Cite this Article
Pang Ming-Bao, Ren Bo-Ning. Effects of rainy weather on traffic accidents of a freeway using cellular automata model. Chinese Physics B, 2017, 26(10): 108901  
Permissions
Effects of rainy weather on traffic accidents of a freeway using cellular automata model
Pang Ming-Bao †, Ren Bo-Ning ‡
School of Civil and Transportation, Hebei University of Technology, Tianjin 300401, China

 

† Corresponding author. E-mail: pmbpgy@hebut.edu.cn rbn0525@163.com

Project supported by the National Natural Science Foundation of China (Grant No. 50478088) and the Natural Science Foundation of Hebei Province, China (Grant No. E2015202266)

Abstract

The aim of this work is to investigate the influence of rainy weather on traffic accidents of a freeway. The micro-scale driving behaviors in rainy weather and possible vehicle rear-end and sideslip accidents are analyzed. An improved CA model of two lanes one-way freeway is presented, where some vehicle accidents will occur when the necessary conditions are simultaneously satisfied. The characteristics of traffic flow under different rainfall intensities are discussed and the accident probabilities are analyzed via the simulation experiments by using variable speed limit (VSL) and incoming flow control. The results indicate that the measures are effective especially during heavy rainstorms or short-time heavy rainfall. According to different rainfall intensities, an appropriate strategy should be adopted in order to reduce the probability of vehicle accidents and enhance traffic flux as well.

PACS: 89.40.Bb;89.40-a;02.60.-x
Keyword:cellular automata (CA) model;freeway;rainy weather;rear-end;sideslip
1. Introduction

Driving on a highway in rainy weather can become unsafe.[1–3] It may become difficult to control the vehicle when a pavement with a layer of water fails to offer the required amount of friction, especially at high speed even for a highly skilled and alert driver.[4,5] At the same time low visibility may not guarantee enough safe sight distance when the rainfall intensity is large. This increases the safety risks, e.g., resulting in single or multiple rear-end accidents, or a sideslip accident. It means that the road flux will drop. As is well known, there are many influencing factors on traffic safety, such as road geometric condition, driver character and state, vehicle type, weather, and other traffic states. All these factors interact in complicated ways, making the traffic accident size, e.g., the occurrence of accident and accident rate, have a nonlinear relationship with the factors.[6–10] Now, the point is how to describe the complex dynamic process microscopically by using a model and then providing the effect of rainy weather on road safety?

On the whole, the approaches of road traffic safety in rainy weather can be classified as three categories. Firstly, a number of previous studies were devoted to the effect of rainy weather on road traffic safety by using macro data and statistical methods.[1,4,6,8–13] Some analytic equations or models were used to map the relationships among the rainfall intensity, other variables, and traffic accident size.[6,8,9,11] For example, Keay and Simmonds investigated the effect of weather variables on traffic flow at a site in Melbourne, Australia,in the period 1989–1996.[6] Rainfall was the strongest correlated weather parameter and it had the greatest influence in winter and spring, when traffic volume decreased on wet days. A novel and rigorous approach was presented to analyze the influence of rainfall on road traffic accidents in urban areas by Jaroszweski and McNamara.[8] Cai et al. developed a quantitative model to analyze driving risks under rainy weather conditions and built a multi-ordered discrete choice model to analyze those risk factors and their influence degrees.[9] Those studies show that the road factors, driver factors and environment factors are strongly related to the accident size, and some control advice, e.g., variable speed limit (VSL), is provided for the traffic management department. But the complex dynamic process of traffic flow, e.g., the micro-scale driver behavior and the occurrence of traffic accident, are not described. Secondly, some are devoted to the estimation of vehicle sideslip from the angle of vehicle engineering caused by tire force, wheel cornering stiffness, road friction coefficient, etc.[14,15] Traffic flow and its nonlinear evolution in rainy weather have not been discussed. Thirdly, some research focused on the traffic accident avoidance and road safety improvement in adverse weather conditions by using the microscopic simulation models of traffic flow.[3,5,7] Using the car-following model, Wang et al. estimated the emergency braking distance of passenger vehicles with respect to the following interval that should be kept as a “gap” between two consecutive vehicles moving in the same lane.[7] The theoretical models for lane change and operational risk are used to study the multi-lane freeway at a microscopic level in disaster weather. Wan et al. discussed a dynamic speed control strategy to reduce collision risks on freeways by using a car-following model to simulate the traffic operation in adverse weather.[5] An indicator, chosen risk index (CRI), was defined for describing the chosen risk level for drivers in a car-following case by Hjelkrem and Ryeng[3] Obviously, only a car-following model was used to describe the traffic flow process, and the complex time-space evolution in rainy weather has not been discussed.

As an excellent tool, cellular automata (CA) models have been used widely to investigate the traffic flow behaviors. In particular, many researchers have studied the occurrence of car accidents by using the extended CA models,[16–26] e.g., the deterministic NS model proposed firstly by Boccara et al.[20] Only the traffic influences of low visibility weather, e.g., foggy weather, on a freeway including the fraction of real vehicle rear-end accidents and road traffic capacity were studied by using the established CA model. The traffic flow model in rainy weather has not been established and the possible traffic accident has not been discussed. In the present work, according to those and symmetric two-lane Nagel–Schreckenberg (STNS) model, we analyze the micro-scale driving behaviors in rainy weather and possible vehicle rear-end and sideslip accidents. An improved CA model of two lanes one-way freeway is presented. The characteristics of traffic flow under different rainfall intensities and traffic demand are discussed and the different effects are analyzed via the simulation experiments by using VSL and incoming flow control. The optimal strategies are provided under different conditions.

2. Analyses of driving behaviors and possible vehicle accidents in rainy weather
2.1. Cause analysis of vehicle rear-end accident

After it rains for some time, the road surface will be covered with rain water. This makes the tyre surface become smooth, for the tire tread gaps are also filled with rain water. There is not enough time to squeeze out the water from the smooth wheel tires especially in a heavy rainstorm or short-time heavy rainfall. The water film will gather in the rotating wheel and form a wedge. For a concrete road, the relationship between the depth of surface water (water film) and rainfall intensity is described as follows:[27]

where D denotes the surface water depth (mm), W the width of pavement (m), Q the rainfall intensity (mm/min), S′ = S/Sc, and , with Sl being the longitudinal slope (%), and Sc the slope of pavement cross section (%).

The water film leads to the decreasing of contact area between tire and road surface and makes the adhesion coefficient decrease with the increase of wedge length. The reduced friction coefficient (φ) can be fitted by a linear formula as follows:[2]

where v denotes the speed (km/h).

The decreasing of adhesion coefficient makes the braking distance lengthen, which may occur in single or multiple rear-end accidents. So the the safety distance Ssafe between a vehicle and its preceding vehicle should increase. By using the classical vehicle safety braking model, Ssafe can be calculated from formula (3) including adverse weather, e.g., fog, rain, and snow, where the decreasing of sight distance is also considered in rainy weather when rainfall intensity reaches 0.206 mm/min.[7,28]

where v(i,t) denotes the velocity of vehicle i at time t and the velocity of its predecessor is v(i – 1,t). The safe stopping distance L1 represents the minimum distance between two vehicles when their velocities are zero, where its values are set to be 2 m for a car and 5 m for a truck. The ts represents the time of normal response for a driver, and tw refers to the increasing response time on a rainy day.

Obviously, some rear-end accidents will happen if the distance between a vehicle and its predecessor is not larger than Ssafe, meaning that the safety distances are not met and the drivers cannot brake in time.

2.2. Cause analysis of vehicle sideslip accident

In the driving course, the influence of many forces on the vehicle, e.g., side wind, braking imbalance between left and right wheels of automobile, and steering brake, can cause its lateral displacement even sideslip, which makes the vehicle deviate from the right direction. Considering the fact that the vehicle sideslip in rainy weather is mainly caused by lateral gravity component due to the decrease of friction coefficient, we only study the case of a transverse slope. As shown in Fig. 1, the differential equation of vehicle motion in the early period of braking deceleration is defined as follows:[29]

where I denotes the rotation inertia of the vehicle front wheel vertical axis (kg·m2), r the vehicle yaw rate (°/s), M the vehicle mass (kg), g the acceleration of gravity, 9.8 m/s2, γ the pavement transverse slope angle (°), b the distance between front axle and the height of the vehicle center of mass (m), and L the wheel base (m).

Fig. 1. Movement condition of vehicle rear axle sideslip.

Fy denotes the lateral force acting on the center of mass and is calculated from

where v is the instantaneous speed when a vehicle starts to move. Fz denotes the braking force of rear wheel and is calculated from
where a denotes the braking deceleration (m/s2), h the height of the vehicle center of mass (m), Fx the braking inertia force and is calculated from
where α denotes the angle of rear wheel lateral displacement. Since they are relatively small at the beginning of the slip, we assume that
where β is the angle of mass center.

According to Fig. 1, we can obtain the following formulae

Then
Substituting Eqs. (5)–(12) into Eq. (4), the differential equation of vehicle motion of the slip is transformed into formula (13)

If the above formula is integrated, we can derive vehicle yaw rate model as shown in formula (14). Here the changes of instantaneous speed v and deceleration a are ignored when the vehicle starts to slip.

where

If r in formula (14) is integrated, we can obtain the vehicle steering angle θ when it is slipping.

For a vehicle driving at speed v, lateral gravity component leads to its steering angle θ due to the decrease of friction coefficient. At the same time, the driver makes the vehicle return to normal driving conditions by braking and adjusting the direction after the reaction time T0. But the longitudinal displacement and lateral displacement will appear.

where Sx denotes longitudinal displacement during the driver’s reaction time, Sy the lateral displacement, and T0 = ts + tw.

If Sy is large enough to make the vehicle deviate from the original lane, a sideslip motion occurs and part of sideslip motions form a traffic accident. For only one mainline on a freeway with no ramp as shown in Fig. 2, the road is composed of four parts, named marginal strip, left lane, right lane, and shoulder. Several types of sideslip accidents may occur.

Sy for a left lane vehicle with the left sideslip direction is larger than the sum of the width of marginal strip and the width between its left front corner and the lane left line;

Sy for a right lane vehicle with the right sideslip direction is larger than the sum of the shoulder width and the width between its right front corner and the lane right line;

Sy for a left lane vehicle with the right sideslip direction is larger than the distance between its right and the left of right lane vehicle if the position is occupied with a vehicle.

Sy for a right lane vehicle with the left sideslip direction is larger than the distance between its left and the right of left lane vehicle if the position is occupied with a vehicle.

Fig. 2. Studied object.
3. CA model with the occurrence of vehicle accidents

As shown in Fig. 2, only one mainline on a freeway with no ramp, which possesses continuous traffic flow characteristics, is used as the research object to illustrate the problem. The widths of marginal strip, shoulder, and lane are wl, wR, and w, respectively. The width of a vehicle is wc, where we use wc1 in place of wc for a car and wc2 in place of wc for a truck. As shown in Fig. 3, the roads, named left lane, right lane and shoulder, are divided into discrete cells, where left lane consists of left lane and marginal strip and its width is wc+w. The widths of right lane cell and shoulder cell are their original ones, respectively. According to traffic regulations, vehicles are prohibited to drive on the shoulder under normal conditions. But a vehicle may be driven on the shoulder if a sideslip occurs towards the right or a vehicle may be temporarily stopped for some reason. The length of each lane is L0. The length of each cell is equal to 1 m, which means that the number of cells of each lane is equal to the length of the mainline. We assume that the vehicle is driving on the middle position of the original lane. The lateral distance between a vehicle on the left lane and the road left guardrail is w1 + 0.5 × (w − wc). The lateral distance between a vehicle on the left lane and the road right guardrail is 0.5 × (w − wc) + w + wR. The lateral distance between a vehicle on the left lane and another vehicle on the right lane is w − wc. The lateral distance between a vehicle on the right lane and the road left guardrail is w1 + w + 0.5 × (w − wc). The lateral distance between the right front corner of a vehicle on the right lane and the road right guardrail is equal to 0.5 × (w − wc) + wR.

Fig. 3. Cell partition of studied object.

Each cell may be either empty or occupied by one vehicle with an integer velocity v between zero and the maximal speed limit vmax, where we use vmax1 in place of vmax for a car and vmax2 in place of vmax for a truck and Pcar denotes the proportion of car. The vmax is a stable value when no VSL signal is inputted and a variable value when a VSL signal is inputted. Two speed limit values are set for car and truck, respectively. In order to describe the traffic flow processing of the studied object, we establish an extended CA model based on symmetric Nagel–Schreckenberg (NS) model with the occurrence of vehicle accidents in rainy weather. The x(i, t) denotes the position of vehicle i at discrete time step t. The first vehicle is marked as 1, and the following vehicles are marked as 2, 3,...,i. The d(i, t) denotes the empty cells between vehicle i and its predecessor at time t, d(i, t)front and d(i, t)back refer to the empty cells between vehicle i and its preceding vehicle and between vehicle i and its successor on the adjacent road, respectively. The a denotes the acceleration if it is greater than zero or denotes the deceleration if it is smaller than zero.

3.1. Basic rules

Under normal circumstances, the vehicle evolution rules are as follows.

The lane-changing rules of mainline vehicle are as follows.

3.2. Rules in rainy weather

In rainy weather, the driver sight distance is affected when the rainfall intensity reaches 0.206 mm/min.[28] At the same time, the driver will open the fog lamps in order to find the preceding vehicle, which makes his actual sight distance longer than that for visibility. The actual sight distance is set to be 1.1 times that for visibility in the present study for describing the actual reaction of driver.[24] For each vehicle, Ssafe in each simulation step is calculated by using formula (3) in Subsection 2.1. The vehicle evolution rules are as follows.

3.3. Criterion rules of accident for a vehicle
3.3.1. Criterion rules of rear-end accident for a vehicle

In a basic model, the rule is designed to decelerate to any value immediately for a vehicle in order to keep the safety distance. So a vehicle rear-end accident will not occur. As discussed in Subsection 2.1, the safety distance between a vehicle and its preceding vehicle will increase in rainy weather. Some rear-end accidents may happen because the safety distances are not met and the drivers do not brake in time either. Thus, the criteria of a rear-end accident are as follows (we name the criterion of rear-end accident as CRA).

If one of the above conditions is met, a rear-end accident occurs once during or after time T0. The number of the rear-end accident occurrences N1ac is increased by 1 under the assumption of neglecting time correlations proposed by Boccara et al.[20] The vehicle rear-end accident does not really occur in the simulation. These dangerous situations are calculated and considered to be the signal of the occurrence of accidents. The rear-end accident probability P1ac is defined as N1ac/N, where N is the total number of vehicles.

3.3.2. Criterion rules of sideslip and probably accident for a vehicle

As discussed in Subsection 2.1, a sideslip motion may happen and partially form sideslip accident if Sy is large enough to make the vehicle deviate from the original lane. The criteria of a sideslip accident are as follows (we name criterion of sideslip accident as CSA).

3.4. Total vehicle accident statistics

The total number of vehicles Nac is equal to N1ac plus N2ac. The total accident probability Pac is defined as Nac/N and also equal to P1ac plus P2ac.

3.5. Boundary conditions

The boundary conditions are open. In each time step, when the update of vehicles on the freeway is finished, the position xlast of the last vehicle on each lane is checked. If xlast > vmax, a vehicle with velocity vmax is injected with the entering probability Pe at the cell min{vmax, xlast − vmax}. If rand2 > Pcar, the injected vehicle is a truck, otherwise it is a car. The leading vehicle on each lane is removed, if its position xfirst > L0 and its following vehicle becomes the new leader.

4. Simulation results and discussion

The freeway section described in Section 3 is simulated, where the length of the two-lane mainline is 5000 m. The length of each cell is 1 m. A car is considered to be six-cell-long, a truck is considered to be twelve-cell-long, and each time step is 1 s. The value of vmax1 is 33 for a car and vmax2 is 25 for a truck. The proportion of car Pcar is 0.8 and randomization probability pr is 0.03. The maximum acceleration amax is 3 cells for a car and 2 cells for a truck according to vehicle dynamic behavior and based on the driving comfort degree. Considering that the value of maximum deceleration restriction is 3.4 m/s2 in the parking stadia model,[13] the maximum deceleration amax is set to be 3 cells for a car and 2 cells for a truck. According to the survey that about 1.9% drivers always have distracted their driving attention, p′ is set to be 1.9%. Although a driver reaction time may vary with traffic condition and the action of his preceding vehicle, its value T0 is still set to be 1 s, considering that the average reaction time of drivers is 3/4 second presented by the National Safety Council.[24,30] According to Technical Standard of Highway Engineering (JTG B01-2014), w is 3.75 m.[31] The other parameters are set as follows: wl = 0.75 m, wR = 3 m, wc1 = 1.8 m, wc2 = 2.5 m, w1 = 1.725 m, w2 = 1.95 m, w3 = 7.725 m, w4 = 1.6 m, w5 = 7.375 m, w6 = 1.25 m, w7 = 1.375 m, w8 = 5.475 m, w9 = 3.975 m, w10 = 5.125 m, and w11 = 3.625 m. The total simulation time for each experiment is 9000 s. The first 2000 time steps are discarded to avoid transient behavior. The flux is obtained by counting the vehicles in the later 7000 time steps. Meanwhile, each result shown here is the value averaged over 20 experimental data in order to reduce stochastic influence.

According to actual statistics in traffic engineering, the values of accident rate AH under different rainfall intensities are in a range from 0.76 to 160 number/billion vehicle·km.[32] It means that comparable accident rate AH1 is transformed due to unity of units varies from 0.0532 to 11.2 (‰) number/vehicle· 5 km·7000 s. The simulated accident probabilities in rainy weather is in a range from 0.5 to 8.5 (‰) number/vehicle· 5 km·7000 s. Obviously the accident probability of the simulated CA model is in a range of the actual statistics. The validity is preliminarily proved.

Figure 10 shows a comparison of phase diagram between the actual statistics data and the simulation results, where the rainfall intensity is 0.007 mm/min and the inlet traffic volume is 2000 veh/h and the corresponding upper speed limits are 100 km/h and 70 km/h, respectively. The two fitting curves are basically the same. The validity of the proposed CA model is proved again.

Fig. 10. Comparison of phase diagram between the actual statistics and the simulation result.
4.1. Effect of rainfall

Figure 11 shows a comparison among flow-density plots, and figure 12 shows a comparison among speed-density plots. Figure 13 shows a comparison among the rainfall-intensity-dependent accident probabilities, where the inlet traffic volumes are 2000, 1500, 1000, and 500 veh/h, respectively. No VSL signal is input which means that the stable upper speed limit vmax1 is used, where vmax1 = 33 cells is corresponding to 120 km/h and vmax2 = 25 cells is corresponding to 90 km/h. The achieved findings are as follows.

Fig. 11. Comparison of flow-density plots.
Fig. 12. Comparison among speed-density plots. In Figs. 11 and 12, the curves “a”, “b”, “c”, “d” correspond to the rainfall intensities of 0, 0.04 mm/min, 0.2 mm/min, and 0.66 mm/min, respectively.
Fig. 13. Wrecked vehicles fraction Nac/N as a function of rainfall intensity.
4.2. Analysis of VSL

Figure 14 shows comparisons among rainfall-intensity-dependent accident probabilities obtained by using the different speed limit upper values. The inlet traffic volumes are 2000 veh/h for Fig. 14(a), 1500 veh/h for Fig. 14(b), 1000 veh/h for Fig. 14(c), and 500 veh/h for Fig. 14(d), respectively. The achieved findings are as follows.

Fig. 14. Rainfall-intensity dependent accident probabilities with VSLs of (a) 2000 veh/h, (b) 1500 veh/h, (c) 1000 veh/h, and (d) 500 veh/h. The curve “a” indicates the results of Nac/N which experimented with vmax1 = 120 km/h and vmax2 = 90 km/h, “b” indicates the results with vmax1 = 100 km/h and vmax2 = 70 km/h, “c” indicates the results with vmax1 = 80 km/h and vmax2 = 50 km/h, “d” indicates the results with vmax1 = 60 km/h and vmax2 = 40 km/h, “e” indicates the results with vmax1 = 40 km/h and vmax2 = 30 km/h.
4.3. Analysis of incoming flow control

Figure 15 shows comparisons among the rainfall-intensity-dependent accident probabilities obtained by using the different inlet traffic volumes. The upper speed limit values are 100(70) km/h for Fig. 15(a), 80(50) km/h for Fig. 15(b), 60(40) km/h for Fig. 15(c), and 40(30) km/h for Fig. 15(d), respectively. The achieved findings are as follows.

Fig. 15. Rainfall-intensity-dependent accident probabilities at (a) vmax1 = 100 km/h and vmax2 = 70 km/h, (b) vmax1 = 80 km/h and vmax2 = 50 km/h,(c) vmax1 = 60 km/h and vmax2 = 40 km/h, and (d) vmax1 = 40 km/h and vmax2 = 30 km/h. Curves “a”, “b”, “c”, and “d” indicate the results at inlet traffic volumes of 2500 veh/h, 1500 veh/h, 1000 veh/h, and 500 veh/h.
4.4. Analysis of control mode

Figure 16 shows the simulation results of the phase diagram in (inflow, rainfall intensity) space. The space can be divided into five regions. The traffic flow is free in region I and region II, while it is congested in region III, region IV, and region V. We can obtain the optimal strategy under different conditions.

Fig. 16. Phase diagram in (inflow, rainfall intensity) space.
5. Conclusions and perspectives

The micro-scale driving behaviors in rainy weather and possible vehicle rear-end and sideslip accidents are analyzed. The influences of traffic accident in rainy weather and the management strategies are studied by using an improved CA model for a two-lane freeway mainline. The simulation results indicate that controlling the incoming flow and inputting VSL signal are effective especially when there is a heavy rainstorm or short-time heavy rainfall. According to different rainfall and traffic demand, the appropriate control strategies should be adopted in order to reduce the probability of vehicle accidents and enhance traffic flux as well. These findings may provide reference values for freeway management and control.

The formula for the micro-scale driving behaviors in rainy weather is still relatively simple and realistic. Vehicle accidents do not really occur in the simulation and these dangerous situations are only calculated and considered to be the signal of the occurrence of accidents. These problems will be further studied in future.

Reference
[1] Brodsky H Hakkert A S 1998 Accid. Anal. Prev. 20 161
[2] Zhang W H Yan R Feng Z X Wang K 2016 Acta Phys. Sin. 65 090701 in Chinese
[3] Hjelkrem O A Ryeng E O 2016 Accid. Anal. Prev. 95 227
[4] Bergel-Hayat R Debbarh M Antoniou C 2013 Accid. Anal. Prev. 60 456
[5] Wan Q Li W Liang Q Wang H Li Z 2014 14th Cota International Conference of Transportation Professionals June 2014 Changsha, China 3743
[6] Keay K Simmonds I 2005 Accid. Anal. Prev. 37 109
[7] Wan H F Liu Z Wang H C 2013 Procedia Soc. Behav. Sci. 96 70
[8] Jaroszweski D McNamara T 2014 Trav. Behav. Soc. 1 15
[9] Cai X N Lu J J Xing Y Y Jiang C M Lu W J 2013 Procedia Soc. Behav. Sci. 96 2563
[10] Liu S X Chen W S Chi Q Y Yan H 2017 Acta Phys. Sin. 66 060501 in Chinese
[11] Lee J Y Chung J H Son B 2008 Accid. Anal. Prev. 40 1955
[12] Xu C C Wang W Liu P 2013 J. Safety Res. 46 135
[13] Martensen H Focant N Diependaele K 2016 Transport. Res. Procedia 14 96
[14] Fwa T F Kumar S S Ong G P Huang C J H 2008 Transportation research record, TRR 2068 109
[15] Baffet G Charara A Lechner D 2009 Control Eng. Pract. 17 1255
[16] Ma X Zheng W F Jiang B S Zhang J Y 2016 Chin. Phys. B 25 108902
[17] Sun X Y Zhu J F 2015 Acta Phys. Sin. 64 114502 in Chinese
[18] Zheng W F Zhang J Y Wang M W Tang D M 2014 Acta Phys. Sin. 63 228901 in Chinese
[19] Wang Y Chen Y Y 2015 Chin. Phys. B 24 038902
[20] Boccara N Fuks H Zeng Q 1997 J. Phys. A: Math. Gen. 30 3329
[21] Gokce S Kayacan O 2016 Chin. Phys. B 25 010508
[22] Nagatani T Sugiyama N 2013 Physica A 392 851
[23] Nagatani T 2015 Physica A 49 1
[24] Pang M B Zheng S S Cai Z H 2015 Physica A 433 161
[25] Pang M B Ye L H Pei Y N 2016 Chin. Phys. B 25 88901
[26] Zheng W F Zhang J Y 2015 Chin. Phys. B 24 058902
[27] Jung S Xiao Q Noyce D A 2011 Transportation research record, TRR 2237 134
[28] Peng P Li C W Yang S 2015 Fifth International Conference on Instrumentation and Measurement, Computer, Communication and Control September 18-20, 2015 Qinhuangdao, China 449
[29] Xiong J 1996 Auto. Eng. 18 6
[30] Green M 2000 Transport. Hum. Factors 2 195
[31] Ministry of Transport of People’s Republic of China 2014 Technical Standard of Highway Engineering (JTG B01 2014), 2015 Beijing China Communications Press 11 in Chinese
[32] Liu W 2015 Research on Traffic Safety Technology under Adverse Climate in Mountainous Areas Ph. D. Thesis Xi’an Chang’ an University in Chinese