Study on the Rationality of Lane Imbalance Design in Freeway Diverging Areas

Currently, a lane imbalance design scheme without auxiliary lanes for two-lane exits is increasing. To study the rationality of this exit scheme, the relationship between lane balance and traffic efficiency in the diverging area is investigated using a drone and image recognition software. The Kalman filter is used to optimize the original data and simplify the process of extracting the traffic volume, density and speed by Frenet coordinate transformation. Under the three states of free flow, saturated flow and supersaturated flow, lane balanced exit and lane imbalanced exit simulation models were constructed by using VISSIM. Based on the traffic flow theory, the curve of the relationship between traffic volume and density was fitted. The traffic volume corresponding to the difference between two schemes at the same density not exceeding 5% or 10% is calculated, and this traffic volume is defined as the scheme selection limit value. The results show that the traffic efficiency of lane imbalance scheme is consistently lower than that of lane balance scheme under all traffic conditions at the freeway exits. However, the difference in traffic efficiency between the two schemes is not fixed but increases as the upstream input traffic volume increases. When the exit forecast service traffic volume is lower than the “scheme selection limit value” (SSLV), the difference in traffic efficiency between the two schemes will not exceed 5% or 10%. In conclusion, the lane imbalance scheme can be used in the diverging area under certain traffic volume conditions, thus reducing the land, engineering volume and cost requirements. It also provides ideas for the study of three-lane exit ramp design schemes.


I. INTRODUCTION
The freeway exit area, as the section connecting the ramp to the mainline freeway, is one of the areas of the freeway where lane changes and slowdown behavior most frequently occur [1].Horizontal and vertical disturbances in diverging areas could pose a significant security risks [2], [3].Studies have shown that approximately 30% of freeway accidents occur in the exit area, and the accident rate at exits is even twice as high as that at entrances [4], [5].Drivers exiting the freeway need to slow down and change lanes in a short period of time, significantly increasing the operational load.Bayesian networks were used to model the association between driving behavior parameters and traffic The associate editor coordinating the review of this manuscript and approving it for publication was Tamas Tettamanti .conflicts in the diverging area and show that deceleration and lane-changing behavior are the main factors influencing traffic conflicts.
To improve the safety of the exit area, researchers have performed much work on crash models, driving behavior studies and safety evaluation.In particular, crash prediction models can be used to assess the impact of various risk factors on crash rates in freeway diverging areas [6], [7].By collecting data on drivers driving naturally in the deceleration lane, traffic conflicts are considered to be directly caused by driving behavior [8].When crash data are incomplete, safety evaluation methods are generally used to estimate the safety of the diverging area.Researchers often examine traffic safety based on live observation or video capture, using traffic conflict theory to examine vehicle interactions [9].
A large number of interleaving and lane-changing behaviors often occur in the freeway diverging area, which interferes with the stable operation of traffic flow to a certain extent [10], [11].Some research data show that the occurrence of bottlenecks in diverging areas is not only affected by the exit ramp outflow but also depends on the operating speed of the vehicles in adjacent lanes and the lane change behavior near the exit ramp [12].When the traffic volume on the exit ramp in the diverging area is oversaturated, a queue propagates upstream, and the vehicles move laterally, resulting in a reduction in the speed and flow of vehicles in all lanes; eventually, the travel speed in all lanes becomes essentially equal [13].Some academics have observed that occupancy of the shoulder lane upstream of congested exit ramps is higher than that of other lanes.Since the geometric characteristics of the diverging area, traffic volume, ramp exit type and variable speed lane length all affect freeway operating levels [14], [15], improving the diverging area capacity will help improve the overall traffic operations of the freeway section.
The current methods for researching capacity are generally divided into regression analysis of actual measurement data and traffic simulation analysis.Some scholars conducted real-world experiments on freeway deceleration lanes, collected microscopic traffic parameters such as section speed, vehicle trajectory, and lane position, and analyzed the lane change characteristics and speed distribution of different types of drivers.Significant differences were found between different groups of drivers, reflecting the risks associated with the different groups.It has also been found that there are differences in the lane change behavior under different traffic flow conditions [16].The Weibull model was used to estimate the capacity at the freeway bottleneck and obtained its long-term variation, and the results showed a long-term decreasing trend in traffic at the 5th percentile of the traffic collapse probability [17].In addition, the diverging area serves as an intertwined roadway, and numerous studies have been conducted to estimate the level of service and the traffic capacity of the intertwined roadway [18], [19], [20].
When field measurement conditions are limited, simulating the traffic in the diverging area can reflect to some extent the impact of different variables on the capacity and operational performance [21].Simulations were conducted for different configurations of freeway exit ramps, and the existing traffic flow with an exponentially increasing average delay was used as the section capacity.It was found that lane balance and deceleration lane length had significant effects on the capacity of the diverging area [22].Based on motion wave theory, moving bottleneck theory is used to calculate the effective flow and relative capacity through the diverging area, and a capacity analysis model is proposed [23].In recent years, the research and development of intelligent transportation systems (ITSs) has been emerging, and Markov models have been used to implement large-scale traffic flow simulations [24].
Considering the low feasibility of expanding the existing infrastructure, traffic control has been proposed and used as an effective method to alleviate freeway exit congestion to improve the capacity of the diverging area [25].In terms of freeway driver behavior, prohibiting drivers from making lane changes near exit ramps through the use of pavement markings has proven to be an effective measure; however, in some instances, prohibiting lane changes only causes the bottleneck to shift to another upstream location where lane changes are allowed [7].Analysis of field data on exit ramps has shown that the occurrence of traffic bottlenecks is closely related to the exit ramp queue overflow [26].Some other researchers have suggested that a sudden increase in the exit ramp exit flow occurs when the queue on the exit ramp is about to overflow onto the freeway, but this action may detour some of the traffic traveling on the surface street network [27], [28].To coordinate the traffic transition between surface streets and freeways, a merging traffic control algorithm is proposed that aims to maximize the outflow from the merging area of surface streets while preventing the exit ramp queue from overflowing into the mainline of the freeway [29].For exit ramps where the capacity cannot be changed, various local route rerouting policies are proposed to prevent exit ramp queue overflow and the resulting traffic congestion through alternative routes by rerouting exiting vehicles within a feasible time and space frame [30].
The number of lanes and the arrangement form of the ramp are particularly important when designing a freeway exit ramp.As for freeway design, the Green Book is recognized as a practical work in the field of international highway engineering, which provides a reference for the formulation of design codes in many countries [31].Several inherent exit ramp design methods are proposed in the Green Book, such as single-lane exits, dual-lane exits, direct exits and parallel exits.According to lane balance theory, the number of lanes added to an isolated freeway off-ramp should not exceed 1.Therefore, a single-lane exit ramp can meet the lane balance requirements, whether it is direct or parallel, but parallel is safer than direct [7], [32].With the increasing traffic volume, two-lane exit ramps have become the mainstream means of construction, and three-lane exit ramps have been adopted by some multilane freeways with large amounts of diverging traffic, so the lane balance problem becomes a problem that cannot be ignored.
A study in Florida collected crash data from 343 freeway segments in the state, analyzed the relationship between different types of exit ramps and safety benefits, and used crash prediction models to demonstrate that lane balancing designs can significantly reduce crash rates in diverging areas [33].Another study used crash data from the Ohio Department of Public Safety (ODPS) to select six exit ramp types and used a statistical model that they developed to verify that the number of ramps had a significant effect on the incidence of serious injuries in the diverging impact area [34].The lane imbalance design in the diversion area is less inductive for outgoing vehicles, resulting in chaos in the straight traffic flow, which will significantly increase the number of collisions and the severity of injuries during long-term operation [35].The results of the impact of auxiliary lanes on crash rate at freeway diverge segments are provided in HSM.In the process of calculating traffic conflict modification factors (TCMFs), compared with the case without auxiliary lanes, the installation of auxiliary lanes can reduce the frequency of traffic conflicts by 3 percent to 100 percent, and achieve considerable safety benefits in mitigating traffic conflicts [36].
Installing auxiliary lanes is an effective measure to ensure the balancing of exit lanes.The presence of auxiliary lanes reduces traffic delays due to increased traffic volumes and, as an additional lane, provides drivers with sufficient time to react and reduces the rate of exit crashes.In an evaluation of five freeway exit bottlenecks in Texas before and after the installation of auxiliary lanes, it was found that the operational and economic benefits were significantly improved after the installation of auxiliary lanes [37].A study by Japanese scholars also confirmed the positive effect of auxiliary lanes on the improvement of traffic operations in interchange areas, significantly reducing the likelihood of traffic congestion [38], [39].In summary, part of the current research on lane balance has shown that lane balancing designs have fewer collisions by building collision prediction models.Another part explores the impact of lane balancing designs on traffic operation with the aim of alleviating traffic congestion.While the traffic flow characteristics intuitively reflect the vehicle operation, few studies have explored the rationality of lane imbalance design in the diversion area through the relationship between the three parameters of traffic flow.
With the gradual acceleration of urbanization, urban expressway networks have become increasingly dense, and traffic congestion, environmental pollution and other problems have gradually come to the forefront, with traffic accidents occurring frequently.To effectively use land resources, the urban traffic network structure has developed from the grid type to the circular radial type of structure [40].Compared with ordinary city roads, expressways run fast, have large capacities, have no level crossings, and generally do not produce traffic interruptions, so the efficiency of urban road traffic systems directly depends on whether the layout of expressways is reasonable [41].
Classic road network design problems can be divided into two categories, namely, continuous network design problems (CNDPs) [42] and discrete network design problems (DNDPs) [43].The CNDP is mainly achieved by adding a new road to the network, while the DNDP focuses on improving the capacity of the lanes [44], and both have been widely used in traffic network infrastructure construction.Currently, the expressway networks of many first-tier cities have been completely built, the road alignment are basically fixed, and the existence of the surrounding buildings leads to road land restrictions, which increase the difficulty of laying auxiliary lanes.To solve this problem, the number of lanes in the diverging area needs to be analyzed to balance the need to determine the conditions for setting auxiliary lanes.
Traffic flow theory, as an important element of traffic engineering, has an irreplaceable role in the study of roadway capacity [45].Some physical quantities used to describe the operational characteristics of traffic flow are defined as traffic flow parameters, and the regularity of the parameter changes reflects the basic characteristics of traffic flow [46].Flow, speed and density are the three basic parameters that describe the characteristics of traffic flow, and the relationship between them is the basis of the accepted traffic flow theory [47], [48].The purpose of setting auxiliary lanes is to ensure continuous traffic flow with no blockages, and our study will consider the intrinsic mechanism of lane balance from the perspective of traffic flow theory in terms of the capacity of the diverging area.
As early as the 1930s, scholars Greenshields et al. conducted a study on the relationship between the three parameters of traffic flow and, for the first time, used field photogrammetry to propose a linear relationship between speed (km/h) and density (veh/km) and, thus, derived a parabolic model of speed-flow [49].Subsequent studies devoted to the improvement of the three-parameter model, logarithmic model [50], exponential model, generalized single-segment model [51], [52], [53], multisegment model [54], etc., have emerged.The basic relationship among the three parameters is flow = density × speed, which shows that under free flow conditions, if the expressions of the relationship between any two parameters are known, the relationship between the remaining parameters can be easily obtained.
As a simulation modeling tool based on time intervals and driving behavior, VISSIM software can be used to analyze traffic operations under various traffic conditions and is widely used in the field of traffic engineering [55], [56], [57].The VISSIM following and lane change parameters were calibrated for the German highway diverging and merging area, reproducing the highway capacity and speed-flow curves given in the HBS (the German Highway Capacity Manual) guidelines [58].Different following and lane change models produce different results, and the user can simulate real traffic flow conditions by calibrating the parameter values in the model [59].The performance of the simulation packages is largely limited by the driver behavior model when the model is calibrated to find the parameter values that best reflect real-world conditions [60].A driver behavior model was developed to reproduce freeways with complex traffic flow and congestion patterns for bottlenecks with exit and entrance ramps [61].
The Green Book states that when a freeway exit is a two-lane ramp, auxiliary lanes should be provided to meet both the lane balance and the basic lane number requirements.The Design Specification for Highway Alignment (JTG D20-2017) of China [62] also stipulates that the balance of the number of lanes should be maintained at the diversion and confluence of the main line and ramp, that is, the number of lanes of the main line before diversion should not be less than that of all lanes of the main line and ramp after diversion.However, there are several two-lane exits on the Xi'an bypass in China that do not have auxiliary lanes and do not follow the lane balance requirement, but no significant traffic congestion has been observed during operation.At present, with the popularity of UAVs and the gradual maturity of target detection technology, YOLO series algorithms are increasingly used in the field of traffic engineering.YOLOv3 can further improve the detection accuracy on the basis of maintaining real-time detection [63].In this paper, we used the image recognition software developed based on YOLOv3 to extract vehicle trajectories from aerial videos and optimized them by Kalman filtering and Frenet coordinate transformation.The traffic simulation models were constructed using VISSIM to verify the feasibility of the lane imbalance scheme by observing the effect of whether to set auxiliary lanes on the traffic flow state.

II. PROBLEM STATEMENT
The Green Book proposes that consistency should be maintained in the number of lanes provided along any route of arterial character.Thus, the basic number of lanes should be established for a substantial length of freeway and should not be changed through pairs of interchanges simply because there are substantial volumes of traffic entering and leaving the freeway.The purpose of this regulation is to avoid traffic bottlenecks where lanes have been eliminated at a lane reduction on a freeway between interchanges and to reduce confusion for through traffic on the freeway.In addition, at exits, the number of approach lanes on the freeway should be equal to the number of lanes on the freeway beyond the exit, plus the number of lanes on the exit, minus one [31].That is, the lane balance principle should be satisfied, as shown in Equation (1).
where N C denotes the number of mainline lanes before divergence or after merging; N F denotes the number of mainline lanes after diverging or before merging; and N E denotes the number of lanes on the ramp.Generally, in the diverging and merging areas, a singlelane ramp can meet the lane balance requirement when the basic number of lanes is consistent, as shown in Figure 1; the two-lane ramp cannot meet the lane balance and basic lane number requirements at the same time, so it is necessary to set up auxiliary lanes before the diverging point to solve the contradiction, as shown in Figure 2. According to the survey on the ring freeway in Xi'an, China, several interchanges with direct two-lane exit ramps do not have auxiliary lanes, and  the lane balance principle is not ensured within the adjacent section of the exit, as shown in Figures 3 and 4, but no significant congestion or high accident risk was found for this scheme during the road operation phase.Theoretically, when the mainline merges with the ramp, the traffic volume downstream of the merge point increases, while the number of lanes in the merge area decreases, leading to a reduction in capacity, which is a contradiction.If the lane balance design is not used, the number of lanes is reduced by more than one at a time, and the road capacity is suddenly reduced, which will lead to a mismatch of upstream and downstream capacity in the merging area, forming a traffic bottleneck and causing congestion.When the mainline and the ramp diverge, the traffic volume upstream of the diverging point remains the same, but the number of lanes in the diverging area increases and the capacity increases, which are not contradictory.Although the traffic volume distribution in the diverging area is constantly adjusted due to the diverging behavior and the traffic flow is not stable relative to the basic roadway, the diverging area only suffers from the impact caused by the diverging behavior without the traffic pressure caused by the change in traffic volume compared to the merging area.Therefore, whether it is reasonable to use a nonlane balancing design in the diverging area needs further study.
The two-lane exit ramp design scheme without auxiliary lanes has a lower engineering volume and occupies less land than the scheme with auxiliary lanes and is suitable for projects with tight land use requirements or very high construction costs.Therefore, this study takes the two-lane exit with or without auxiliary lanes as the research object and investigates the difference in capacity and safety between the two schemes by investigating the actual traffic data and combining it with simulation methods to analyze the feasibility and applicability conditions of using the scheme without auxiliary lanes in the interchange diverging area.

III. TRAFFIC FLOW THEORY
Traffic volume Q, travel speed v, and traffic density K are the three basic parameters that represent the characteristics of traffic flow.When there are more vehicles on the road, the vehicle density increases while the vehicle speed decreases accordingly.By fitting the observed data, when the traffic density is moderate, there is a linear relationship between the speed v and the density K , which is in accordance with the Greenshields linear model [49], as shown in Equation (2).
where v f denotes the maximum speed (km/h), which is the average speed when the vehicle density tends to zero, and K j denotes the blockage density (veh/km), which is the density when the traffic is so dense that the vehicle cannot move.The relationship between the three parameters can be represented by a three-dimensional curve, and when the speed is linearly related to the density, the three-dimensional curve is projected to the two-dimensional plane to obtain Figure 5.
In Figure 5, Q m denotes the extreme traffic volume (veh/h); K m denotes the optimum density (veh/km); and v m denotes the critical speed (km/h).
When the speed-density relationship is determined, the density and traffic volume relationships are also determined.The density-flow relationship is obtained according to the Greenshields equation ( 2) and the three-parameter basic relationship, as shown in equation (3).
Equation ( 3) is plotted as a plane curve, as shown in Figure 6. Figure 6 indicates that when the density is zero, the speed is the free-flowing speed, and the traffic volume is zero, while when the road is at a density causing blockage, the speed is zero, and the traffic volume is also zero.Between zero density and blockage density, there is a maximum point Q m in the process of flow variation, which represents the capacity of the road or the maximum traffic volume, and its corresponding density is the optimal density K m .Before this point, the flow increases with increasing density and is referred to as the uncongested zone; after this point, the flow decreases with increasing density and is referred to as the congested zone.Traffic bottlenecks can form in the diverging and merging areas due to diverging and merging behavior within the entrance and exit areas of the freeway.The capacity of the bottleneck section is generally smaller than the capacity of the basic section.According to Figure 6, the road capacity can be expressed by the maximum flow point in the density-flow curve, so the density-flow curve's relative relationship between the basic section and the bottleneck section can be represented by Figure 7.In summary, plotting the density-flow curve of a road section can be used to analyze road bottleneck traffic.Therefore, the impact on traffic operating conditions caused by the use of a design scheme that satisfies the lane balance requirement in a freeway's diverging areas can be studied by comparing the differences between the density-flow curves using different schemes in the same section.

IV. DATA COLLECTION AND PROCESSING A. DATA COLLECTION PURPOSE
Traffic data are the premise and foundation of traffic theory research.The investigation, statistics and analysis of a large amount of relevant traffic data are used to accurately grasp the current traffic situation and the characteristics of changes.For example, the traffic flow characteristics of a road section are represented by the magnitude and variation patterns of three specific parameters, i.e., traffic volume, travel speed, and density, so that the traffic operation of the road facility can be analyzed.By the end of 2021, Xi'an has more than 4 million motor vehicles, which has reached the level of new first-tier cities.As the significant increase in the number of motor vehicles affects the size of road traffic, the expressway operation in Xi'an is representative to a certain extent.The data collection area is the Xi'an Xiwu Interchange (Figure 8), which has eight lanes in both directions on the mainline and two-lane ramps on the exit and a design speed of 120 km/h on the mainline and 60 km/h on the ramps.Using this interchange as the research object, the K -Q relationship curve was drawn by collecting the three parameters of real traffic flow to analyze the capacity of the exit section.

B. DATA COLLECTION METHOD
The data collection equipment mainly includes a UAV, RTK mobile stations and image recognition software.Aerial video of the vehicle operation in the exit section was taken using a UAV in the field, and the video was processed and analyzed by image recognition software.RTK mobile stations were used to assist in calibrating the actual coordinates of the feature points and improving the software processing accuracy.Compared with traditional radar and laser survey instruments, the use of UAVs for surveys effectively reduces the traffic data collection costs, increases the spatial-temporal coverage dimension of measurements, supports the diversity of survey environments, and provides a high degree of flexibility.In addition, the overall actual operation of the vehicle is stored in video form so that the actual operating conditions can be restored to the maximum extent during the research phase.However, this acquisition method has high image recognition software requirements, where the image recognition software needs to not only achieve the functions of recognition, analysis and statistics but also needs to have sufficient accuracy.
A DJI Air 2S drone was used for the measurement.The drone hovered at an altitude of 230 m above the point to be measured, and the shooting area included the diverging point and the area 1 km upstream of the road section.When the height of the UAV is fixed, the length of the single shot section is also fixed.With the lane width 3.75 m as the benchmarking pole, a frame in the aerial video is intercepted, in which the single segment length is measured to be 400 m.Aerial photography was taken four times for 20 continuous minutes each time at different vehicle density periods between peak flow and lower flow.The density and flow values of the surveyed sections were measured every 1 minute, and a total of 80 sets of actual values were obtained.The image recognition software is developed based on YOLOv3 and is capable of extracting high resolution vehicle trajectory data from video.The vehicle track database constructed by the software statistics includes parameters such as the number of vehicles, location coordinates, number of lanes, vehicle length, and vehicle width.When the UAV is shooting at high altitude, there is a certain angle between the camera and the road on both sides of the video screen, resulting in the picture stretching at the edges of the aerial video.To ensure that this problem does not affect the measurement accuracy, it is necessary to calibrate the screen with the actual measurement coordinates of some feature points and reconstruct the screen coordinate network before video analysis is performed.Therefore, when conducting UAV aerial photography, it is necessary to use RTK mobile stations to locate and measure the feature points on both sides of the investigated road.

C. DATA ANALYSIS PROCESS 1) ORIGINAL DATA
After the aerial drone video is processed by the image recognition software, a numerical file will be generated with the vehicle as the unit, which contains the vehicle ID, frame number, vehicle coordinates, etc.The image recognition software can obtain the driving trajectory data of individual vehicles, but it cannot directly obtain the traffic characteristic parameters of the characteristic section or the measured road section, such as the section passing speed, the average speed of the interval, the average density, the traffic volume and other parameters, so the original measurement data need to be preprocessed, and the statistical calculation is performed after excluding the problematic vehicle data.

2) DATA FILTERING
The vehicle trajectory is plotted using the vehicle coordinates from the original data, as shown in Figure 9.The figure shows that the transient offset of the original vehicle trajectory is too large and does not match the actual vehicle operation characteristics.The reason is that the drone inevitably shakes slightly during aerial photography, resulting in panning, rotation or scale changes in the captured images.In addition, external environmental conditions change from moment to moment, such as changes in light intensity, temperature, image exposure, color temperature, etc., all of which can lead to deviations in the measurements of vehicle locations extracted from the video.In the high altitude view of the drone, the vehicle occupies a relatively small percentage of pixels in the frame, which may lead to frame misses and recognition errors.To minimize the effect of measurement deviations and obtain optimal estimates of the true trajectory, data filtering techniques are required for processing.To minimize the effect of measurement deviations and obtain optimal estimates of the true trajectory, data filtering techniques are required for processing.Kalman filtering is an optimal autoregressive data processing algorithm that uses the linear system state equation to optimally estimate the system state from the input and output observations [64].In the field of target tracking, Kalman filtering predicts the position of the next state of an object from a set of position data containing measurement errors and uses all the information available to make an optimal prediction of the next state of the target in combination with the actual measurement data.
Assuming that the system state at the moment is represented by a three-dimensional vector X (t) = x t y t v t T , the state transfer equation at the next moment is shown in Equation (4) according to the above algorithm.
where x t denotes the x coordinate in CGCS2000 coordinate system; y t denotes the y coordinate in CGCS2000 coordinate system; v t denotes the speed; t denotes the time difference between adjacent moments; θ t denotes the speed deflection angle; u t denotes the acceleration.
The measured video shooting frame rate is 30 frames/s, and the interval between adjacent moments is short, so the vehicle running speed between adjacent moments can be considered constant, i.e., the acceleration is 0, and the state transfer matrix Equation ( 5) is obtained.In addition, the third polynomial fitting curve of scattered data is used as the trajectory prediction curve, the curve is smooth and continuous, and the direction of the vehicle running speed at any moment is tangent to the trajectory curve.Then, the speed declination angle is calculated using Equation (6). tan The optimal prediction trajectory is obtained by Kalman filtering the vehicle position data with the above formula.The original data trajectory and Kalman filtered trajectory are shown in Figure 9.The Kalman filtered trajectory is more consistent with the vehicle operation characteristics than the original point position data trajectory.

3) SPATIAL COORDINATE SYSTEM CONVERSION a: GAUSSIAN PLANE CARTESIAN COORDINATE SYSTEM
In the original numerical file, the coordinates describing the vehicle position use a Gaussian Cartesian coordinate system converted from the CGCS2000 coordinate system, i.e., the central meridian and equatorial intersection O as the origin, with the Y-axis pointing east and the X-axis pointing north, as shown in Figure 10(a).A Gaussian plane right-angle coordinate system can be used to describe the position of the vehicle in the local range.However, the road is not exactly a straight line parallel to the x-axis or y-axis; it also contains circular curves with different radii and gentle curves with constantly changing curvatures, so knowing only the position coordinates (y, x) of the vehicle without knowing the road position makes it very difficult to describe the distance the vehicle travels on the road and the position of the vehicle from the centerline of the road.When investigating freeway traffic flow characteristic parameters, it is necessary to know how far the vehicle has traveled along the road to determine where the vehicle is in the road and how far the vehicle is from the centerline of the road to determine which lane the vehicle is traveling in on the road.However, the Gaussian plane Cartesian coordinate system cannot meet the above requirements to directly represent the relative positions of vehicles on the road, so the Gaussian plane Cartesian coordinate system is transformed into the Frenet coordinate system.

b: FRENET COORDINATE SYSTEM
The Frenet coordinate system takes the road centerline as the reference line and establishes the coordinate system based on the tangent vector and normal vector of the reference line [65], as shown in Figure 10(b).The vehicle position is represented by (s, l), where s denotes the distance the vehicle travels along the road in the longitudinal direction, and l denotes the lateral offset distance of the vehicle from the road centerline in the cross-section.

c: COORDINATE SYSTEM CONVERSION METHOD
As shown in Figure 10(c), sample points (y s , x s ) of the road reference line are collected in the target detection area, and the road reference line s(y) is fitted.The vertical axis S of the Frenet coordinate system is established based on s(y), and the horizontal axis L is established based on the normal vector at the starting point of the vertical axis S. The vehicle position under the Frenet coordinate system is represented by (s, l).Assuming that the vehicle has coordinates (y x , x x ) in the Gaussian plane right-angle coordinate system and the nearest reference point (y r , x r ) from (y x , x x ) on s(x) is found according to Equation (7), the vehicle position (s, l) in Frenet coordinates is calculated by Equation ( 8) and Equation (9).
where s denotes the length of the longitudinal motion of the vehicle in the Frenet coordinate system and the arc length of s(y) in the Gaussian plane right-angle coordinate system; l denotes the vehicle lateral offset distance in the Frenet coordinate system; s(y) denotes the fitted road reference line; s (y) denotes the derivative of the road reference line s(y); (y x , x x ) denotes the position of the vehicle in the Gaussian plane right-angle coordinate system; and (y r , x r ) denotes the nearest point to the vehicle position on s(x) in the Gaussian plane right-angle coordinate system.
By the above calculation, the vehicle trajectory data (y, x) in the Gaussian plane Cartesian coordinate system in the original value file is converted into the vehicle trajectory data (s, l) in the Frenet coordinate system.

4) DATA EXTRACTION
After the coordinate system conversion is completed, the vehicle trajectory data are represented by (s, l), the corresponding time t is converted by the number of video frames.To facilitate the calculation of the flow rate, average density and interval average speed of the road section, we defined the longitudinal position of the nth vehicle at moment t as s n (t).

a: FLOW RATE
Flow rate refers to the number of equivalent hourly vehicles through the measurement section in a time interval if less than 1 h, calculated according to Equations (10) and (11).
Define the function T n (s) at the time slot (t i − t m /2, t i + t m /2).
Then, the flow rate of the road section during the time period is as follows: where t i denotes the middle value of the calculation period (s), starting from 2.5 min; t m denotes the duration of the calculation (s), taken as 5 min; T n (s) indicates the determination function of whether the nth vehicle passes the detection section, with 1 for passing and 0 for failing; s m denotes the longitudinal position (m) at which the measured section is located; q denotes the flow rate (veh/h); and N denotes the vehicle number.Authorized licensed use limited to the terms of the applicable license agreement with IEEE.Restrictions apply.measurement time; when the measurement length is certain, the average speed is the average of the reconciliation of the location speed observations, calculated according to Equation (12).
where vs denotes the average speed (km/h); N Q denotes the number of vehicles passing through the measurement section during the measurement time; s r denotes the length of the measured section (m); and t n denotes the time (s) for the nth vehicle to pass through the measured section.

c: AVERAGE DENSITY
The traffic density is the number of vehicles on a 1 km road section at a certain moment.In the 5 min period, the number of vehicles on the road section is calculated every 30 s, and the average of 10 measurements of density is taken as the average density in 5 min after converting to density.Define the function P n (s) at moment t j .
Then, the density K j of the road section at moment t j is as follows: The average density of the measured section in 5 min is as follows: where P n (s) denotes the determination function of whether the nth vehicle at moment t j is within the measurement range, which is 1 if it is and 0 if it is not; s s denotes the position of the starting point of the section to be measured (m); s e denotes the position of the end of the section to be measured (m).

5) DATA EXTRACTION RESULT
Processing the survey data by using the above method, the data of density K and traffic volume Q of the surveyed road section are obtained as shown in Figure 11.Because no significant congestion occurred on the investigated road section during the measurement, Figure 11 shows that both K and Q are at low values.The traffic volume Q barely exceeds 3000 veh/h, indicating that the road section is almost at LOS A. These data can only reflect the free flow state of the road section and lack the data under the congestion state, so the K -Q relationship curve cannot be fitted correctly.Therefore, the simulation method is considered to obtain the traffic flow parameters under different congestion levels.The simulation parameters will be adjusted based on the data from this survey to obtain simulation results that are close to the actual driving behavior, as shown in Table 1.

V. VISSIM SIMULATION AND ANALYSIS A. BUILD THE SIMULATION MODEL
To analyze the impact of the addition of an auxiliary lane for the dual-lane exit ramp based on the traffic operation condition of the whole exit section, the method of controlling variables should be adopted, where the two design options are used as independent variables, the three parameters of traffic flow are used as dependent variables, while the remaining variables, such as driving behavior, desired speed, vehicle composition [66], diverging ratio (DR) and other parameters, are controlled at constant values.The volume ratio has a significant impact on the capacity of the weaving sections, and in the diversion area, it corresponds to the diverging ratio [20].
When the diverging ratio changes, the traffic volume of the road section also changes, which can complete transition from congestion to non-congestion [13].DR is defined as the ratio of the off-ramp traffic volume to the total traffic volume of the exit section as Equation (17).
where DR denotes the diverging ratio; Q d denotes the off-ramp traffic volume (veh/h); Q a denotes the total traffic volume of the exit section (veh/h).However, in realistic conditions, there are no two sections that satisfy the above requirements.The level of service (LOS) reflects the state of traffic flow.When the traffic volume is less than 4950 veh/h (LOS A-C), the traffic flow is free flow; between 4950 veh/h and 6600 veh/h (LOS C-E), saturated flow; more than 6600 veh/h (LOS F), oversaturated flow.To plot the K -Q relationship of the road section, it is necessary to collect the traffic flow data in the following three states: free flow, saturated flow, and supersaturated flow.However, the freeway congestion state is episodic and requires a large amount of data acquisition, and according to the results of this data survey, the traffic flow is only in the free-flow state.Therefore, a combination of traffic simulation is needed to obtain the three traffic flow parameters.
First, a simulation model (Scheme A) with the same geometric configuration as the exit section of the Xiwu Interchange is constructed, and the model is calibrated using field survey data so that the K -Q relationship obtained from the simulation has a high degree of fit with the measured results to ensure that the simulation model can better simulate the actual road conditions.Second, a simulation model (Scheme B) with the same configuration as the exit section of the Xiwu Interchange except that no auxiliary lane is constructed and the same simulation parameters as those used in Scenario A are used.Finally, the basic freeway section model was constructed as the baseline control group (Scheme C).The three traffic flow parameters are extracted by adjusting the model parameters to simulate the traffic flow operating conditions in different states.

B. EXRACTION OF THREE PARAMETERS OF TRAFFIC FLOW
After the simulation, the three traffic flow parameters are extracted from the evaluation -results list -section segment evaluation results.Since the VISSIM section evaluation results are output in terms of simulation sections and connectors, to obtain the values of the three parameters for the entire range of exit sections, the following equation is required.
where K denotes the average density of the exit section; K i denotes the measured density of a section or connector; l i denotes the length of a segment or connector; v denotes the average speed of the exit section v i denotes the average speed of vehicles on a segment or connector; Q denotes the traffic volume of the exit section; and Q max(i) denotes the traffic volume of the last section or connector of the exit section.This simulation has 3 scenario models.Each model includes 30 groups of input traffic volumes and 4 groups of diverging ratios, and each traffic group combination is simulated 10 times, so the total number of simulations is 3 × 30 × 4 × 10 = 3600 times.Finally, 14,400 groups of three-parameter data are obtained, and then the three-parameter simulation results are calculated according to Equations ( 18) - (20).

C. DATA FITTING
The K and Q simulation results are plotted as scatter plots, as shown in Figures 12,13 and 14, and it can be observed that the simulation results are similar to the K -Q relationship plot in Figure 6: the traffic volume increases with density and starts to decrease after reaching the peak.To further verify whether the simulation results are consistent with the K -Q relationship (3) in Greenshields' formula, a quadratic polynomial fit of the K and Q data was performed 28332 VOLUME 12, 2024 Authorized licensed use limited to the terms of the applicable license agreement with IEEE.Restrictions apply.using quantitative with a control curve intercept of 0 (Q = aK + bK 2 ).The results are shown in Table 2, and the fitted curves are shown in Figures 12,13 and 14.Based on the K -Q relationship diagram and the fitting the process and conclusions are as follows.1) The K and Q data in this simulation show obvious peaks and decreasing trends, and the results are close to the simulation expectation.The quadratic polynomial fitting of the K and Q data, R 2 are greater than 0.99, and K and Q are significantly in accordance with Greenshields' formula (3), which proves that this simulation setup is reasonable and the simulation results have analytical value.2) When the traffic volume Q does not reach the peak and is lower than 6600 veh/h, the K and Q data are more continuous, while when the traffic volume is greater than 6600 veh/h, the data dispersion increases.When the diverging ratio is 40%, there is an obvious inflection point in exit section K with the auxiliary lane after reaching 6600 veh/h, the data change trend deviates from the quadratic polynomial, and K cannot reach the maximum peak.This means that after K is greater  than 6600 veh/h, the operation condition of the whole section becomes unstable, and the unstable condition becomes more serious with the increase in the diverging ratio.3) Regarding the fitted quadratic curve obtained from the K and Q data, the larger the proportion of diversion is, the worse the overlap with the original data.When K is lower than 6600 veh/h (higher than the tertiary service level), the traffic flow is in a free-flow state, with less interference between vehicles, and K and Q relationship of the road section in this interval is closest to the theoretical Greenshields formula, which can best reflect the traffic flow characteristics of the road.However, the fitted curve cannot better overlap with the K and Q data when the traffic volume is lower than 6600 veh/h.Therefore, we defined the curve obtained by fitting the data with density below 150 veh/km and traffic volume below 6600 veh/h as the theoretical curve, so as to better fit the data under low traffic volume conditions.4) The theoretical curve represents the traffic flow characteristics in the ideal state when there is no serious interference between the vehicles themselves; the fitted curve represents the traffic flow characteristics in the actual operation of the road when there is serious interference under heavy traffic volume due to the influence of driver behavior.According to the peak curve comparison in Table 2 and the relationship between the two curve positions in the figure, the fitted curve is always lower than the theoretical curve, and the difference between the two indicates that the road capacity is reduced due to the influence of the driver's behavior.

VOLUME 12, 2024
Authorized licensed use limited to the terms of the applicable license agreement with IEEE.Restrictions apply.

D. ANALYSIS FOR THE SAME SCHEME WITH DIFFERENT DIVERGING RATIOS
To compare the road traffic flow characteristics of the same scheme more intuitively under different bifurcation ratios, the simulation results of the same scheme are summarized as shown in Figure 15 and Figure 16 and combined with the above for a comprehensive analysis.
FIGURE Q-K relationship graph for the exit section of the same scheme with different diverging ratios.

a: EXIT SECTION WITH AUXILIARY LANES
According to Figure 12, the larger the diverging ratio is, the larger the difference between the fitted curve and the theoretical curve.When the diverging proportion is 40%, the ratio of the peak of the fitted curve to the theoretical curve is 0.87, which indicates that the actual operation is influenced by the driving behavior, resulting in the maximum capacity of the road section reaching only 87% of the theoretical maximum.
According to Figure 15, the changes in K and Q with different diverging ratios for the exit section with auxiliary lanes are very similar when Q is below 6600 veh/h, indicating that the traffic flow status of the section meeting the level of service C is independent of the diverging ratio.Since the K and Q data are close when Q is lower than 6600 veh/h, the theoretical curves obtained are similar, and the peaks are not very different.When Q is higher than 6600 veh/h, the FIGURE 16.Q-v relationship graph for the same scheme exit section with different diverging ratios.
differences between the K and Q data of the different diverging ratios increase significantly; the larger the diverging ratio is, the more serious the impact of diverging behavior, the lower the Q under the same K , the lower the peak of the fitted curve, and the lower the actual maximum capacity of the exit section.
According to Table 2, the peak of the theoretical curve increases slightly when the diverging ratio increases.The reason for this is that the diverging ratio increases the utilization rate of the auxiliary lane, thus increasing the capacity of the entire roadway.In addition, when the diverging ratio exceeds 30%, the peak of the theoretical curve can reach the basic capacity of 8800 veh/h of the road section, as stipulated in the specification; however, under the actual operating conditions, the peak of the fitted curve decreases with the increase in the diverging ratio, and the peak is less than the 8800 veh/h stipulated in the specification.The basic capacity needs to be discounted on the basis of the specification, and the adjustment factor is the ratio of the peak value of the fitted curve to the specification value.
According to Figure 16, the trend of the v-Q simulation data is similar to that in Figure 5.The average speed v of the road section first decreases with increasing Q, and after reaching the maximum traffic volume, it decreases with decreasing Q.The larger the diverging ratio is, the larger the diverging ratio and the smaller v under the same Q condition, indicating that the diverging behavior of the exit section affects the vehicle traffic efficiency.

b: EXIT SECTION WITHOUT AUXILIARY LANES
According to Figure 13, the difference between the fitted curve and the theoretical curve also increases with the increase in the diverging ratio.However, the degree of difference is lower compared to the section with auxiliary lanes.The actual maximum capacity is 93% of the theoretical maximum when the diverging ratio is 40%.Under the condition that both K and the diverging ratio are the same, the degree of disturbance of the diverging behavior of the exit section is similar with or without the auxiliary lane, and the theoretical value is similar to the fitted value, indicating that the exit section without the auxiliary lane has its own defects under a high traffic volume, resulting in a lower theoretical maximum capacity.
According to Figure 15, the K -Q data vary continuously when the exit section without an auxiliary lane is below 6000 veh/h at Q.The data values at different diverging ratios are similar when Q is low, but the degree of difference increases with the traffic volume, so the peak of the theoretical curve obtained differs widely and decreases with the increase in the diverging ratio.The differences in the simulation data are larger when Q is higher than 6000 veh/h.The larger the diverging ratio is, the more serious the influence of diverging behavior, the lower the Q under the same K , the lower the peak of the fitted curve, and the lower the actual maximum capacity of the exit section.
According to Table 2, the theoretical peak of the exit section without an auxiliary lane is lower than the basic capacity of 8800 veh/h stipulated in the specification.When the diverging ratio is 40%, the theoretical maximum capacity is only 7089 veh/h, which is much lower than the specified value, indicating that the theoretical capacity of the exit section without an auxiliary lane has been seriously reduced under the large diverging ratio.The theoretical peak of the exit section without an auxiliary lane decreases significantly with the diverging ratio, indicating that the traffic flow characteristics of the scheme are seriously affected by the diverging behavior, and the ability of the scheme to regulate the diverging behavior is worse than that of the exit section with an auxiliary lane.Considering the interference of driving behavior, the lowest peak of the fitted curve is 6626 veh/h, and the actual capacity of the exit section is even lower.Therefore, the specified value of the baseline capacity in the specification should also be discounted, and the discount method is the same as that in the section with auxiliary lanes.
According to Figure 16, the trend of the v-Q simulation data is the same as that of the section with auxiliary lanes, but the difference in operating speed under different diverging ratios is greater than that of the section with auxiliary lanes, which further indicates that the regulation of diverging behavior in the exit section without auxiliary lanes is weaker than that with auxiliary lanes, and the overall traffic efficiency is lower.

c: BASIC CAPACITY ADJUSTMENT FACTOR FOR THE EXIT SECTION
According to the above analysis, considering the exit section's own ability to regulate diverging behavior and the influence of diverging driving behavior, the exit section capacity does not reach the benchmark capacity specified in the specification, so a discount should be made according to the actual conditions when using the specification value.In summary, the capacity reduction factor of the two-lane ramp exit section of the two-way eight-lane expressway is shown in Table 3.

VI. LANE NUMBER BALANCE ANALYSIS A. K-Q RELATIONSHIP ANALYSIS OF DIFFERENT SCHEMES WITH THE SAME DIVERGING RATIO
According to the peak curve analysis, the ability of the exit section without auxiliary lanes to regulate the diversion behavior is weaker than that of the exit section with auxiliary lanes, and the difference between them is not constant but is related to the traffic volume.Therefore, in this section the traffic flow characteristics of the two schemes with and without auxiliary lanes at full traffic volume conditions are compared, and the importance of lane number balance is analyzed on this basis.
For comparison, the simulation results of different schemes with the same diverging ratio are plotted within the same figure.According to the needs at the time of actual construction, the expressway should meet LOS C, so the design speed of 120 km/h expressway service traffic volume should not exceed 6600 veh/h, and the two schemes should be compared within this traffic volume interval.According to the above, the theoretical curve fits better for data with traffic volumes below 6600 veh/h, so the theoretical curve is used as the object of analysis in this section, and the theoretical curves for different schemes with the same diverging ratio are plotted within another figure, as shown in Figure 17.
As Figure 17 shows, the Q of the exit section without auxiliary lanes is always lower than that of the exit section with auxiliary lanes at any K value for the same diverging ratio, while the Q of the exit section with auxiliary lanes is always lower than that of the base section, which indicates that the road capacity decreases in the exit section due to the diverging behavior, and the provision of auxiliary lanes is better than that with no auxiliary lanes, i.e., maintaining the balance of the number of lanes has a positive impact on improving the capacity of the diverging area.

B. CALCULATION AND CORRECTION OF SCHEME SELECTION LIMIT VALUE
However, the difference between the two schemes increases with K .Therefore, the difference in capacity between the two schemes is not significant when K is small.Considering that in actual construction, the exit section with an auxiliary lane will have one more lane than that without an auxiliary lane, the construction volume and cost are higher in comparison.Therefore, when the difference between the two options Q is not large, the nonauxiliary lane scheme with lower engineering and construction costs is also an option to be considered.
In mathematical statistics, the acceptable confidence level is generally chosen to be 95% or 90%; thus, when the difference between the Q values of the two schemes at the same K is no more than 5% or 10%, the two passage capacities can be regarded as having no major difference.The lower limit of the traffic volume corresponding to this Ka is called the '' scheme selection limit value '' (SSLV), which means that when the forecast traffic volume of the exit section does not exceed the SSLV, the nonauxiliary lane scheme can be considered.
where f set (K ) denotes the K -Q theoretical curve function for the exit section with auxiliary lanes; and f none (K ) denotes the K -Q theoretical curve function for the exit section without auxiliary lanes.The results of the calculation of the SSLV are shown in Table 4, and the corresponding reference lines are plotted in the theoretical curve summary in Figure 17.As the figure shows, the difference between the exit section without the auxiliary lane and the exit section with the auxiliary lane has not yet reached the allowable difference when the theoretical optimum density (K corresponding to the symmetry axis) is reached for diverging ratios of 10% and 20%.The Q-difference ratio at the optimal density of the exit section without auxiliary lanes is shown in Table 2, which shows that the difference ratio is only 3.1% for a diverging ratio of 10% and 8% for a diverging ratio of 20%.
Therefore, when the acceptable difference is greater than 3.1% and 8%, the calculated density K a of Equation ( 21) is greater than the optimal density of the road section, and the corresponding traffic volume Q is already below the peak and is located in the decreasing zone.However, in practice, the traffic volume between this Q and the peak still satisfies the difference acceptance condition.Therefore, when the calculated K a is greater than the optimal density of the road section, it is selected according to the optimal density.The results in Table 4 are corrected according to this rule, and the corrected values are shown in Table 5.

C. THE RECOMMENDED VALUE OF THE SSLV
The corrected SSLVs from Table 5 are plotted in a graph and analyzed in conjunction with the freeway level of service, as shown in Figure 18.According to Figure 18, the SSLV under some conditions has exceeded the maximum service traffic volume of the freeway LOS C. In the actual design process, the number of freeway lanes calculated from the predicted traffic volume must meet the LOS C, which indicates that there is a small probability that the freeway will have a traffic volume higher than 6600 veh/h during operation.
Considering the above two reasons, the SSLV is revised twice, and an SSLV greater than 6600 veh/h is changed to 6600 veh/h and that below 6600 veh/h is rounded down by 50 veh/h to obtain the recommended value of the final SSLV; see Table 6.

D. MEANING AND USAGE OF SSLV
The meaning of SSLV in Table 6 is as follows: after determining the exit diverging ratio of the freeway to be designed, when the predicted traffic volume does not exceed the SSLV in the table, the meaning of SSLV in Table 6 is as follows: after determining the exit diversion ratio of the freeway to be designed, when the predicted traffic volume does not exceed the program comparison limits in the table, a two-lane ramp scheme without auxiliary lanes can be considered, and the capacity is reduced by no more than 5% or 10% compared with the scheme with auxiliary lanes.
The SSLVs in Table 6 are used as follows.Determine the vision peak hourly traffic volume, calculate the diverging ratio, determine the acceptable difference and find the SSLV in Table 6 based on the diverging ratio.If the freeway vision peak hour traffic volume is higher than the SSLV, the exit section of the freeway must ensure lane balance, that is, the two-lane exit ramp must be set up with auxiliary lanes; if the freeway vision peak hour traffic volume is lower than the SSLV, the lane imbalance scheme can be used, which means the scheme without auxiliary lanes can be used in the exit section of the freeway with a two-lane ramp according to the engineering situation.

E. LANE BALANCE ANALYSIS
According to the above analysis, when two-lane exit ramps are set up in the exit section of the freeway, the capacity 28338 VOLUME 12, 2024 Authorized licensed use limited to the terms of the applicable license agreement with IEEE.Restrictions apply. of the exit section without auxiliary lanes is always lower than that of the exit section with auxiliary lanes, proving that maintaining lane balance at the diverging area is effective in improving the capacity.However, the difference in the capacities of the two schemes increases as the upstream input traffic volume increases, and when the upstream input traffic volume is low, the capacity difference between the two schemes is negligible.
With the development of the economy, the traffic volume along freeways is increasing rapidly.When the demand for diverging is greater than the capacity of two-lane ramps, designers need to consider increasing the number of lanes on the ramps to ensure the efficiency of traffic flow.According to the above study, the freeway exit section can be designed with lane imbalance in the diverging area under certain traffic volume conditions.Therefore, when a three-lane exit ramp is used for the exit section of a multilane expressway, the ''SSLV'' for the exit section with different configurations can also be calculated according to the above analysis method.The lane imbalance design can be used when the predicted peak hour traffic volume is lower than the SSLV.By constructing an auxiliary lane with one less section, in addition to reducing the engineering volume and cost, it also avoids the impact on the adjacent interchange layout due to constructing an auxiliary lane that is too long.Therefore, several design schemes of three-lane exit ramps for freeways are proposed, as shown in Figure 19, and these schemes provide some inspiration for the design of three-lane exit ramps.

VII. CONCLUSION
According to the requirements of the Green Book, auxiliary lanes should be provided to ensure that both the requirements regarding lane balancing and the number of basic lanes are met when two-lane exit ramps are constructed.However, according to the survey, there are several two-lane exits on the Xi'an City Bypass in China that do not have auxiliary lanes, but no significant traffic congestion has been observed during operation.To demonstrate the feasibility of using the lane imbalance scheme for freeway exits, the research in this paper was carried out.Therefore, by comparing the differences between the three indicators of traffic volume, speed and density when using the lane balancing scheme and the lane imbalancing scheme on the exit section, we analyze the efficiency and operational effectiveness of the two schemes for the exit.
Xiwu Interchange in Xi'an was selected as the research object, and traffic data were collected using drone and image recognition software.The collected original data are optimized using Kalman filtering to ensure that the measured

FIGURE 3 .
FIGURE 3. Direct two-lane exit without an auxiliary lane on the Xi'an ring freeway.

FIGURE 8 .
FIGURE 8.The Xi'an Xiwu Interchange.The blue line indicates the auxiliary lane of the freeway.
b: AVERAGE SPEED Average speed refers to the average of the speeds of all vehicles within a specific length of the road during the 28330VOLUME 12, 2024

FIGURE 11 .
FIGURE 11.Q and K data are obtained by extraction.

FIGURE 12 .
FIGURE 12. Q-K relationship graph for the exit section with auxiliary lanes.

FIGURE
FIGURE Q-K relationship graph for the exit section without auxiliary lanes.

FIGURE 14 .
FIGURE 14. Q-K relationship graph for basic freeway sections.

FIGURE 17 .
FIGURE 17. Q-K relationship curves for different scheme exit sections with the same diverging ratio.

TABLE
Simulation of the K and Q data fitting results.

TABLE 3 .
The capacity reduction factor of a two-lane ramp exit section of a two-way eight-lane expressway.