A study of vehicle lateral position characteristics and passenger cars' special lane width on expressways

Lane width is crucial for traffic safety management. Previous studies have shown that inappropriate width will lead to an increase in accident probability and unsafe driving behaviors. However, there have been limited studies on determination method of special lane width for different models, especially for passenger cars. To tackle this problem, the lateral driving behavior characteristics of the expressway need to be clarified. This work aims to obtain the appropriate lane width according to the vehicles' width and lateral position characteristics. In this study, the lane lateral residual width (the distance between the vehicle body's contour and the lane marking on the same side) and the lateral safety margin are extracted as characterization indices of vehicle lateral characteristics from natural driving trajectory data of expressways. The effect of vehicle type, driving speed, and lane position on the expressway's trajectory behavior is investigated. The results show that the utilization rate of lane width is higher in the outer lane compared to the inner lane. As driving speed increases, vehicles in the inner and middle lanes exhibit shy away effect, moving away from obstacles. Substantial variations exist in the lateral width of lanes among different vehicle types. When driving in the same lane, passenger cars' lane lateral residual width that is 0.4–0.5 m wider than that of heavy vehicles. The recommended lane width for the safe operation of trucks on expressways is 3.75 m. After a comprehensive analysis of vehicle width, trajectory oscillation, and lateral safety margin, this study proposes a minimum lane width of 3.25 m and a recommended general width of 3.5 m for a passenger car‐only expressway. This study holds great significance in enhancing road safety and provides a valuable theoretical foundation for the design of lane width in a passenger car‐only expressway.


INTRODUCTION
With the rapid development of the economy, the popularity of passenger cars and travel demand are increasing in many countries.For example, in China's economically developed areas, the proportion of passenger cars on trunk expressways is generally 60%-80%, and the proportion of passenger cars on branch expressways is even higher, reaching 90% on some roads.Passenger cars have various interactions with other heavy vehicles, such as trucks, including overtaking, following, and paralleling.In comparison to heavy vehicles, passenger cars have lightweight, good dynamic performance, fast driving speed, and high maneuverability, so they are referred to as light duty vehicles (LDVs).The mixed-traffic environment will not only reduce the expressway's traffic efficiency but will also exacerbate the harm caused by traffic accidents due to the difference in speed and body quality between the different types.Special expressway systems or lanes for passenger cars are built in some cities to reduce this interaction and the likelihood of risk events on expressways.However, how to determine the width of passenger car-dedicated lanes is still inconclusive.Lane width represents the space allocated by the designer to the driver as the right-of-way or runnable space.In generally, to ensure safe and efficient operations for all vehicles, heavy vehicle is used as a reference to determine the geometric features and lane width, so the standard value of lane width in different countries is usually above 3.5 m. [1][2][3][4][5] For example, China, which has the most expressway mileage in the world, specifies the width of expressway lanes based on the maximum width of designed vehicles (2.55 m width of vehicles) and the extra width required for overtaking and parallel vehicles. 6The lane width is 3.75 m when the designed speed is 80 km/h or higher.If we continue to construct passenger car lanes with the traditional lane width, it will not only fail to reflect the characteristics of compact body, small outline size (1.9 m wide for typical cars), and excellent handling performance, but it will also waste land resources and increase construction costs.R, many studies show that the wider lane causes lateral deviation of the vehicle position relative to the lane centerline (the distance between the vehicle center point and the road center line), as well as an increase in vehicle lane change rate, speeding events, and unsafe driving behavior, resulting in a decrease in traffic flow regularity. 7As a result, it is the foundation of the cross-section design of a passenger car-specific expressway, as well as the main study topic of increasing expressway traffic safety, to acquire insights into vehicle lateral position characteristics.
Optimizing road design is a crucial approach to enhance traffic safety, with particular emphasis on the design of lane width.Several studies have examined the impact of lane width on vehicle lateral position. 8Dijksterhuis et al. 9 conducted a simulator-based investigation to explore the effects of lane width on drivers' mental effort, risk perception, and lane-keeping ability.The findings indicate that narrowing the lane increases drivers' mental effort while improving their ability to maintain a central position within the lane.Mecheri et al. 10 observed that narrowing the lane width brings vehicles closer to the center of the road, compensating for the reduced driving space by positioning closer to the shoulder.Liu et al. 11 use driving simulator to study the relationship between different lane widths and lane departure in a tunnel environment, revealing that vehicles tend to be further away from the wall when driving in the lane adjacent to it.Previous research has also highlighted the influence of shoulder width and lane position on driver's lane-keeping strategy.For instance, a wider shoulder reduces the occurrence of hazardous lateral movements, and increasing shoulder width prompts vehicles to approach the lane edge line. 12ane width has been shown to have an impact on vehicle speed.Shackel et al. conducted a study based on urban road observations and found that overtaking speed is influenced by road infrastructure and vehicle types, with wider lane widths often leading to increased overtaking speeds. 7,8Kondyli et al. 13 discovered that reducing lane and shoulder width has a significant effect on free-flow speeds, with a decrease of 1 m/h for every foot of width reduction.Godley et al. 14 and other researchers found that narrowing the lane width to 3.0 m is an effective method for reducing driving speed compared to wider lanes.This is because the narrower lane width increases the driver's steering workload, requiring more attentive monitoring of the road and frequent steering wheel corrections.Some researchers argue that while drivers may not consciously perceive changes in lane width, they exhibit behavioral adaptations.For example, the increase in vehicle speed resulting from wider roads may offset overall safety improvements and lead to unexpected behaviors. 15,16In summary, research findings suggest that narrowing lane width can be considered a powerful approach to influence road user behavior. 17It helps reduce driving speed, decrease lateral position variability, and promote positioning closer to the center of the road.
Many studies have examined the relationship between lane width and traffic safety, often using the number of traffic accidents to develop safety performance functions. 18,19In traditional design concepts, wider lanes are believed to provide an additional safety margin, while narrower lanes are associated with increased collision probabilities. 20,21However, some researchers have reported that wider lanes tend to encourage speeding, overtaking, and unsafe driving behaviors, leading to disruptions in traffic flow stability.This is because wider lanes can diminish drivers' risk perception. 7Karim, 23 utilizing collision databases in urban areas, has analyzed lane width and found that excessively wide lanes (3.1-3.2 m) and excessively narrow lanes (<2.8 m) increase the risk of collisions.Wu et al. 24 also investigated the influence of urban lane width on the probability of various traffic accidents and arrived at a similar conclusion, suggesting that standard lane widths (average lane width around 3.45 m) show a lower collision probability.Most research findings indicate that beyond a certain range, the safety benefits of wider lane widths reach their lowest point. 21,22,25However, a definitive conclusion regarding the relationship between lane width and safety has not yet been established.Table 1 provides a comparison of studies on lane width.
In conclusion, researchers have conducted extensive studies on the impact of lane width on driving behavior.However, the research methods primarily involve driving simulations, data collection from cross-sections, and accident statistics.Most of the research sites are low-grade highways located in urban and rural areas.There is a lack of research on the natural driving process along continuous sections of expressways.The limitations of using driving simulators include the difficulty in accurately replicating the influence of actual road environments on driving behavior and the lack of support from large-scale vehicle trajectory data.Consequently, their applicability in engineering design and the revision of standards and specifications is limited.
This study is aim to investigate the lateral driving behavior and position characteristics of drivers and examine the impact of driving speed, lane position, road facilities, and vehicle types on vehicle trajectory control behavior.A novel index called lane lateral residual width, which reflects the lateral driving behavior of vehicles, is introduced for the first time.The study analyzes the trajectory behavior in a wider and higher speed range within the straight sections of an expressway.The findings of this research provide valuable data and theoretical support for establishing cross-section indices for passenger car-only expressway.
In Section 4, we examine the statistical distribution of vehicle widths for a sample of 4764 passenger cars available in the Chinese market.Based on this analysis, we derive design models that are suitable for passenger car-only expressways.By integrating our previous work, we propose a methodology to determine both the general value and minimum value of lane width for passenger car-only expressways.This methodology considers three key factors: lane width, trajectory oscillation, and lateral safety margin.To the best of the authors' knowledge, this study represents the first attempt to determine carriageway width based on the analysis of lateral driving characteristics.

Study Research scene Resolved issue
Lateral position Dijksterhuis 9 Highway The relationship between lane width and the lateral positioning of vehicles was explored Mecheri, 10

Trajectory dataset
In this article, the vehicle trajectory dataset of expressway is used as the basic data source to analyze the lateral position of vehicles, including the highD open dataset of German expressways and the trajectory data of two expressways in Chongqing, China.highD dateset is a large-scale natural vehicle trajectory dataset recorded on German expressways using drone. 26The collection work is done from 8:00 a.m. to 5:00 p.m. in sunny, windless weather.The extracted trajectory position error is typically less than 10 cm when the advanced computer vision algorithm (U-Net) is used to semantically segment the vehicle and the road background.The dataset includes detailed information such as vehicle size, vehicle category, driving direction, speed, and descriptions of surrounding vehicles, as well as the center position information (trajectory point) and movement situation of vehicles appearing in each frame.The highD dataset records the trajectory of 110,500 vehicles over a total driving distance of more than 45,000 km, which has advantages in static and dynamic scene description, natural driving behavior, data type and volume, and is the primary research object of this article.
The method of highD dataset recording was used in the trajectory data record process in China.Traffic on Chongqing Ring Expressway (G5001) and Chongqing-Chengdu Expressway (G5013) were record by a drone.The total collection time is 200 min, and there are approximately 5000 vehicles.The video is stabilized first by the computer vision algorithm Scale-Invariant Feature Transform (SIFT), then the image processing algorithm obtains vehicle running characteristic parameters such as vehicle type, vehicle position, and speed.Finally, the trajectory data is preprocessed to form a formatted trajectory dataset.The precision validation experiments exhibits a high level of accuracy, with the majority of errors falling within a range of 10 cm compared to the ground truth.The speed offset is within 1.5 km/h, indicating that the accuracy meets the requirements for research purposes.It should be noted that the trajectory dataset of China is far less than the highD dataset currently.As a result, it is only used to compare and validate the differences in trajectory lateral position characteristics between China and Germany.

Location of observation
The highD dataset includes six different expressway locations near Cologne, Germany, with two or three lanes in each direction, and the photographed road section recorded has a range of about 420 m.

F I G U R E 6
The kernel density of vehicle speed.
Germany does not set a speed limit for some expressways with good road conditions, so the trajectory data in a wide speed range can be observed in the dataset.Road traffic rules and driving habits are similar to those found in China.Vehicles travel on the right side of the road, with the inside lane is for light passenger vehicles and the outside lane is for passenger and freight vehicles.There are no restrictions on the use of lanes when the gross weight of vehicle is less than 3.5 t.When the gross weight of vehicle is greater than 3.5 t, the vehicle must drive in the outer lane, and adjacent lanes can be used for overtaking.The vehicle speed distribution range of the highD dataset is shown in Figure 5. Figure 6 shows the heatmaps of the speed kernel densities, with peak values around 80 and 120 km/h representing typical truck and passenger car speeds.

INDEX OF VEHICLE LATERAL POSITION CHARACTERISTICS
Marking is used to assist driving behavior and is also an important basis for defining road rights.In an ideal situation, vehicles tend to driving on the center of the lane, but the existence of roadside facilities, adjacent vehicles and drivers' experience will cause lateral deviation of vehicles. 21,27What factors lead to the lateral position deviation of vehicles is worth exploring, which is the basic logic to guide the design of safety facilities, so the minimum value is adopted to reflect this deviation trend.Second, the existing lane width is superfluous for passenger cars.By studying the sum of the minimum values on both sides, we can get the lane width actually used by passenger cars, and make clear the right of way needed by passenger cars.In addition, exploring the minimum value can understand how drivers use lane markings and their acceptable distance from lane markings.As a result, the lane lateral residual width (LLRW) index is proposed in this article to describe the trajectory control behavior of vehicles in the lane.Figure 7 shows an example of parameter calculation.The distance between the vehicle body contour and the lane line on the same side when the driver stays in the lane represents the driver's perception and control of lateral safety and is a characteristic parameter to measure the vehicle's trajectory control behavior in the lane.The rectangular coordinate system is established with the upper left corner of the video screen as the coordinate origin when calculating the characteristic parameters, and the incomplete vehicle trajectory is eliminated.Vehicles that have not changed lanes are chosen as the research object.y left,i represent the left side lines of lane i; y mid,i represents the lane center line of lane i; and y right,i is the right side line of lane i.Finally, the coordinates of the vehicle's trajectory points and the road marking line are superimposed in the same coordinate system, The wheel trajectory on the left/right sides of the vehicle can be obtained based on the width of vehicle body, and the lateral distance between the wheel trajectory and the lane lines can then be calculated.Their smallest values are the lane left/right residual widths (LRW/RRW).Their total is the lane lateral residual width (LLRW).The following is the calculation formula: where, i is the lane position of the vehicle, and n is the number of the vehicle trajectory point; y left,n and y right,n respectively represent the trajectory points of left and right wheel; in m.The reason for the negative value may be that some vehicles are distracted driving or trying to overtake, resulting in driving on the lane markings.The negative value should be viewed as an indication of bad lateral control.Figure 8 depicts the lateral safety margin (LSM) index calculation method, which can be used to measure the overall utilization degree of lane width.Take the middle lane as an example, select the 15th percentile of the LRW and RRW of all vehicles in the middle lane, and the sum of them is the lane width margin after meets the driving swing demand of 85% drivers in the middle lane.The calculation formula is as follows.
where LRW 15 and RRW 15 are the 15th percentile values for the lane's left and right residual widths, respectively.The unit is meter.The lower the LSM, the higher the lane utilization, and vice versa.

Four-lanes divided expressway
The lane lateral residual width reflects the driver's control of the lateral position of the vehicle body, as well as the influence of lane position and roadside environment on the driver's lateral driving behavior, it can provide reference for the value of lane width.The frequency distribution (F.D.) and cumulative frequency (C.F.) curve of the four-lanes divided expressway is shown in Figure 9, The utilization of the outside lane width is higher than that of the inside lane, resulting in a lower remaining width for the outside lane compared to the inside lane, once the driving demand is met.Table 2 shows that the LSM of the outside and inside lanes is 0.365 and 0.745 m, respectively.The utilization rate of the outside lane is greater than that of the inside lane.This is due to the fact that the proportion of trucks in the outside lane is mostly, the wider body leads to a higher road occupancy rate, and the light vehicles in the inside lane account for a greater proportion, so the trajectory oscillation demand of the body occupies less road.

Six-lanes divided expressway
The frequency distribution (F.D.) and cumulative frequency (C.F.) curve of lane lateral residual width of different lanes of six-lanes divided expressway is shown in Figure 10.Table 3 shows the statistical characteristic values    of the left and right residual widths, and it can be seen that the LRW of vehicles in the outside lane is greater than that in the inside and middle lanes.The deviation value of vehicles driving in the outside lane of a six-lanes divided expressway is greater than that of a four-lanes divided expressway, which could be because the adjacent lane of the two-way six-lanes outside lane is narrower (3.5 m).Furthermore, the right side of the outside lane has a higher utilization rate and dispersion degree than the other two lanes, as is the probability of riding on the marking behavior.This could be because the shoulder provides a safe clearance for the drivers, which drivers perceive as extra driving space, and driving on the right side of the center line helps to reduce the driver's psychological load.Furthermore, Table 3 shows the lateral safety margins (LSM) of the outside, middle, and inside lanes are 0.16, 0.36, and 0.60 m, respectively.The difference in vehicle composition in different lanes causes this phenomenon.The inside lane is dominated by light vehicles, and there is a larger margin width compared to the outside lane, which can be used as data support to reduce the lane width value of light expressways.

4.2
The effect of speed on the lane lateral residual width The purpose of considering lateral clearance in road design is to meet the driver's psychological safety distance, reduce the pressure of the guardrail on the driver, and thus reduce the likelihood of traffic accidents.However, it is worth discussing how the vehicle's demand for safety clear distance changes at different running speeds.As a result, the lateral margin of trajectory with different speed range is chosen for comparison in order to investigate the influence of driving speed on the lateral margin.The neighborhood of 10 times in the interval of [100-140 km/h] is chosen as the speed The relationship between the left residual width and driving speed on four-lanes divided expressway is shown in Figure 11.The one-way analysis of variance (ANOVA) showed that there are significant differences in the left residual width at different speeds on four-lanes divided expressways when significance level of 0.05 (p < 0.05).It shows that average values of the outside lane's left residual width decrease, while the values of the inside lane's left residual width increase, indicating that vehicles in the inside lane will stay away from the guardrail as driving speed increases, and the driver will stay away from roadside obstacles by increasing the lateral clear distance to ensure driving safety.Vehicles in the outside lane are driving away from the right side of lane line and toward the center of the road.According to the research conclusion of Reference 28, road marking can improve the driver's attention, provide a warning function, or convey danger information, indicating that the restraint and warning function of vehicle markings are strengthened as driving speed increases.Furthermore, as the speed increases, the distribution range of left residual width of the inside lane decreases, indicating that the driver will strengthen control of the vehicle body and the range of vehicle swing decreases.
Figure 12 depicts the relationship between the vehicle speed of six-lanes divided expressway and the left residual width.The one-way analysis of variance (ANOVA) showed that there are significant differences in the left residual width at different speeds on six-lanes divided expressway when significance level of 0.05 (p < 0.05).It demonstrates that as the vehicle speed increases, the average value of the left residual width of the inside lane shows an upward trend, the left residual width of the middle lane shows a gradual decrease trend, and the left residual width of the outside lane shows a gradual decrease trend.That is, as speed increases, vehicles in the inside lane maintain a greater lateral distance from the crash barrier, vehicles in the outside lane maintain a closer center of mass to the lane center line, and vehicles in the middle lane tend to drive on the left side of the lane center line.
Drivers will adjust their driving behavior based on their perceived risks, according to the theory of safety potential field. 28The energy generated by colliding with the guardrail increases as driving speed increases, so vehicles driving in the inside lane will stay away from the guardrail side; as the vehicle in the middle lane accelerates, the driving sight distance is affected by the occlusion of the right truck, so the driver chooses to drive to the left from the center line to seek better sight distance.Furthermore, trucks primarily use the right lane.Because trucks have a larger total mass, the field force (the safety risk) generated by vehicles during the driving process is greater than that of vehicles with small mass, implying that there is a virtual "external force" acting on vehicles in the middle lane, forcing them to change their own motion state during acceleration and move to the left to away from the trucks.

The effect of vehicle types on lane lateral residual width and safety margin
The  4, it is discovered that there are significant differences in lane lateral residual width of different vehicles types in the same lane, and the average of LRW and RRW of trucks is smaller than that of passenger cars, indicating that trucks use more lane width than passenger cars.Furthermore, the cumulative frequency curve of trucks approaches a straight line, indicating that drivers use the lane width evenly, whereas the cumulative frequency curve of passenger cars has obvious abrupt points, that is, there are obvious aggregation areas in the use of road surface by passenger car bodies, demonstrating that passenger car drivers' trajectory control behavior differs significantly from that of truck drivers, and it is also demonstrated that the lane width of 3.75 m can be reduced for light vehicles.The lateral safety margins that meet 85% of the trajectory oscillation requirements of trucks and passenger cars in the same driving environment (outside lane) are 0.30 and 0.695 m, respectively, indicating that the lane width of light vehicles can be lower than that of trucks.The cumulative frequency curve and vehicle position of the middle lane of the six-lanes divided expressway are depicted schematically in Figure 14.From Figure 14 and Table 5, it is evident that the average and 15th percentile values of the lateral residual width for trucks are narrower compared to passenger cars in the middle lane (3.5 m).The cumulative frequency of trucks follows a nearly straight line, while there is a noticeable inflection point in the cumulative frequency of passenger cars, which is similar to that observed in the four-lane divided expressway.According to Table 5, in the passenger and freight lane (3.5 m middle lane), the LSM (lateral safety margin) values for trucks and passenger cars are 0.02 and 0.495 m, respectively.Passenger cars can have a lane width requirement that is 0.493 m less than that of trucks.This indicates that trucks make the most of the lane width of 3.5 m, leaving no surplus lateral space after accommodating their normal driving needs.To ensure safe operations, it is recommended to provide extra lateral safety space for truck models.Therefore, we recommend a lane width of 3.75 m for truck safe operations in expressways.The figure shows that the average value of the left lane width of the truck in the middle lane (3.5 m) and the value of LRW15 are smaller than that of the passenger car, indicating that the truck has a high utilization degree of the lane width of 3.5 m and basically has no surplus lateral width, indicating that the lane width suitable for the truck types is 3.75 m.The cumulative frequency tendency of trucks is close to a straight line, and the cumulative frequency of passenger cars has obvious mutation points, which is the same as that of the two-way four-lanes outside lane.

TA B L E 4
Figure 15 depicts the frequency distribution (F.D.) and cumulative frequency (C.F.) curve of the preferred lateral position for various vehicle types.The intuitive probability distribution curve cannot accurately reflect the influence of different vehicles on the preferred deviation.To test the differences between vehicles types, statistical tools should be used.The preferred lateral position is tested by T-test to see if the difference in lateral residual width between two types of vehicle samples is caused by different centroid positions.The statistical results are significant when the test result is less than 0.05, and Cohen's d values of 0.20, 0.50, and 0.80 correspond to small, medium, and large critical points, respectively.According to the inspection results in Table 6, the Cohen's d values of the four-lanes divided expressway outside lane and the six-lanes divided expressway middle lane are 0.081 and 0.334, respectively, indicating a small difference in lateral position preference between the two types of vehicles in the same lane.It demonstrates that in the same lane, the main factor contributing to the difference in lateral residual width between large and passenger cars is the body width, that is, passenger cars use less lane width than trucks due to the narrower vehicle body; after deducting the difference in body width, the lateral position characteristics of the center of mass of passenger cars are essentially the same as those of large trucks.
The above analysis method is used to process expressway vehicle trajectory data in China, and the frequency distribution histogram and cumulative frequency curve of LLRW of passenger cars and trucks are shown in Figure 16.Compared with highD dataset, Table 7 show that the LLRW of passenger cars in China is 0.043 m higher and the 15th percentile value is 0.055 m lower, but the overall distribution pattern, mode value, and range are extremely close to the analysis results of the highD dataset (German expressway).On the other hand, the cumulative frequency curve and the statistical characteristic values of trucks, show significant differences.The LLRW of trucks in China is 0.192 m lower than that of German expressways, and the 15th percentile is 0.324 m lower, which could be attributed to differences in truck conditions and driving habits between the two countries; or maybe the middle and inside lanes in Germany are 3.5 m.

WIDTH OF EXPRESSWAY SPECIAL LANE FOR PASSENGER CAR
In highway design, the term "design vehicle" is used to refer to the specific type of vehicle that is considered to have the most unfavorable characteristics for the design.The design vehicle of passenger car-only expressway should represent the largest or longest vehicle in the passenger car category.Therefore, we collected 4764 public profile parameters of passenger cars to examine the distribution of their widths, as illustrated in Figure 17.Our analysis reveals that passenger cars follow the profile dimension sequence: minivan < sedan < SUV < MPV <9-passenger van.Thus, it is recommended to adopt 9 passenger van as design vehicle, with a width of 2098 mm specifically for passenger car design.In regions with restricted terrain conditions, the width of design vehicle can also consider the 85th percentile width of passenger cars, which is 1930 mm.To ensure safe vehicle operation, the lane must accommodate lateral trajectory oscillation and provide an adequate lateral safety margin (see Figure 18).Building upon our previous research, this study proposes the utilization of vehicle width, trajectory oscillation, and lane lateral safety margin as control factors for determining the lane width of dedicated expressways for passenger cars.The specific calculation method is outlined below: Lane width = width of design vehicle + trajectory oscillation + lateral safety margin (LSM).
The lateral safety margin of inside lane is 0.6 m (0.3 on one side), the 85th of trajectory oscillation is 0.75 m, 30 and the width of design vehicle is 2.1 m (the minimum value can be 1.9 m).As a result, with a design speed of 100-120 km/h, the lane width of expressway dedicated to passenger cars is as follows: (1) General value of lane width for passenger cars:  F I G U R E Lane width and cross section layout of dedicated passenger car lanes of expressway.

DISCUSSION
In this study, we have shown that the lateral position distribution characteristics and trajectory control behavior of vehicles on the expressway, and analyze the influence of road design elements on vehicle lateral position.In comparison to previous research, the sample size for analysis is larger, and the vehicle trajectories are longer.For the first time, the lane width of passenger car-only expressway is proposed based on an analysis of German and Chinese trajectory data.
According to the research findings, vehicles in the outside lane tend to drive on the right side of the lane center line due to the presence of the shoulder 10 ; there are also significant differences in the width utilization rate of different lanes in the same direction.Typically, the higher the proportion of passenger cars, the lower the lane width utilization rate.Second, when cars and trucks share the same lane, there is no significant difference in their centroid positions, demonstrating that the lane width is most affected by the body width.Third, it is discovered that the expressway guardrail has a "side wall effect," which is consistent with previous research results on underground expressways, namely that as speed increases, vehicles will avoid the side with obstacles.Finally, when the trajectory data from China and Germany are compared, it is discovered that there is no significant difference in the distribution shape and statistical characteristic value of passenger cars, demonstrating that the width of passenger car lanes can be reduced, thereby saving road construction costs and land resources.
The limitations of this study are as follows: first, it simplifies the classification of vehicle types, it does not further subdivide truck types; second, due to the limitations of drone data record, it is not possible to include more microscopic perspectives, such as the driver's psychological and physiological parameters; third, the sample size of the China trajectory dataset used for verification is insufficient to allow for a more detailed comparison.
According to the existing criteria, the outer lane is a mixed passenger-cargo lane and the inner lane is a passenger car lane/ fast lane, and the uniform width is adopted instead of the differential design of lanes, which leads some truck drivers to occupy the passenger car lane/ fast lane, and the excessively wide lane indirectly encourages the passenger car drivers to overspeed.The cross section of the expressway can be reallocated to replace the lane design with the same width, for example, the mix-traffic lane is 3.75 m, and the special lane for passenger car is set to 3.5 m.This is conducive to the separation of passenger cars and trucks.
It should be noted that this study has analyzed only trajectory lateral position change law, there is no further experiment on the influence of lane width change on driving speed and capacity.With respect to this issue, many studies have shown that lane width is similar to the "smile curve" for accident probability, 22 and various accidents are very low around 3.2-3.3m, that is, too low/high width will lead to an increase in accident probability, perhaps speeding/deviation or rear-end collision. 7The goal of studying the lane width is to select the appropriate lane width according to the size of the vehicle, and at the same time, to clarify the right-of-way space.The work of this study observes whether there are differences in the practical lane width between different models and the reasons for the differences, and puts forward the appropriate width to restrict the operating speed of the passenger car.
With regard to traffic capacity, the remaining space after remodeling can increase the number of lanes and improve the stability of traffic flow.This concept of multimodal lane is proposed to adapt to different types of lane widths, and its total capacity will not decrease.HCM mentioned that the impact of lane width on traffic capacity is limited, which is also mentioned in document CHEN. 29After remodeling, we can adjust the roadside space and carry out people-oriented design.Of course, any cross-sectional remodeling needs engineering research.
So, other complicated research is required in the further, such as designing a new cross-sectional layout in driving simulation equipment, or using eye tracker and heart rate acquisition equipment to carry out real vehicle experiments to quantify the change in risk perception and capacity of passenger car drivers after lane width reduction.

CONCLUSIONS
Based on an in-depth analysis of German and Chinese trajectory datasets, we analyze vehicle trajectory control characteristics in various road environments, and clarifies the influence of driving speed, vehicle types, and lane position on the lateral residual width, yielding the following research conclusions: (1) In the four-lane and six-lane divided expressways configuration, the outer lane is higher in lane width utilization compared to the inner lane.Specifically, as vehicles approach the median, the utilization rate of lane width decreases.
(2) When vehicles travel in the inner lane and accelerate, drivers tend to steer away from the median guardrail, indicating an evasive effect.Hence, in cases where the design speed is increased, designers should consider increasing the clearance between the guardrail and the lane to ensure a safe distance that is acceptable to drivers.Similarly, vehicles in the middle lane have a tendency to move away from the outside lane when accelerating, it is due to the compressive force experienced while overtaking heavy vehicles.
(3) Notable disparities exist in the distribution characteristics of lane lateral residual width (LLRW) among different vehicle types.Passenger cars demonstrate lower lane width utilization compared to heavy vehicles, specifically around 0.4-0.5 m lower.The recommended lane width for the safe operation of trucks on expressways is 3.75 m.
(4) the LLRW of passenger cars on Chinese expressways closely approximates that of German expressways, slightly exceeding the German on average.The findings suggest that the lateral position characteristics exhibit minimal variations across different countries, indicating their potential for generalizability and widespread application.
(5) For the design of expressways or dedicated lanes for passenger cars, it is recommended to adopt a design vehicle based on 9-passenger van with a width of 2.1 m.In cases where land availability is limited, the 85th percentile value of 1.9 m can be utilized.
(6) Vehicle width, trajectory oscillation, and lateral safety width can serve as key factors for guiding the design of lane width for passenger car-only expressways.Based on these considerations, it is proposed that the minimum lane width for passenger car-only expressways with a design speed of 100-120 km/h should be 3.25 m, while a general value of 3.5 m is recommended.
Figures 1 and 2 depict the roadside environment, cross-sectional composition, and geometric dimensions of the collection site.The body widths of the most common passenger cars and trucks on the road are 1.8 and 2.5 m, respectively.The Chinese trajectory dataset chooses four straight sections of the Chongqing Ring Expressway and the Chongqing-Chengdu Expressway.Each section has a length of 420 m and a speed limit of 120 km/h.The cross section is six-lanes divided expressway layout with a carriageway width of 3.75 m and a medium strip of 4.5 m, with a 0.75 m left marginal strip and a 3 m hard shoulder.Figures3 and 4depicts the cross-section configuration and component dimensions of locations observed.F I G U R E 1Guardrail and roadside environment at the collection sites of highD dataset.

F
I G U R E Illustrates of the cross-section at sites of highD dataset (unit:m).

F
I G U R E Locations of recorded and length of road.F I G U R E Cross section elements of photographed sites at Chongqing Ring expressway and Chongqing Chengdu expressway.

F I G U R E 5
Vehicle speed distribution in highD dataset.

F I G U R E 7
Illustration of lane lateral residual width.F I G U R E 8Illustration of lateral safety margin.

F I G U R E 9
Lane lateral residual width distribution on four-lanes divided expressways.(A) Left residual width (LRW); (B) Right residual width (RRW).

F I G U R E 10
Lane lateral residual width distribution on six-lanes divided expressways.(A) Left residual width (LRW); (B) Right residual width (RRW).

F I G U R E 11
Relationship between the left side residual width and driving speed on four-lanes divided expressways.(A) Inside lane; (B) Outside lane.retrieval condition, and the neighborhood's floating threshold is [−3, +3 km/h], and the sample size is approximately 300 vehicles under each speed condition.Because of the relative relationship between the left and right residual width, this section only lists the changes in the left residual width as driving speed increases to avoid lengthy and complicated content.

F I G U R E 12
Relationship between the left side residual width and driving speed on six-lanes divided expressway.(A) Inside lane; (B) middle lane.(C) outside lane.
outside lane of a two-way four-lanes expressway and the middle lane of a six-lanes divided expressway with the same road conditions are chosen as research examples to investigate the difference in lane lateral residual width of different vehicle types.To represent the preference of different vehicles types in the lateral position, the average value of the trajectory's lateral position in the lane is extracted.At the same time, the LRW and RRW of passenger cars and trucks is being compared and analyzed.Figure 13A,B depict the frequency curves of the LRW and RRW of passenger and trucks in the outside lane of a four-lanes divided expressway, and Figure 13C depicts a cross-sectional view of the preferred lateral position of different vehicles types in the outside lane, with the dotted line representing the lane marking, the dashed line representing the lane center line, and the solid line representing the lateral preferred position of the vehicles in this lane.According to the characteristic values in Table

F I G U R E 13
Lane lateral residual width distribution of different vehicle types in outside lane of four-lanes divided expressways.(A) Left residual width (LRW); (B) right residual width (RRW); (C) lateral position distribution of centroid of vehicles.

F I G U R E 14
Lane lateral residual width distribution of different vehicle types in middle lane of six-lanes divided expressways. (A) Left residual width (LRW); (B) right residual width (RRW); (C) lateral position distribution of centroid of vehicles.TA B L E 5 Statistics of lateral residual width of in middle lane for six-lanes divided expressways.

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I G U R E 15 Distribution of the preferred lateral position of vehicle mass center of different vehicle types.(A) Outside lane in four-lanes divided expressways; (B) middle lane in six-lanes divided expressways.TA B L E 6 Test for variability in lateral position of centroid of different vehicle types.p-value <0.01; ** p-value <0.05; * p-value <0.1.

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I G U R E 16 Lane lateral residual width of expressways at Chongqing, China, and comparing with same indicators of highD.(A) passenger cars; (B) trucks.

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I G U R E Distribution of passenger car body widths.F I G U R E Calculation indicators for the width of lanes dedicated to passenger cars.

METHODS OF RESEARCH AND DATA SOURCES
Statistics of lateral residual width for four-lanes divided expressways.
Statistics of lateral residual width for six-lanes divided expressways.

types Sample size Average speed/(km/h) Residual width Mean Std.Dev 15th LSM (m)
Statistics of lateral residual width of in outside lane for four-lanes divided expressways.

Vehicle types Sample size Average speed/(km/h) Residual width Mean Std.Dev 15th LSM (m)
Statistics of the lane lateral residual width indicators.