehicle flow and the distance from the town center point for the highway segments crossing the small towns in these four cities is shown in Figure 16.

It can be seen from Figure 16 that the distance–speed scatter of non-motorized travel on highways segments crossing small towns in the four cities, Luoyang, Jiaozuo, Hebi, and Puyang, is basically consistent with the computational model. The correctness of the model can thus be verified.

6. Conclusions

This article investigates the cycling behavior, and spatial and temporal distribution characteristics of cyclists on highway segments crossing small towns. The travel time of cyclists on road sections crossing small towns varies significantly during the morning and evening peak hours. There are thresholds for time and distance traveled by non-motorized vehicles, with a riding time threshold of 30 min and a riding distance threshold of 5 km.

The relationship model of flow rate, speed, and density was constructed by analyzing the traffic flow of non-motorized vehicles on highway segments crossing small towns. The flow rate–density relationship of non-motorized traffic flow shows a linear relationship. In the non-congested state (density < 0.2 vehicles/m²), the speed of mixed non-motorized vehicles is distributed in the interval of 5 m/s~10 m/s. In the congested state (0.2~0.4 vehicles/m²), the traffic flow shows following traffic, and the speed–density shows an exponential relationship. The larger the density, the more significant the decrease in traffic speed until complete blockage and stagnation. In the speed–frequency scatter diagram, the median value of the speed interval corresponding to the uniform distribution points was used to describe the characteristic value of speed, study the relationship between speed and distance, and establish the cubic function model of the speed and distance of non-motor vehicle riding. At the same time, the correctness of the model was analyzed to demonstrate its wide applicability to other regional highway segments crossing small towns.

The research results of this article can be practically used to determine the scope of non-motorized lane setting for the sections of highways crossing small towns, so as to improve the road utilization rate, enhance the efficiency of non-motorized travel, and improve the environment for non-motorized travel. However, the research results are only applicable to plain areas and without hard separation facilities for motor vehicles and non-motorized vehicles. It is not applicable to other road types and countries where non-motorized vehicles are prohibited on highways. In the future, the survey sample and survey scope can be expanded to study the spatial and temporal distribution and traffic flow parameters of non-motorized vehicles under different conditions.