Overtaking Safety Evaluation and Setting of Auxiliary Lane on Two-Lane Highway in China

1School of Transportation Science and Engineering, Harbin Institute of Technology, Harbin 150090, China 2School of Transportation Science and Engineering, Jilin Jianzhu University, Changchun 130018, China 3School of Civil Engineering, Changchun Institute of Technology, Changchun 130012, China 4School of Water Conservancy and Civil Engineering, Northeast Agricultural University, Harbin 150030, China


Introduction
By the end of 2013, the total mileage of Chinese classified highway has reached 3.7556 million km and the ratios of the second-class highway, the third-class highway, and the fourth-class highway are 82 percent.In China, the secondclass highway and the third-class highway are all two-lane highways, and the fourth-class highway can be two-lane or single-lane highway.There is crash risk for overtaking on twolane highway because drivers need overtake on the opposing lane.The overtaking behavior becomes one of the main causes of traffic conflict on two-lane highway.Research on overtaking safety evaluation can provide important evidence for traffic accident prevention of two-lane highway.And setting auxiliary lane can improve the safety level of two-lane highway.
Vlahogianni analyzed factors which may influence the duration of overtaking on two-lane highways [1].Farah et al. developed models that explain the minimum time to collision and passing gap acceptance by simulator and analyzed age and gender differences in overtaking maneuvers on two-lane rural highways [2][3][4].Schneider et al. used the negative binomial model to evaluate the effects of geometric characteristics on rural two-lane highway safety [5].Montella et al. evaluated drivers' behavior on horizontal curves of two-lane rural highways by simulator [6].Wu et al. developed mixed logit models to analyze driver injury severities in single-vehicle and multivehicle crashes on rural two-lane highways in New Mexico [7].Vlahogianni and Golias employed Bayesian networks to model the uncertainty hindering in the overtaking behavior of young drivers on two-lane highways and reveal the related traffic microscopic characteristics that may influence the decision to overtake [8].Bauer and Harwood studied the safety effects of horizontal curve and grade combinations on rural two-lane highways [9].[18].Liu and Bie compared hookturn scheme with U-turn scheme on highway [19].Bie et al. calibrated platoon dispersion parameter considering the impact of the number of lanes [20].In summary, recent related researches have mostly focused on risk evaluation by simulator, traffic accidents, affecting factors of safety, and safety countermeasures on twolane highways.A study on setting auxiliary lane on two-lane highway based on conflicts analysis by field experiment was conducted in this paper.In Section 2, an experiment was designed to get conflict data and drivers' risk perception.Subsequently, Section 3 studied the overtaking safety evaluation method and traffic volume condition of setting auxiliary lane on two-lane highway.Finally, a conclusion was made in Section 4.

Experiment
2.1.Overtaking Process Analysis.The overtaking process on two-lane highway is shown in Figure 1.In Figure 1,  is the safe distance, and  is overtaking distance.
Firstly, overtaking vehicle drives into the lane of opposing direction to overtake forward vehicles, and there is a traffic conflict between overtaking vehicle and opposing vehicle.Then overtaking vehicle drives back into the original lane, and there is a traffic conflict between overtaking vehicle and overtaken vehicle.However, overtaking driver will choose a safe chance to drive back into original lane, so the object of the research is the traffic conflict between overtaking vehicle and opposing vehicle.At present, there are mainly two kinds of methods to measure the severity of traffic conflict, that is, time and space distance methods.Considering the convenience of data collection, the time distance was selected as the index to measure the severity of traffic conflict.In Figure 1,   is defined as overtaking conflict time.It is the time difference between the time of driving back to the original lane and the time of meeting with the first opposing vehicle.

Experiment Design.
Two second-class highways and two third-class highways in Harbin, China, were selected as experimental highways.The experiments were conducted from March 10 to April 10, 2013.This experimental scheme was designed to collect the data of overtaking conflict time and record driver's feeling on overtaking risk.Recorder should record the memberships of driver's feeling on overtaking risk.The memberships belong to (0, 1), and the more risk the driver feels, the bigger the membership is.Other collected data include speed of overtaking and overtaken vehicle and traffic volume.The data of overtaking conflicts time were obtained by stop watch.The data of speed were obtained by laser speed measurement.And the data of traffic volume were obtained by erecting camera on the experimental section.
It is acceptable when the experimental sample size is greater than or equal to 3 times of the number of independent variables.In this paper, the relation model has three variables, that is, overtaking conflict time, traffic volume, and design speed.Considering the risk of experiment, experimental sample size was determined as 10.It met the statistic demand.The experimental data were listed in Table 1.

Overtaking Safety Evaluation.
In order to describe the severity of traffic conflict accurately, Delphi method and assignment method based on the fuzzy theory were adopted to analyze the traffic conflict qualitatively, and then the membership function of overtaking conflict time was given.Conflicts were classified into serious, general, and minor conflicts.

The Membership Function.
In order to get the membership function of overtaking conflict time, the original data must be analyzed statistically.Table 1 showed that the minimum value of   is 1 s and the maximum value of   is 10 s.According to the incremental order of   in Table 1, overtaking conflict time and membership were arranged as follows: (1, 0.95), (2, 0.9), (3, 0.8), (3, 0.75), (4, 0.65), (5, 0.5), (5, 0.55), (7, 0.3), (10, 0.1), and (10, 0.05).Then the trend curve of membership function was obtained and it was shown in Figure 2. In Figure 2, the horizontal axis stands for overtaking conflict time (unit: s) and the vertical axis stands for membership.It can be regarded as the original shape of membership function curve of overtaking conflict time.
Through analyzing the relation between overtaking conflict time and membership in Figure 2, it can be found that it is a monotone decreasing function which is consistent with the  membership function form.Therefore Cauchy distribution function was chosen as membership function of overtaking conflict time.Cauchy distribution function was shown as follows: Figure 2 showed that  equals 2 s.According to data in Figure 2, parameters of formula (1) can be calibrated; that is,  = 1/5 and  = 2. Then the membership function of overtaking conflicts was shown as follows: (2)

Membership Thresholds.
Considering the fuzzy characteristic of traffic conflict degree, Delphi method was used to determine the membership thresholds of serious conflict, general conflict, and minor conflict.After three times where Delphi method is used, final expert prediction values can be obtained.The third surveying results by Delphi method were shown in Table 2.
(1) Calculation of Arithmetic Mean Value.According to the data in Table 2, arithmetic mean values of the membership threshold can be calculated.Arithmetic mean value of membership threshold between minor and general conflicts is (0.24 + 0.36 + 0.48)/3 = 0.36.Arithmetic mean value of membership threshold between general and serious conflicts is (0.58 + 0.75 + 0.86)/3 = 0.73.
(2) Calculation of Weighted Average Value.Making the minimum, the suitable, and the maximum membership thresholds in Table 2 multiplied by the weights of 0.2, 0.6, and 0.2, respectively, weighted average values of the membership threshold can be calculated.
(3) Calculation of Weighted Median Value.According to the minimum, the suitable, and the maximum values in Table 2, the median values can also be obtained.Then these median values were multiplied by weights of 0.2, 0.6, and 0.2, respectively.
In the above three kinds of analysis method, the membership threshold between minor and general conflicts focused on 0.37, and the membership threshold between general and serious conflicts focused on 0.74.Thus, the membership of minor conflict belongs to (0, 0.37), the membership of general conflict belongs to [0.37, 0.74), and the membership of serious conflict belongs to [0.74, 1).

Thresholds of Overtaking Conflict Time. By formula
(2), thresholds of overtaking conflict time corresponding to each traffic conflict degree were gotten and they were 3.33 s, 4.92 s, and 8 s, respectively.The overtaking conflict time corresponding to serious conflict belongs to (0 s, 3.33 s), and the overtaking conflict time corresponding to general conflict belongs to [3.33 s, 4.92 s), and the overtaking conflict time corresponding to minor conflict belongs to [4.92 s, 8 s].
Therefore, the different conflict degrees by overtaking conflict time   are measured as follows: (1)   ∈ (8s, +∞).There is no traffic conflict and overtaking can be completed successfully.(2)   ∈ [4.92 s, 8 s].There is minor conflict and drivers need to observe opposing traffic condition to overtake.(3)   ∈ [3.33 s, 4.92 s).There is general conflict.Drivers need to pay attention to the potential risk and determine whether overtaking or not according to the actual conditions.
(4)   ∈ (0 s, 3.33 s).There is serious conflict and drivers need to pay high attention.Traffic accident will happen very likely if drivers overtake, so overtaking determination should be given up.At the same time, managers should study whether the highway capacity of this section is enough.
Results show that the quantitative results are consistent with the actual circumstances.Some of the experimental twolane highways have serious traffic conflict, and they are also the black spots in fact.Thus it can be used for safety evaluation on two-lane highway.

Setting of Auxiliary Lane on Two-Lane Highway.
It can be seen from the above analysis that overtaking is very dangerous if opposing traffic volume is more than certain value.Setting auxiliary lane on the right of original lane can provide space for low-speed vehicle and then high-speed vehicle can overtake using original lane instead of opposing lane so as to guarantee overtaking safety on two-lane highway.Auxiliary lane is shown in Figure 3.
Setting of auxiliary lane on two-lane highway has not been prescribed in Chinese Technical Standard of Highway Engineering (JTG B01-2014) and Design Specification for Highway Alignment (JTG D20-2006).Its setting condition of traffic volume was studied in the following part of this paper.

Relation among Overtaking Conflict Time, Traffic
Volume, and Design Speed.It was assumed that the speed of overtaking vehicle after driving back into original lane was the same as the speed of opposing vehicle.It can be seen according to Figure 1 that headway of opposing traffic flow should be the sum of overtaking time , overtaking conflict time   , and driving time of opposing vehicle from meeting location to starting point of overtaking, which equals the sum of   and the time for driving the distance of .Then the following formula was obtained: where  is traffic volume of opposing lane, veh/h/ln;  is overtaking time, s; V 0 is design speed, km/h;  is the ratio between opposing headway in certain process of overtaking and opposing average headway;  is the ratio between design speed V 0 and the speed of opposing vehicle.
In formula (3),  can be calculated by the following formula: where V 2 is the speed of overtaken vehicle, km/h, and  is the ratio between the value of safe distance  and the value of design speed V 0 .Thus, the following formula can be obtained: In formula (5), overtaking time  is related to overtaking speed V 1 and the speed of overtaken vehicle V 2 .And it is inversely proportional to the difference between V 1 and V 2 .Therefore, their relation was assumed as follows: where V 1 is overtaking speed, km/h, and  is the undetermined parameter.
Combining formulas ( 5) and ( 6), the following formula can be obtained: In formula (7), making 1800 , /2 = , 3.6 = , then the following formula can be obtained: where  is half of opposing average headway, s;  is the reciprocal of the difference between overtaking speed V 1 and the speed of overtaken vehicle V 2 , h/km;  is the product of  and the ratio between the speed of overtaken vehicle V 2 and design speed V 0 , h/km; , , , and  are undetermined parameters.
The variables in formula (8) are not data obtained directly by experiment, so data processing is needed.The processed data were listed in Table 3. SPSS software was used to calibrate model parameters; the calibration results were shown in Table 4.It can be seen from Table 4 that  values of three model variables are 20.656,−3.232, and −2.347, respectively.Given significance level  = 0.05, the critical value   (36) = 2.029.Three absolute values of  were all more than this critical value, so three variables all passed the significant test under 95% confidence level.
Then the following formula can be obtained: According to observed data, the relation among V 1 , V 2 , and V 0 can be obtained; that is, V 2 = 0.65V 0 ∼ 0.75V 0 , and In formula (11),   can be determined by traffic conflict degree.Therefore, traffic volume of opposing lane that needs setting auxiliary lane on two-lane highway can be calculated according to traffic conflict and design speed V 0 .The calculated results were listed in Table 5.
It is suggested that auxiliary lane should be set when traffic volume of opposing lane exceeds the boundary value between minor and general conflicts because serious conflict is very dangerous.

Conclusions
Based on experiments on two-lane highway, the traffic conflict degree was analyzed qualitatively.The memberships of traffic conflict and the judgmental indexes on two-lane highway in China were obtained.The overtaking conflict time ranges of serious conflict, general conflict, and minor conflict are (0 s, 3. It is suggested that auxiliary lane should be set on two-lane highway when traffic volumes of opposing lane are more than 398 veh/h/ln, 370 veh/h/ln, 326 veh/h/ln, and 290 veh/h/ln, respectively, on the two-lane highway with the design speed of 80 km/h, 60 km/h, 40 km/h, and 30 km/h.Auxiliary lane on two-lane highway can provide safe overtaking chance for car by using original lane instead of opposite lane.Thus safety benefit is produced by avoiding traffic accidents.After setting up auxiliary lane on twolane highway, more overtaking opportunities for fast vehicles are provided, so highway capacity and vehicle speed will increase, and traveling delay will reduce.However, setting auxiliary lane will increase the costs of highway construction and maintenance.Setting space of auxiliary lane influences and the relation model among overtaking 3 s], (3.3 s, 4.92 s], and (4.92 s, 8 s], respectively.The relation model was established among overtaking conflict time, traffic volume of opposing lane, and design speed.According to this model, traffic volumes of opposing lane that need setting auxiliary lane on two-lane highway were given.
Takemoto et al. analyzed the effects of road surface and visibility conditions [16]lane highways[15].Correia and Silva studied the speed limit setting on two-lane highway[16].Wanget al. developed a safety-based approaching behavioural model with driving characteristics [17].Jiang et al. analyzed the time to collision in traffic conflict

Table 2 :
Surveying results by Delphi method.

Table 3 :
The processed data.

Table 5 :
Traffic volumes of opposing lane that need setting auxiliary lane (unit: veh/h/ln).