Sustainable Transportation Design: Examining the Application Effect of Auxiliary Lanes on Dual-Lane Exit Ramps on Chinese Freeways

Abstract

Numerous design cases of abandoning auxiliary lanes for freeway dual-lane ramps with low traffic volumes exist, adapting to complex engineering conditions and reducing construction costs, but the national specifications have not posed specific setup conditions for auxiliary lanes. Thus, this paper uses traffic flow theory and simulation tools to study the critical traffic conditions applicable to auxiliary lanes on dual-lane exit ramps of freeways. Initially, the vehicle operation data in the UAV (unmanned aerial vehicle) aerial video were extracted using an object detection algorithm. Subsequently, the VISSIM simulation calibration procedure was developed based on traffic flow theory and the orthogonal experimental method. The impact of auxiliary lanes on the capacity of the freeway diverging area was analyzed through the simulation results based on traffic flow theory. Eventually, the critical traffic conditions applicable to auxiliary lanes were proposed. The results show that the maximum traffic volume applicable to non-auxiliary lane designs decreases with increasing diverging ratios. The research findings define the application conditions for auxiliary lanes on dual-lane ramp exits, contributing to the sustainable development of transportation design and operations. The VISSIM simulation calibration procedure based on data collection and traffic flow theory developed in this paper also provides an innovative and sustainable approach to road design issues.

1. Introduction

Serving as critical nodes connecting road networks, freeway interchanges have consistently faced challenges regarding traffic efficiency and safety [1,2,3]. Studies indicate that more than 30% of highway accidents occur in exit diversion areas, with accident rates being twice as those in merging areas, making them the most hazardous sections [4,5]. Additionally, empirical studies have reported a capacity reduction in diverging areas, with values ranging from 5% to 30%, and have identified diverging areas as the most frequent bottleneck sections for localized delays and congestion [6]. Therefore, scholars have been seeking to address or mitigate the access issues of interchanges with their work, of which geometric design strategy optimization can be realized as a critical approach [7,8].

To alleviate the traffic pressure in diverging areas, specifications in multiple countries state that auxiliary lanes should be installed to provide speed transition for vehicles, thereby reducing collision rates and improving capacity to some extent [9]. However, the application logic of auxiliary lanes exhibits significant regional differences. The Green Book of the U.S.A. mandates that the auxiliary lanes must be used to connect dual-lane ramps and the mainline, satisfying the lane balance principle [10]. In contrast, constrained by limited land resources, Japan prioritizes compact ramp layouts and allows the elimination of auxiliary lanes on low-traffic sections to reduce land use and construction costs. European countries, such as Germany and Switzerland, widely adopt parallel dual-lane exit designs on mountainous freeways, alleviating lane-change pressure by increasing the length of tapers.

Global literature on auxiliary lanes has focused on the impact of lane balance design on efficiency and safety. These studies were conducted mainly through data observation and analysis in the past. An evaluation of five highway exit bottlenecks in Texas, U.S.A, based on continuous observation before and after the installation of auxiliary lanes indicated that auxiliary lanes contribute to significant operational and economic benefits [11]. Another study collected geometric, traffic characteristics, and crash data for 404 freeway segments in California and Washington State, and pointed out the effect of installing auxiliary lanes on the probability and severity of crashes based on regression analysis [12]. The interweaving area capacity and level of service calculation models documented in the HCM also provide another avenue of research, allowing theoretical calculations to understand the impact of installing auxiliary lanes under different traffic conditions [13]. Additionally, a study in China confirmed that auxiliary lanes positively improved traffic conditions in weaving areas, significantly reducing the frequency of congestion [14].

However, some studies have begun to question the necessity of auxiliary lanes in diverging areas. A case study of a certain freeway section in Houston, USA, suggested that inserting auxiliary lanes in weaving segments of freeways can achieve more efficient operations under certain conditions [15].

In practical engineering, there are numerous cases where auxiliary lanes are omitted in dual-lane exit ramps. Particularly in China, the uniqueness and complexity of the highway network have amplified the debate and controversy surrounding the necessity of auxiliary lanes. Although China’s Technical Standard of Highway Engineering recommend that auxiliary lanes should ideally be provided on dual-lane exit ramps, the lack of quantifiable thresholds has led to reliance on empirical judgment in engineering practice, resulting in numerous unreasonable design cases [16]. In some urban areas, freeway diverging areas are forced to adopt non-standard designs by shortening or omitting auxiliary lanes due to land use constraints, leading to a significant increase in congestion and conflict rates during peak hours, as shown in Figure 1. In contrast, on mountainous freeways, few dual-lane ramps experience high traffic volumes, resulting in very low utilization rates of auxiliary lanes in these sections. Therefore, studies suggest that design decisions should carefully balance traffic efficiency and construction costs to meet the goals of sustainable development [7,17].

Recently, researchers have launched more in-depth thinking and exploration of the necessity of lane balance, proposing the issue should be related to traffic conditions including traffic volumes and diverging or merging ratios. With slight traffic pressure, lane imbalance design in the diverging or merging areas would not disturb the smooth traffic flow [17,18]. However, few studies have reported on the quantitative application effect evaluation and traffic adaptability analysis of auxiliary lanes on dual-lane ramps.

With the rapid development of transportation simulation, the construction of digital twins of road networks helps to realize efficient and low-cost continuous observation of the study object [19,20,21]. This provides a more effective approach for studying auxiliary lanes. Researchers have extensively utilized VISSIM simulation and proven its reliability in topics on freeway interchange sections in the past few years. Using VISSIM simulation to calculate the capacity of Anhua Interchange, the literature presents a relationship between the capacity and the turning vehicle proportions [22]. Another study developed the simulation models of six interchange design schemes, discussing their access efficiency based on the case of the E. Mississippi Ave. and I-225 interchange in Aurora, Colorado [23].

Notably, the VISSIM simulation accuracy depends on the rigorous calibration procedure, where actual traffic data must be measured to calibrate and adjust the simulation parameters to restore the actual traffic flow [24,25]. Therefore, traffic data acquisition is the essential step in determining the rationality of the auxiliary lane study. Traditional surveys were conducted using the tools of roadside radar or vehicle detectors and scholars proposed expanding the data sources through predictive algorithms [26,27,28]. Nevertheless, with the emergence and innovation of target detection algorithms, using UAVs to observe traffic data has taken advantage of their efficiency and cost-effectiveness [29,30]. Numerous studies have confirmed the authenticity and reliability of traffic data extracted from UAV videos, mirroring the promising application of this approach in transportation research [31,32].

In VISSIM simulation parameter calibration, commonly used accuracy calibration metrics include the Mean Absolute Percentage Error (MAPE), characterizing the error between the simulation and reality [33,34]. However, it has been suggested that a single MAPE is not sufficient to support accuracy calibration and the fitting of simulation results to the Greenshields Model would be an essential supplement [7,17]. Regarding specific parameter calibration methods, the optimization techniques provided in studies offer valuable references for this work, including orthogonal experimental design, nonlinear optimization, and error optimization methods [35,36,37,38].

To summarize, this paper will quantitatively discuss the capacity and application conditions of auxiliary lanes and non-auxiliary lane designs to address the issue of the necessity of lane balance for dual-lane exit ramps on freeways. Two core steps will facilitate this process: using UVA to acquire actual traffic data and calibrating the VISSIM model. Specifically, the data measurement process using UAVs is proposed and refined, and then ample diverging areas of two-lane ramps of freeways in Shaanxi are investigated. Subsequently, the calibration procedure of the VISSIM simulation model is proposed based on the theory of the traffic flow three parameters, proving the accuracy and credibility of this study. Finally, the application conditions of auxiliary lanes of dual-lane ramps are proposed by comparing and analyzing the simulation results of the capacity.

This initiative achieved a technological breakthrough in the transportation research field, presenting an innovative approach addressing road design concerns with the systematic application of simulation technology. The research results can fill the gap of quantitative research on the application conditions of auxiliary lanes, providing recommendations for revising Chinese specifications. The application conditions proposed in the study not only focus on improving traffic capacity and reducing congestion, but also consider the reduction in construction and land use costs under low traffic demand, aiming to enhance resource utilization efficiency. This approach promotes the shift towards sustainable road design and supports the development of greener and more efficient road transportation systems.

The remainder of the paper is organized as follows: Section 2 presents the problem statement and analysis, and summarizes three auxiliary lane design options. Section 3 outlines the methodology of the study, including data collection and analysis, as well as the development and calibration of the VISSIM simulation. Section 4 presents the data measurement and simulation results, followed by an analysis of the findings. Section 5 develops a discussion of the results; the conclusions are deduced in Section 6.

2. Problem Statement

The Green Book indicates that freeway two-lane exit ramps comprise both tapered two-lane exit ramps (TTERs) and parallel two-lane exit ramps (PTERs), typically requiring the use of auxiliary lanes to connect the mainline, as shown in Figure 2 and Figure 3. Both types possess respective advantages and disadvantages, with TTER facilitating vehicle operation and PTER facilitating driver identification. Furthermore, from the perspective of capacity, it is clear that PTER accommodates higher traffic volumes as the number of lanes increases significantly. However, specifications in each country have not harmonized the forms of exit ramps: TTERs are frequently employed on freeways in China, while Germany more commonly uses PTERs.

Additionally, there still exists non-auxiliary lane tapered two-lane exit ramps (NTTERs) that are widely used, although they fail to meet the lane balance principle. Figure 4 presents a diagrammatic example of this option. NTTERs provide less capacity storage space and also create more urgent diverging processes for vehicles. However, evidence suggests that designs omitting the auxiliary lanes are sufficient to support the smooth flow of vehicles at low traffic volumes [18]. Furthermore, NTTERs possess the advantage of reducing space and cost, which is particularly important in the context of sustainable development goals.

Currently, no clear boundaries exist regarding the conditions applicable to the three types of two-lane exit ramps. But in practice, the three types have not been operating at the same efficiency, nor adapted to the same traffic conditions. Therefore, further research is necessary to clarify the most applicable design traffic conditions of each design.

3. Methodology

3.1. Data Measurement and Analysis

3.1.1. Data Measurement Method

Serving as the three essential parameters in traffic flow theory to describe the characteristics of traffic flow, the relationship between the volume, density, and speed presented in Equation (1) forms the basis of the recognized traffic flow theory [39]. Therefore, this paper will measure the traffic flow three parameters on certain freeway sections to support developing and calibrating the micro-simulation model to restore the actual traffic flow.

Q = V·K,

(1)

where Q denotes traffic volume, V denotes vehicle speed and K denotes vehicle density.

Given their wide overview, large spatial coverage, and great efficiency, UAVs have been regarded as the preferred method of data measurement. Before extracting the data from the aerial video images, it is first required to establish the precise coordinate system. This process can be achieved using a GPS-RTK mobile station to measure certain marked points on the objective road section, such as positions of signs, marking change points, or other locations with identification features, as shown in Figure 5.

It is important to note that the accuracy and completeness of data measurement by UAVs may be affected by various environmental conditions, such as adverse weather and insufficient lighting. Thus, all data measurement was conducted under favorable weather conditions, in order to avoid errors caused by unstable UAV flight in strong winds or rain, and image quality degradation due to low light at night. Additionally, it should be ensured that data collection locations are free from visible accidents or ongoing maintenance, and to avoid significant traffic congestion and disruptions [7].

After continuously taking aerial photographs of traffic flow in diverging areas, an appropriate object detection algorithm must be selected to extract vehicle movement data. Given the complexity of freeway traffic scenarios in this study, including high-speed vehicles and continuous traffic flow, efficient real-time detection capability is crucial to ensure the accuracy of data extraction.

Table 1. Comparison of several mainstream object detection algorithms.

Algorithm	Advantages	Disadvantages	Applicable Scenarios
YOLOv3 [40]	Efficient real-time detection; high precision and recall	Less accurate detection of smaller objects	Complex traffic flow scenarios with multi-lane freeways and high vehicle speeds
Faster R-CNN [41]	High detection accuracy	High computational effort and slow detection	Static or low to medium vehicle speed scenes
SSD [42]	Efficient real-time detection, better calculation speeds	May have more false detections and missed detections in complex scenarios	Medium and low speed traffic scenarios with low real-time detection requirements
RetinaNet [43]	High accuracy, especially good at detecting small objects	Slower reasoning with less real-time performance	Small object detection with high accuracy and low real-time requirements

compares several mainstream object detection algorithms, and the comparison results indicate that the YOLOv3 (You Only Look Once) algorithm is more suitable as the tool for extracting vehicle movement data in this study.

To further validate the effectiveness of YOLOv3 in the context of this study, we evaluated the algorithm’s performance using the publicly available UA-DETRAC traffic dataset [44]. The test results on the public dataset demonstrate that YOLOv3 outperforms other algorithms in terms of both vehicle detection accuracy and speed. As shown in

Table 2. Accuracy test results of different object detection algorithms on the UA-DETRAC public dataset.

Metric	YOLOv3	Faster R-CNN	SSD	RetinaNet
mAP@0.5 (%)	89.2	86.5	82.4	84.2
Recall (%)	88.7	86.1	83.9	85.1
FPS	30–40	10–15	20–25	15–20

, under the standard hardware configuration of an NVIDIA Titan X GPU, YOLOv3 achieves an average precision (mAP@0.5) of 89.2%, a recall rate of 88.7%, and a Frames Per Second (FPS) of 30–40 for detecting vehicles traveling at speeds of 80–120 km/h, highlighting its strong performance in handling high-speed, complex traffic flow scenarios. Therefore, this study ultimately employs a trained vehicle detection model based on the YOLOv3 object detection algorithm to perform frame-by-frame analysis of the video, thereby extracting vehicle operation data including the vehicle ID, world coordinates, vehicle class, and vehicle speed [45].

3.1.2. Kalman Filter Processing

In this study, Kalman filtering was applied to correct jitter and positioning errors in the drone data. During flight, UAVs can be affected by environmental factors (such as wind speed variations or air turbulence), causing slight shifts in target positions in aerial images, which in turn affects the accuracy of object detection. To minimize these effects and obtain an optimal estimate of the true trajectory, Kalman filtering was employed to smooth the trajectory data, thereby improving the accuracy of object detection results. Kalman filtering is a recursive optimal estimation algorithm that can dynamically correct position deviations in real-time within a system. Its advantage lies in its ability to effectively eliminate small-scale jitter and noise by combining measurement data with the system’s prediction model, thus estimating the true trajectory of the object and reducing the impact of noise and errors on the results.

UAVs always generate certain jitter uncontrollably during flight owing to airflow, shifting the aerial photography angle slightly. Consequently, this affects the vehicle position in the video, causing data errors. To minimize the effect and obtain the optimal estimation of the true trajectory, studies present the use of Kalman filtering for trajectory data smoothing. Kalman filtering has been widely applied in current research on vehicle dynamic trajectory data extraction and has been proven to effectively improve data accuracy [46,47]. Equation (2) shows the processing procedure of Kalman filtering.

$$\left\{\begin{array}{l}{\widehat{x}}_t^{-}=F{\widehat{x}}_{t-1}+B{u}_{t-1}\\ P_t^{-}=F{P}_{t-1}{F}^T+Q\\ K_t=P_t^{-}{H}^T{(H{P}_t^{-}{H}^T+R)}^{-1}\\ {\widehat{x}}_t={\widehat{x}}_t^{-}+K_t(z_t-H{\widehat{x}}_t^{-})\\ P_t=(I-K_{t}H)P_t^{-}\end{array}\right.,$$

(2)

where ${\widehat{x}}_t$ denotes the predicted and optimal estimate value of system state at moment t, respectively. u_t−1 denotes the acceleration and z_t denotes the measured position value. K_t serves as the Kalman coefficient. P_t⁻ and P_t represent the covariance estimation matrix and optimal estimation matrix, respectively. F and B serve as the state transfer matrix, and the predicted noise covariance matrix, the observed matrix, the observed noise covariance matrix, and the unit matrices are denoted as Q, H, R, and I, respectively.

Equation (3) presents the system state at moment t described with the three-dimensional vectors.

x(t) = (x_t y_t v_t)^T,

(3)

where x_t and y_t denote x and y coordinates in the world coordinate system. v_t denotes the vehicle speed, and the velocity deflection can be denoted as θ_t. Figure 6 illustrates this state transfer process.

Since UAV aerial photography works only at 30 frames/s, few changes in the motion state of the vehicle are produced in the two adjacent frames, occurring with negligible acceleration and deceleration. Thus, it can be assumed that vehicles move at a constant speed with the previous frame speed during the frame interval time, and the matrix of the state transfer equation can be derived as Equation (4).

$$\left(\begin{array}{c}{x}_t\\ y_t\\ v_t\end{array}\right)=\left(\begin{array}{ccc}1& 0& \Delta t\cos {\theta }_{t-1}\\ 0& 1& \Delta t\sin {\theta }_{t-1}\\ 0& 0& 1\end{array}\right)\left(\begin{array}{c}{x}_{t-1}\\ y_{t-1}\\ v_{t-1}\end{array}\right)$$

(4)

The least squares method can be used to fit the third-degree polynomial to the trajectory curve of each vehicle since vehicle trajectories should be continuous and smooth. The fitted curve is used as the Kalman filter prediction curve, the velocity direction is tangent to the current driving trajectory at each moment, and the final expression of the velocity declination can be obtained as shown in Equation (5).

$$\tan {\theta }_t=y^{\prime }(x_t)$$

(5)

3.1.3. Coordinate Conversion

The coordinates of a vehicle will change to varying degrees over time in a world coordinate system. Therefore, the use of the world coordinate system to describe the vehicles’ trajectory can be considerably more complicated on curved road sections. The Frenet coordinate system provides a more intuitive representation of the vehicle position on the road, with the s-coordinate denoting the longitudinal distance along the road and the l-coordinate denoting the transverse distance perpendicular to the road, as shown in Figure 7. The outer edge line of the main line is selected as the reference line, and a circular curve is used to fit the plane line shape of the measured road section, which can establish a calculation model as shown in Equation (6).

$$\left\{\begin{array}{l}{k}_0=(y_0-n)/(x_0-m)\hfill \\ k_t=(y_t-m)/(x_t-n)\hfill \\ \alpha =\arctan \left|(k_0-k_t)/(1+k_0{k}_t)\right|\hfill \\ s=R\alpha \hfill \\ l=\sqrt{{(x_t-m)}^2+{(y_t-m)}^2}-R\hfill \end{array}\right.,$$

(6)

where (x₀, y₀) denotes the coordinates of the starting point of the road reference line, in which the taper starts. (m, n) denote the coordinates of the center of the circle. (x_t, y_t) denote the coordinates of the vehicle at the moment t. (x_r, y_r) represent the coordinates of the nearest point of the vehicle to the road reference line. k₀ denotes the slope of the line connecting the starting point of the reference line to the center of the circle, and k_t denotes the slope of the line connecting the vehicle position and the center of the circle at moment t. α is the angle between the vehicle position and the start of the reference line. R denotes the radius of the road reference line. s and l denote the longitudinal movement distance and lateral offset distance of the vehicle in the Frenet coordinate system, respectively.

3.2. VISSIM Simulation

In this study, we utilize PTV-VISSIM 2022 software to analyze the traffic flow characteristics under different design schemes, and thus evaluate the application effectiveness of auxiliary lanes. VISSIM is a microscopic traffic simulation software developed by PTV Group in Karlsruhe, Germany. It can simulate real-world traffic operations by meticulously modeling vehicles, driver behaviors, road facilities, and other elements in the traffic system.

The three dual-lane exit ramp design options were replicated in the simulation software. The geometric parameters of the exit section were determined following the Design Specification for Highway Alignment of China. This paper selects the most common unidirectional three-lane mainline as the research object, with significant parameters shown in

Table 3. Geometric parameters of the freeway exit sections.

Design Speed of the Mainline (km/h)		120	100	80
Speed limit (Expected speed) (km/h)	Car	120	100	80
	Truck	80	80	60
Length (m)	Taper	90	80	70
	Auxiliary lane	580	510	440
	Deceleration lane	225	190	170

.

Accurately replicating real-world traffic flow in simulations is fundamental to obtaining reliable research results. Therefore, calibration of the simulation is an unavoidable and crucial step. The credibility of simulation output depends on whether the error between the simulation and actual vehicle operation data is within an acceptable range. In the event of significant errors, simulation parameters must be repeatedly adjusted until the required accuracy is achieved. After completing the routine setup, including vehicle paths, desired speeds, conflict rules, and decision points, it is also necessary to set and calibrate the car-following model parameters, which largely determine the accuracy of the simulation results. Figure 8 illustrates the framework for VISSIM simulation development and calibration.

The PTV VISSIM 2022 User Manual indicates that the VISSIM simulation provides both Wiedemann74 and Wiedemann99 car-following models, of which the latter is frequently used on freeways. The Wiedemann99 model includes 10 parameters. According to the findings of Chinese scholars, the most influential parameters are CC1, CC2, CC3, and CC7. Therefore, an L25 orthogonal experiment was designed to determine the five levels of each factor in the orthogonal experiment, ensuring that each level of every factor was examined across different experimental configurations.

Table 4. Descriptions of the car-following parameters and the L25 orthogonal experiment scheme.

Parameters	Description	Level 1	Level 2	Level 3	Level 4	Level 5
CC1	Time gap the following driver wants to keep behind the lead vehicle	0.8	1.0	1.2	1.4	1.6
CC2	Spacing that the following vehicle keeps in addition to the minimum safety distance before it intentionally accelerates	4	6	8	10	12
CC3	The time between the beginning of deceleration after perceiving a slow-moving leader and starting the unconscious following behavior	−6	−7	−8	−9	−10
CC7	Actual acceleration during oscillation in the unconscious following regime	0.10	0.15	0.20	0.25	0.30

presents the descriptions of each parameter and the design of the L25 orthogonal experiment.

In VISSIM calibration, the Mean Absolute Percentage Error (MAPE) reflects the deviation of the simulation from the measured data, usually used to evaluate the error of the simulation, as shown in Equation (7).

$$MAPE={\displaystyle \frac{1}{n}}{\displaystyle \sum _{i=1}^n\left|\frac{X_f^i-X_v^i}{X_f^i}\right|},$$

(7)

where n denotes the sample size for calibration parameters and $X_f^i$ and $X_v^i$ represent ob-served results and simulated results of calibrated parameters.

Additionally, the volume–density relationship model of traffic flow can be further deduced based on the linear relationship model between vehicle speed and vehicle density proposed by Greenshields in 1935, as shown in Equation (8) [48]. Subsequently, the relationship between the traffic flow three parameters is graphically plotted as shown in Figure 9. The goodness of fit of the simulation results to the Greenshields model will further help evaluate the approximation of the simulation to reality, verifying the accuracy of the simulation model.

$$\left\{\begin{array}{l}Q=VK\\ V=V_f\left(1-K/K_j\right)\\ Q=K{V}_f\left(1-K/K_j\right)\end{array}\right.,$$

(8)

where V_f denotes the smooth speed as density approaches 0 and K_j denotes the jam density.

Therefore, in the VISSIM accuracy calibration, we sequentially input the car-following parameter combinations from the L25 orthogonal experiment and evaluate the simulation error using MAPE, including flow, density, and speed. A smaller MAPE indicates a smaller discrepancy between the simulation and actual data, meaning the car-following parameter combination is closer to real-world conditions. Additionally, it is necessary to verify whether the simulation output adheres to the speed–density relationship of the Greenshields model, in order to determine if the simulation results align with the actual traffic flow characteristics.

4. Results and Discussion

4.1. Data Measurement Results

Data measurements were conducted on several interchange sections of transit freeways in Shaanxi Province, China.

Table 5. General information of investigated sections.

Freeway	Interchange	Design Speed of Mainline	Design Speed of Ramp
G3023	M	120 km/h	60 km/h
G30	E	120 km/h	60 km/h
G30	X	120 km/h	60 km/h

presents the general information of the sections investigated, and Figure 10 shows the actual screen of these.

The period for data measurement should be universally representative; hence, the congestion delay index distribution around Xi’an within 24 h was queried through the AMAP Open Platform prior to the investigation, as shown in Figure 11. Depending on the statistics, peak hours of 7:00~9:00 and 17:00~19:00, and off-peak hours of 11:00~13:00 were selected as the survey hours.

Figure 12 presents the operating speeds of the 1998 vehicles on the mainline versus auxiliary lanes obtained at the three survey locations. The K-S method is utilized to check the normality of the samples, and the significance p for each group exceeds 0.05, indicating that the data conformed to a normal distribution that is statistically significant.

Obviously, vehicle speeds on the mainline and auxiliary lane at Interchange X are significantly lower than on the other two interchanges. Considering that all three exits use the TTER type, the total traffic volume and diversion traffic volume of Interchange X are larger than the other two, leading to a reduction in the capacity of the section, and a consequent reduction in the vehicle speed.

4.2. VISSIM Calibration

Following the procedure outlined in Section 3.2, the simulation parameters were continuously adjusted to calibrate the model. By comparing the MAPE results corresponding to different car-following parameter combinations and performing range analysis, the optimal parameter combination for the Wiedemann99 car-following model was obtained, as shown in

Table 6. Parameter calibration results of the Wiedemann99 car-following model.

Parameter	CC1	CC2	CC3	CC7
Calibrated value	1.2	10	−6	0.20

.

The MAPE results between the simulation outputs and the measured data for the three traffic flow parameters under the corresponding car-following parameter combinations are shown in

Table 7. Calibration results of the traffic flow three parameters in the VISSIM simulation model.

Parameter	Period	Measured Data	Simulated Data	MAPE	Average MAPE
Traffic Volume (veh/h)	7:00~9:00	3527	3506	0.60%	0.76%
	17:00~19:00	3936	3924	0.30%
	11:00~13:00	2906	2866	1.38%
Vehicle Density (veh/km)	7:00~9:00	43.7	44.5	1.83%	3.27%
	17:00~19:00	54.2	56.7	4.61%
	11:00~13:00	29.8	30.8	3.36%
Average Speed (km/h)	7:00~9:00	80.8	79.5	1.61%	4.01%
	17:00~19:00	75.3	71.0	5.71%
	11:00~13:00	97.6	93.0	4.71%

. All the MAPE results remain at a low level, with a maximum of 5.71%. Referring to previous research experiences, the simulation can be regarded as meaningful where the MAPE between simulation and actual is less than 15%. Therefore, it can be inferred that the simulation in this paper possesses high accuracy, providing valuable references for engineering practice.

Furthermore, the simulation results of vehicle speeds and density for the three design options under different diverging ratios (the ratio of traffic volume on the freeway exit ramp to the total traffic volume, used to assess the distribution of traffic flow) are extracted and plotted as scatter plots, as shown in Figure 13.

Figure 13 demonstrates that for the same density, vehicles on the PTERs operate at the highest speeds, while the NTTER performs the worst in this regard. The discrepancy between the three exhibits an increase with the increase in the diverging ratio, proving the superiority of installing auxiliary lanes. The results in

Table 8. Results of fitting the K-V scatter to the Greenshields model.

Design Option	Diverging Ratio (%)	Smooth Speed Vf (km/h)	Jam Density Kj (veh/km)	Goodness of Fit R2
NTTER	10	112.0	213.2	0.9852
	20	109.4	209.8	0.9917
	30	107.2	210.2	0.9920
	40	105.2	210.4	0.9932
TTER	10	111.1	237.5	0.9877
	20	109.5	241.8	0.9875
	30	108.4	242.2	0.9868
	40	107.0	246.2	0.9860
PTER	10	114.1	230.4	0.9752
	20	112.6	230.6	0.9834
	30	110.9	234.5	0.9860
	40	109.4	235.7	0.9900

were obtained using the Greenshields formula to fit the K-V data points for various conditions separately. In particular, the goodness of fit for all groups above 0.97 indicates the validity of the K-V linear relationship, further supporting the research value of the simulation results.

4.3. VISSIM Simulation Results

Based on the basic relationship between the three traffic flow parameters, the quadratic polynomial Q = aK² + bK can be used to fit the relationship between traffic volume and vehicle density. Figure 13 presents the fitting of the simulation results of traffic volume and vehicle density of NTTER with the quadratic polynomial Q = aK² + bK. The mutagenic point represents the locations on the theoretical curve where the curvature mutates as the traffic volume increases with vehicle density.

Analyzing the simulation results in Figure 14, the following arguments can be drawn:

• At the diverging ratio of 10%, the fitted curve can describe the traffic flow characteristics of the exit auxiliary lanes well. Meanwhile, the theoretical curve coincides with the fitted curve;
• At the diverging ratio of 20%, the fitted curves deviate slightly from the original data points, but no sudden mutagenic point of traffic volume occurs at this point, and the optimal capacity of the section is still achieved;
• At the diverging ratio of 30%, the deviation of the fitted curve from the original data points increases, and the mutagenic point on the theoretical curve are more obvious, proving that traffic bottlenecks have been developed as traffic volume exceeds a certain threshold;
• At the diverging ratio of 40%, both the vehicle density and traffic volume corresponding to the mutagenic point are less than that at the 30% diverging ratio, proving that the diverging ratios influence the capacity of the roadway section;

Figure 15 shows the fitting results of traffic volumes and vehicle densities of TTER with the quadratic polynomial. It can be found that the fitted curves for all four diverging ratios deviate from the original data points. The comparison reveals that the mutagenic point occurs at a lower density and traffic volume for a higher diverging ratio, indicating that the roadway capacity decreases as the diverging ratio increases. Additionally, the traffic flow exits the steady state at the vehicle density higher than the density corresponding to the mutagenic point, where traffic congestion gradually develops.

The fitting results of K-Q of TTER with the quadratic polynomial are presented in Figure 16, showing that mutagenic points have not emerged at any of the four diverging ratios. The scatter shows an overall trend of a quadratic polynomial curve, with the fitted curve affixed to the original data points. Therefore, the theoretical curve is still used to characterize the traffic flow of the roadway section to reflect the maximum capacity.

4.4. Analysis and Discussion

To further explore the effect of diverging ratios on the capacity of the diverging areas, K-Q scatter plots of the same exit type at different diverging ratios are developed, as shown in Figure 17. Subsequently, the following corollary can be drawn analytically:

• The capacity of NTTER is strongly influenced by diverging ratios, and the maximum capacity decreases as the diverging ratio increases;
• Diverging ratios show no significant effect on the capacity of the PTER and TTER;
• The installation of auxiliary lanes alleviates congestion in the diverging areas with a high diverging ratio, demonstrating the necessity of auxiliary lane facilities.

Similarly, Figure 18 presents the K-Q scatter plots for different exit types at the same diverging ratio, and certain conclusions can be derived, as shown below:

• The PTER exhibits a higher capacity than the TTER under the same traffic condition, while the NTTER demonstrates a lower capacity. The difference in capacity between the three options increases with the diversion ratio, confirming that the auxiliary lanes perform a more significant effect at higher diverging ratios;
• The maximum capacity of the TTER approaches that of the NTTER at diverging ratios below 20%, and significantly higher than that of the NTTER at ratios above 20%;
• The vehicle density of TTER increases significantly as the traffic volume exceeds a certain threshold. This can be explained by the fact that more lanes and wider cross-sections are installed in the diverging area of the TTER relative to the NTTER, admitting more vehicles to travel within the roadway section of the same length. Benefiting from the parallel section, the PTER offers more superior performance in channeling the diverging traffic.

The theoretical curve does not perfectly describe the traffic flow characteristics of the road section with the existence of the mutagenic point, implying that the capacity under the actual operating condition cannot reach the maximum value of the theoretical curve. It is observed that the maximum value of the capacity of the fitted curve fits better with the maximum value of the capacity in the original scatter plot. Therefore, a quadratic polynomial curve Q = aK² + bK + c. across the mutagenic point can be determined after the mutagenic point, with the maximum value serving as the maximum capacity of the fitted curve. This curve coupled with the theoretical curve prior to the mutagenic point forms the segmental function of roadway capacity, with the fitting results shown in

Table 9. Final results of fitting the K-Q scatter to the quadratic polynomial.

Type	Diverging Ratio (%)		a	b	c
NTTER	10		−0.5732	116.56	0
	20		−0.5570	114.92	0
	30 *	0 ≤ K ≤ 65, K ≥ 146	−0.5299	111.79	0
		65 ≤ K ≤ 146	−0.3298	69.57	1893.16
	40 *	0 ≤ K ≤ 57, K ≥ 156	−0.5171	110.12	0
		57 ≤ K ≤ 156	−0.3428	73.00	1542.00
TTER	10 *	0 ≤ K ≤ 66, K ≥ 183	−0.4554	113.43	0
		66 ≤ K ≤ 183	−0.2535	63.16	2430.84
	20 *	0 ≤ K ≤ 63, K ≥ 192	−0.4379	111.56	0
		63 ≤ K ≤ 192	−0.2399	61.11	2395.66
	30 *	0 ≤ K ≤ 61, K ≥ 196	−0.4297	110.50	0
		61 ≤ K ≤ 196	−0.2291	58.91	2389.34
	40 *	0 ≤ K ≤ 56, K ≥ 206	−0.4229	110.43	0
		56 ≤ K ≤ 206	−0.2367	61.82	2126.05
PTER	10		−0.5500	119.13	0
	20		−0.5313	119.20	0
	30		−0.4910	114.84	0
	40		−0.4766	113.13	0

* Refers to the presence of mutagenic points.

.

In the transportation engineering discipline, a significance level of 5% is widely adopted as a critical condition [49]. Therefore, it is considered that NTTER can be used when the capacity difference between NTTER and TTER is less than 5% under the same vehicle density. Similarly, PTER should be utilized to alleviate congestion at exits when the capacity of PTER exceeds TTER by 5%. Equation (9) presents the calculation of critical values of average density and volume.

$$\left\{\begin{array}{l}{\displaystyle \frac{Q_{TTER}(K)-Q_{NTTER}(K)}{Q_{TTER}(K)}}=0.05\\ {\displaystyle \frac{Q_{PTER}(K)-Q_{TTER}(K)}{Q_{TTER}(K)}}=0.05\end{array}\right.,$$

(9)

where $Q_{PTER}(K)$, $Q_{TTER}(K)$, and $Q_{NTTER}(K)$ denote the capacity of PTER, TTER, and NTTER, respectively.

Notably, Equation (9) potentially calculates multiple critical values of average density and volume with the presence of mutagenic point. Taking the minimum of the critical values as the comparison limit, the upper limit values of density and volume for NTTER and lower limit value for PTER can be obtained, as shown in

Table 10. The upper limit values of density and volume for NTTER and lower limit value for PTER.

Type	Diverging Ratio (%)	The Upper Limit Values of Vehicle Density (veh/km)	The Upper Limit Values of Traffic Volume (veh/h)
NTTER	10	62.61	5317
	20	63.39	5312
	30	56.01	4841
	40	45.21	4128
Type	Diverging Ratio (%)	The Lower Limit Values of Vehicle Density (veh/km)	The Lower Limit Values of Vehicle Density (veh/km)
PTER	10	/	/
	20	72.09	5554.44 (5550)
	30	71.54	5431.34 (5450)
	40	68.47	5249.18 (5250)

.

The results show that the traffic volume threshold of NTTER achieves 5300 veh/h with a diverging ratio of less than 20%, falling between Level of Service (LOS)-C and LOS-D. It can be assumed that the type of exit does not have a significant effect on vehicle diverging behavior at this point. While the diverging ratio reaches 30% to 40%, the traffic volume threshold of the NTTER falls below the capacity of LOS-C, indicating that a higher diverging ratio corresponds to a lower upper limit value of traffic volume for NTTER.

And for PTER, TTER is more suitable for diverging ratios less than 10%, as PTER increases capacity up to 5% relative to TTER. With gradually increasing diverging ratios exceeding 20%, the lower limit value of the traffic volume of PTER decreases, indicating that the PTER adapts to a higher traffic volume under conditions of large diverging ratios.

In summary, the type of exits can be chosen based on the relationship between the projected traffic volume to the upper limit volume for NTTER and lower limit volume for PTER.

Table 11. Applicable traffic volumes for the three types of exits (veh/h·ln).

Diverging Ratio	10%	20%	30%	40%
NTTER	Q ≤ 1770	Q ≤ 1770	Q ≤ 1620	Q ≤ 1385
TTER	1770 ≤ Q	1770 ≤ Q ≤ 1850	1620 ≤ Q ≤ 1820	1385 ≤ Q ≤ 1750
PTER	—	Q ≥ 1850	Q ≥ 1820	Q ≥ 1750

presents the applicable conditions for the three options.

5. Discussion

This study introduced the use of UAVs to acquire actual traffic data, combined with VISSIM simulation and traffic flow theory, and an innovative method was proposed for evaluating the application conditions of auxiliary lanes of dual-lane exit ramps on freeways. The results reveal the specific impact of auxiliary lane design on the capacity of dual-lane exit ramps under different diverging ratios, filling the gap in quantitative research on the application conditions of auxiliary lanes. The findings provide a quantitative basis for freeway exit ramp design. Under high traffic volume conditions, appropriately designed auxiliary lanes help alleviate congestion and reduce traffic conflicts. In contrast, under low traffic volume conditions, avoiding unnecessary auxiliary lane designs can save construction and land costs, thereby improving resource utilization efficiency. This approach promotes the sustainable development of traffic design while ensuring traffic efficiency.

Unlike previous studies that mainly relied on theoretical derivations and small-scale field measurements, this study utilized UAV-acquired actual traffic data to calibrate VISSIM simulations. This approach not only overcomes the challenges of data acquisition and model accuracy in traditional research but also effectively saves research resources. Furthermore, the study quantified the impact of diverging flow ratios on the conditions for auxiliary lane installation, providing clearer evidence for sustainable traffic design.

However, this study also has certain limitations. Due to constraints in research duration and resources, the investigation was restricted to scenarios involving a design speed of 120 km/h and standard cross-sectional widths, without further exploring the influence of other potential geometric features such as roadway width or shoulder width. Additionally, the data collection was primarily concentrated in Shaanxi Province, China, which introduces a regional limitation. To enhance the generalizability of findings, future investigations will aim to expand the sample size by incorporating interchange samples with diverse regional distributions, traffic volumes, and design conditions. Furthermore, in dynamic highway environments, exceptional events such as natural disasters, traffic incidents, or large-scale emergencies could significantly influence traffic flow patterns and lane demand. Subsequent research could explore the impact of such contingencies on the application criteria for auxiliary lanes and establish comprehensive emergency management protocols for traffic flow regulation under exceptional circumstances.

With the advancement of Intelligent Transportation Systems (ITS), future studies could prioritize collaborative frameworks with highway administration authorities. Through long-term dynamic data monitoring, the impact of seasonal and diurnal traffic variations on the application of auxiliary lanes could be further analyzed.

6. Conclusions

Despite specifications in various countries recommending the use of auxiliary lanes to connect the mainline and dual-lane ramps of freeway to meet the lane balance principle, there are still numerous cases involving the abandonment of auxiliary lanes due to constraints in engineering practice. Given that specifications have not indicated specific conditions for the application of auxiliary lanes, this paper explores this highly controversial issue using numerical simulation methods based on traffic flow theory. Firstly, traffic data from operational freeway diverging areas were collected using UAVs and the object detection algorithm. VISSIM simulations for three commonly used dual-lane exit ramp diverging areas were developed. A simulation parameter calibration procedure was then proposed based on the theory of the traffic flow three parameters and orthogonal experimental methods. Finally, the applicable traffic volumes of the three options with different diverging ratios were obtained using the TTER capacity as the baseline and the difference in capacity not exceeding 5% as the critical condition. The results indicate that the conditions applicable to the three exit types are related to the diverging ratio and the maximum traffic volume applicable to the non-auxiliary lane design decreases as the diverging ratio increases. The research findings clearly define the specific application conditions of auxiliary lanes on dual-lane freeway exit ramps, providing insights for the sustainable development of transportation design and operations.

Particularly, this paper provides methods of traffic data acquisition and processing and systematic calibration procedure for micro-simulation. The authors propose to extract the vehicle trajectory data using the YOLOv3 target detection algorithm and eliminate the errors through the steps of coordinate transformation and Kalman filter clean-up. Acceptability of the difference between simulation and actual conditions is reflected using the MAPE between the simulation results of the traffic flow three parameters and the measured data. The introduction of the Greenshields model further confirms the strong approximation of the simulation to the actual situation as its perfect fit to the simulation data. The two calibration methods validate the trust-worthiness of each other, and the combination of the two methods provides an accurate VISSIM simulation calibration procedure. This progress promises to help future researchers to rationally reproduce real traffic flow in a microscopic traffic flow simulation, contributing to more accurate simulation results.