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Estimating Rear-End Accident Probabilities at Signalized Intersections: A Comparison Study of Intersections With and Without Green Signal Countdown Devices a

Ying Ni & Keping Li

a

a

Key Laboratory of Road and Traffic Engineering of the Ministry of Education, Tongji University, Shanghai, China Accepted author version posted online: 27 Sep 2013.Published online: 27 May 2014.

Click for updates To cite this article: Ying Ni & Keping Li (2014) Estimating Rear-End Accident Probabilities at Signalized Intersections: A Comparison Study of Intersections With and Without Green Signal Countdown Devices, Traffic Injury Prevention, 15:6, 583-590, DOI: 10.1080/15389588.2013.845752 To link to this article: http://dx.doi.org/10.1080/15389588.2013.845752

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Traffic Injury Prevention (2014) 15, 583–590 C Taylor & Francis Group, LLC Copyright  ISSN: 1538-9588 print / 1538-957X online DOI: 10.1080/15389588.2013.845752

Estimating Rear-End Accident Probabilities at Signalized Intersections: A Comparison Study of Intersections With and Without Green Signal Countdown Devices YING NI and KEPING LI Key Laboratory of Road and Traffic Engineering of the Ministry of Education, Tongji University, Shanghai, China

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Received 23 April 2013, Accepted 13 September 2013

Objective: Rear-end accidents are the most common accident type at signalized intersections, because the diversity of actions taken increases due to signal change. Green signal countdown devices (GSCDs), which have been widely installed in Asia, are thought to have the potential of improving capacity and reducing accidents, but some negative effects on intersection safety have been observed in practice; for example, an increase in rear-end accidents. Methods: A microscopic modeling approach was applied to estimate rear-end accident probability during the phase transition interval in the study. The rear-end accident probability is determined by the following probabilities: (1) a leading vehicle makes a “stop” decision, which was formulated by using a binary logistic model, and (2) the following vehicle fails to stop in the available stopping distance, which is closely related to the critical deceleration used by the leading vehicle. Based on the field observation carried out at 2 GSCD intersections and 2 NGSCD intersections (i.e., intersections without GSCD devices) along an arterial in Suzhou, the rear-end probabilities at GSCD and NGSCD intersections were calculated using Monte Carlo simulation. Results: The results suggested that, on the one hand, GSCDs caused significantly negative safety effects during the flashing green interval, especially for vehicles in a zone ranging from 15 to 70 m; on the other hand, GSCD devices were helpful in reducing rear-end accidents during the yellow interval, especially in a zone from 0 to 50 m. Conclusions: GSCDs helped shorten indecision zones and reduce rear-end collisions near the stop line during the yellow interval, but they easily resulted in risky car following behavior and much higher rear-end collision probabilities at indecision zones during both flashing green and yellow intervals. GSCDs are recommended to be cautiously installed and education on safe driving behavior should be available. Keywords: signalized intersections, rear-end collision, green signal countdown devices, driving behavior, traffic safety

Background Rear-end accidents are the most common accident type at signalized intersections, because the diversity of actions taken increases due to signal change (Ma et al. 2010), the most typical representative of which is the “dilemma zone” problem. In order to assist drivers’ decision making during the critical phase transition interval, driver warning indicators, distance reference aids, or time reference aids at road side are commonly installed. One time reference aid, green signal countdown devices (GSCDs), display the remaining seconds of the current signal status through synchronization with the traffic signal controller, providing drivers with advance information on termination of the current phase. One example of GSCDs

Associate Editor Clay Gabler oversaw the review of this article Address correspondence to Ying Ni, Key Laboratory of Road and Traffic Engineering of the Ministry of Education, Tongji University, Shanghai, China, 201804. E-mail: ying [email protected]

at intersections can be found in Appendix 1 (see online supplement). GSCDs are now widely used in Asian countries, such as mainland China, Taiwan, Singapore, Malaysia, etc., and they are thought to have the potential to improve capacity and reduce accidents; however, in practice, some negative effects on intersection safety have been observed. Traffic accident data from 187 intersections in Taiwan from 2003 to 2006 showed that the accident rate during the green phase increased by almost 100 percent after the installation of GSCDs (Chen et al. 2007). Similarly, Chiou and Chang (2010) found that GSCDs lowered drivers’ tendency to stop, lengthened the dilemma zone, and resulted in higher rear-end crash rates at the end of the green signal. Do GSCD devices have negative impacts on safety? How and to what extent do GSCD devices affect rear-end accidents at intersections? This article aims to answer the above questions. A literature review of safety effects of GSCD devices and methodologies estimating rear-end accident potential are given in the next section, followed by methodology, results and discussion, and conclusions and recommendations.

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Literature Review There is some literature documenting the impacts of GSCDs on driving behavior and intersection safety from the perspective of red light violations, changes in the dilemma zone, etc.; however, the results varied in different countries and areas. Some argued that GSCDs were able to reduce red light violations (Limanond et al. 2010; Newton et al. 1997), whereas some provided contrary results (Long et al. 2011; Lum and Halim 2006). In a study in Taiwain, Chiou and Chang (2010) found that the dilemma zone was increased by about 28 m and the decision to cross became more inconsistent among the approaching vehicles, creating a potential risk of rear-end crashes. Koll et al. (2004) pointed out that a flashing green resulted in a minimal dilemma zone based on investigation at 10 intersections in Switzerland, Austria, and Germany. Ma et al. (2010) indicated that GSCDs could smooth drivers’ responses to the phase transition and eliminated the dilemma zones in Shanghai. Studies have been conducted on rear-end collisions based on historical accident data (Abdel-Aty and Abdelwahab 2004; Kostyniuk and Eby 1998; Yan et al. 2005) and accident frequency prediction models such as Poisson models, negative binomial models, zero-inflated Poisson regression, and negative binomial models (Mitra et al. 2002; Wang et al. 2003). Different from the above methods, microscopic modeling approaches aiming at exploring accident mechanisms have also been applied to intersection safety studies. Wang (1998) proposed that the probability of a rear-end accident was determined by 2 values: the probability of the leading vehicle’s deceleration because of some disturbance and the probability of the following vehicle’s failure to respond in time. Recent advances in traffic surveillance systems have allowed for obtaining vehicle trajectory data for more precise estimation of rear-end crash potential (Oh and Kim 2010). Previous studies have investigated the safety effects of GSCDs at signalized intersections and there are many mature models to understand rear-end accidents at intersections, but few studies have explicitly analyzed the effects of GSCDs on rear-end accidents. Thus, this article aims to develop a method for estimating rear-end accident probability during the phase transition interval at signalized intersections, explore the effects of GSCD on rear-end accidents, and propose recommendations for the use of GSCDs.

Methodology When the phase transition interval (usually referred to as the yellow signal) starts, a vehicle approaching an intersection makes either “go” or “stop” decision and takes the appropriate action. A rear-end collision is very likely to occur when a leading vehicle makes a stop decision and decelerates and the following vehicle fails to stop in the available stopping distance. Note that in this study we include only 2-vehicle accidents or the collision of the first 2 vehicles in an accident involving more than 2 vehicles. According to the premises of rear-end accidents proposed by Wang (1998), the occurrence of rear-end accidents during the phase transition interval is based on 2 premises: (1) the

Ni and Li leading vehicle makes a “stop” decision and decelerates and (2) the following vehicle fails to stop in the available stopping distance. Because the following vehicle’s failure to avoid a rear-end accident is conditional on the leading vehicle’s stop decision and the deceleration it takes, the probability (P) of a rear-end accident can be estimated using Eq. (1): P = P(S1 ) · P(A1 |S1 ) · P(F2 |S1 A1 ) + P(S1 ) · P(A2 |S1 ) ·P(F2 |S1 A2 ) + · · · P(S1 ) · P(An |S1 ) · P(F2 |S1 An ) (1) P(S1 ) denotes the probability that a leading vehicle makes a stop decision, P(A1 |S1 ), P(A2 |S1 ), . . ., P(An |S1 ) denotes the probability of a certain deceleration taken by the leading vehicle when making a stop decision, {A1 , A2 , . . ., An }is the set of possible decelerations used by the leading vehicle, P(F 2 |S1 A1 ), P(F 2 |S1 A2 ), . . ., P(F 2 |S1 An ) denotes the probability of the following vehicle’s failure to avoid a collision under the condition that the leading vehicle makes a stop decision and decelerates. Equation (1) can then be simply written as Eq. (2): P = P(S1 ) ·

n 

P(Ai |S1 ) · P(F2 |S1 Ai ).

(2)

i =1

In order to investigate how GSCDs affect the probability of rear-end accidents, a “with-and-without analysis” was launched in the study. Field data were firstly collected, followed by formulating probabilities of drivers’ go/stop decisions and the following vehicle’s failure to avoid a collision. Finally, the overall model was applied to calculate rear-end probabilities using a Monte Carlo simulation approach. Data Collection Study Sites The observations were conducted at 4 adjacent signalized intersections along an arterial, Xinghu Street in Suzhou, China (see Appendix 2, online supplement). The northern 2 intersections had GSCDs (i.e., GSCD intersections) and the southern 2 intersections had GSCDs (i.e., NGSCD intersections). The 4 intersections were chosen because they have representative and similar geometries, layout designs, signal timing, and traffic flow patterns, as shown in Appendix 3 (see online supplement). Passenger cars accounted for 98 percent of the traffic and only 2 percent were buses. The majority of observed vehicles at 4 intersections were the same because through traffic was the main stream. Additionally, skyscrapers nearby provided good conditions for video shooting. Signal indications at the 4 intersections followed the same sequence of “steady green–flashing green (FG; 3 s)–yellow (Y; 3 s)–red”; however, given the effects of flashing green on driver behavior (Koll et al. 2004), we considered the total 6 s of flashing green and yellow as the phase transition interval. Field Observation and Data Collection The observations were made from 4:30 p.m. to 6:00 p.m. on a Wednesday and 7:00 a.m. to 9:30 a.m. on a Thursday in March 2012. Four synchronized video cameras were used to videotape

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Table 1. Statistical analysis of collected parameters

Distance (m) GSCD NGSCD Time (s) GSCD NGSCD Speed (km/h) GSCD FG interval Y interval NGSCD FG interval Y interval Acceleration/deceleration (m/s2) GSCD FG interval Y interval NGSCD FG interval Y interval Headway (s) GSCD NGSCD (V ≤ 60 km/h) NGSCD (V > 60 km/h)

N

Min

Max

Mean

SD

Kolmogorov-Smirnov value

P value

2436 1372

0 0

90 90

42.69 42.62

30.50 30.14

— —

— —

— —

— —

2436 1372

0.044 0.005

5.998 5.943

2.593 2.362

1.708 1.449

1125 939

28.55 16.19

79.41 83.20

52.40 46.75

10.38 9.97

0.803 0.769

.540 (> .05) .595 (> .05)

592 503

15.99 25.58

77.59 90.76

52.19 50.54

11.51 12.73

0.560 0.636

.912 (> .05) .814 (> .05)

881 760

−7.14 −5.03

4.55 5.66

−0.62 −0.95

2.19 1.99

0.662 1.004

.773 (> .05) .266 (> .05)

469 394

−5.70 −5.41

4.55 5.14

−0.48 −1.07

2.18 2.38

0.682 0.639

.741 (> .05) .809 (> .05)

1946 775 302

0.32 0.50 0.39

11.72 12.78 11.91

3.39 2.71 4.10

2.63 1.96 3.22

— — —

— — —

Note: FG refers to “flashing green,” Y refers to “yellow.”

the traffic at southern approaches of all intersections, and the cameras were sited to cover at least 90 m upstream to the intersection stop line. A total of 7 virtual detection lines were superimposed at each video image with the spacing of 15 m, as shown in Appendix 4 (see online supplement). The timestamps when vehicles touched each detection line were recorded sequentially. The same vehicle was observed at most 7 times; as a result, a total of 2436 and 1372 samples associated with 385 and 235 vehicles at GSCD and NGSCD intersections were obtained. Based on the recorded distance from the stop line (D) and corresponding time (T), vehicular speeds, accelerations/decelerations, and headways were obtained. The final descriptive statistics are shown in Table 1. Statistical Analysis of Speeds, Acceleration/Deceleration, and Headways Speeds Vehicular speeds were calculated by dividing 15 m by the time difference as the same vehicle touched 2 adjacent detection lines. Speeds during FG and Y intervals at GSCD and NGSCD intersections were collected and validated using the Kolmogorov-Smirnov test; all of them followed a normal distribution, as shown in Table 1. Independent sample t test revealed that speeds during the FG interval and Y interval had significant differences at GSCD intersections (t = 5.127, P < .0001) but not at NGSCD intersections (t = −0.831, P = .407). Additionally, the speeding rate at GSCD and NGSCD intersections are 15 and 16 percent, respectively, with a speed limit of 60 km/h. Accelerations/Decelerations Accelerations/decelerations were roughly estimated according to the speed change between 2 consecutive sections. Accel-

erations/decelerations during FG and Y intervals at GSCD and NGSCD intersections all followed a normal distribution, as shown in Table 1. Accelerations/decelerations during FG and Y intervals had significant differences at GSCD intersections (t = 2.168, P = .031) but not at NGSCD intersections (t = 1.914, P = .058). According to the results of independent sample t test, however, there were no significant differences between GSCD and NGSCD intersections during the FG interval (t = 0.035, P = .972) or the Y interval (t = 0.493, P = .623). Headways Headways were obtained by calculating time differences between 2 successive vehicles as they touched the same detection line. Headways were classified into several groups according to different speed ranges (from 0 to 90 km/h, at 10 km/h intervals) and the analysis of variance showed that headways at GSCD intersections had no significant differences despite speed differences, though they were significantly different at NGSCD intersections when speeds are lower and higher than 60 km/h. The mean headway was 2.71 s when vehicle speed was lower than 60 km/h, and it was 4.10 s at speeds higher than 60 km/h. Al-Ghamdi (2001) found that the Erlang distribution could best model headways at high flow levels, which was consistent with conclusions drawn by Akcelik et al. (1996) and Hamed and Jaber (1997). Because observed traffic flow in the study was high (ca. 800 pcu/h for 2 lanes), headways were assumed to follow an Erlang distribution, which was validated by chi-square test at a 95 percent confidence level that headways at GSCD and NGSCD intersections followed a second-order Erlang distribution with different values of λ; the curves of probability density functions are shown in Figure 1.

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Ni and Li As shown in Eqs. (4) and (5), the approaching speed positively affects a driver’s go decision, indicating that the higher speed, the higher probability that a driver makes a go decision and crosses the intersection. In contrast, both distance from the stop line and time since the flashing green starts are negative factors, suggesting that vehicles that are far from the stop line and approaching the intersection at the end of the transition interval are more prone to make a stop decision. The car-following situation has opposite effects on drivers’ decisions at GSCD and NGSCD intersections. When a vehicle is in a car-following situation, it is more likely to make a go decision at GSCD intersections but more prone to stop at NGSCD intersections. It can be deduced that GSCD devices have some influence on car-following behavior; more detailed analysis is provided in the Discussion section.

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Fig. 1. Probability density functions of headway distribution.

Conditional Probability of Failure to Avoid a Collision

Probability of Drivers’ Stop/Go Decision Assume that a driver’s stop/go decision remains unchanged for all repeated observations in the study. To understand driver decisions during the phase transition interval, the study employed a binary logistic regression to identify the key factors on driver decision. The model can be expressed as follows: Logi t( p) = a0 + a1 D + a2 T + a3 V + a4 C F + a5 S +a6 S × D + a7 S × T + a8 S ×V + a9 S × C F,

Assume ξ to be the random variable of event that the leading vehicle decelerates, and the deceleration is a continuous variable following a probability density function φ(x). P(η|ξ = x) denotes the probability that the following vehicle fails to avoid a collision under the condition that the leading vehicle takes a certain deceleration: n 

(3)

where p denotes the probability that a driver makes a go decision; Logit(p) is the odds ratio of p; D is the distance from the stop line (m); T represents time since the flashing green starts (s); V represents the vehicle’s approaching speed (m/s); CF denotes whether a vehicle is in a car-following situation or not; 3 s was adopted as critical headway for judging carfollowing distance according to the Highway Capacity Manual (2000) and domestic research done by Yu et al. (2009). If the headway time is less than 3 s, CF = 1; otherwise, CF = 0. S is a dummy variable; S = 1 represents the intersection with GSCD; otherwise, S = 0; a0 to a9 are estimated parameters. The last 4 items in Eq. (3) represent the interaction effects between D, T, V , CF, and the presence of GSCD. The estimation results of Eq. (3) are listed in Appendix 5 (see online supplement). The Hosmer and Lemeshow test shows that the model provides a good fit (chi-square = 2.179, p = 0.975 > 0.05); note that all explanatory variables and interaction terms are significant with the anticipated signs to the Logit(p). The final logistic regression models of drivers’ stop/go decision at GSCD and NGSCD intersections can be presented by Eqs. (4) and (5):

 P(Ai |S1 ) · P(F2 |S1 Ai ) =

i =1

ar

−∞

(6) where ar is the required minimum deceleration of the leading vehicle in order to stop safely before the red signal starts, depending on its the distance from stop line (D), current speed (V ), and remaining time until red starts (t0 ), as shown in Eq. (7): ar =

2(D − Vt0 ) . t2

(4)

NGSCD : Logi t( p) = 1.145 − 0.100D − 1.159T +0.589V − 1.225C F.

(5)

(7)

As pointed out by Brill (1972), the minimum deceleration required by the vehicle (k + 1) increases as vehicle k’s deceleration increases; therefore, it can be deduced that if the minimum deceleration required by the following vehicle exceeds the available maximum deceleration it can reach, a rear-end accident cannot be avoided. We define deceleration taken by the leading vehicle under the above circumstance as critical deceleration (ac ), and P(η|ξ = x) = 1 if the leading vehicle’s deceleration exceeds ac ; otherwise, P(η|ξ = x) = 0; therefore, Eq. (7) can be written as follows: n 

 P(Ai |S1 ) · P(F2 |S1 Ai ) =

i =1

GSCD : Logi t( p) = −1.307 − 0.122D − 0.564T +0.698V + 1.214C F

φ(x) · P(η |ξ = x) d x,

max(ar ,ac )

−∞

φ(x)d x.

(8)

Given normal distribution of the accelerations/decelerations discussed previously, there is the probability density function φ(x) = √

1 2π σ

e

−(x−μ)2 2σ 2

,

(9)

Rear-End Accidents at Signalized Intersections

587

Fig. 3. Analytical diagram of vehicle braking (change of deceleration). Fig. 2a. Initial positions of 2 adjacent vehicles.

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When the leading vehicle decelerates with a deceleration a1 , the distance moved in a time interval t can be expressed as where the values of acceleration/deceleration (x) are between −7.8 and 6.0 m/s2. For the FG interval, μ = −0.58, б = 2.18, and for the Y interval, μ = −0.98, б = 2.10. Determination of Critical Acceleration/Deceleration Figures 2a and 2b describe the relative positions of 2 adjacent vehicles before and after the leading vehicle brakes and the following vehicle responds accordingly. Assume that the initial distance between 2 vehicles is h0 ; then the leading vehicle brakes and moves for a distance of D1 in a time interval t; meanwhile the following vehicle driver perceives, reacts, and moves forward for a distance of D2 , and the final distance between 2 vehicles becomes h. If h > 0, it is safe; otherwise, a rear-end accident occurs. Assume that the following vehicle’s braking procedure follows Figure 3, where the X-axis is time and the Y -axis is deceleration. The performance of the driver in the following vehicle can be viewed as 3 successive components: perception of changes in the traffic enviornment, the decision according to these changes, and an action (Wang et al. 2003). The first 2 components correspond to the driver’s reaction time (tr ). Wang et al. (2003) assumed the drivers’ reaction time follows a Weibull distribution. Lu et al. (2011) validated drivers’ reaction times as a log normal distribution of (0.17, 0.44) according to a Chinese context, and Lu et al.’s (2011) results were used in the study. When a driver takes an action, it also takes time until the vehicle reaches its maximum deceleration and finally stops, which includes brake system response time (tb ), set as 0.05 s; and the time needed from the response of brake system to the acceleration reaches the maximum value (tb  ), set as 0.2 s, according to the Roadway Design Code (2006); and braking time until the following vehicle stops (tc ).

1 D1 = v1 t + a1 t 2 . 2

The distance moved by the following vehicle D2 can be expressed by Eq. (11), depending on at what time the accident occurs:

D2 =

⎧ v2 t ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ v2 tr + v2 tb + 12 v2 (t − tr − tb ) ⎪ ⎪ ⎪ ⎪ ⎨

0 < t < tr + tb tr + tb ≤ t < tr +tb + tb

. v2 tr + v2 tb + 12 vtb tr + tb + tb ≤ t ≤ tr ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ +v2 (t − tr − tb − tb ) +tb + tb + tc ⎪ ⎪ ⎪ ⎪ ⎩ + 12 a2 (t − tr − tb − tb )2 (11) Then, we get the final distance h between 2 vehicles, expressed in Eqs. (12) and (13): h = h 0 + D1 − D2 − l1 h 0 = v2 th ,

(12) (13)

where v1 , v2 and a1 , a2 are speeds and decelerations of the leading vehicle and following vehicle, respectively; th is the headway of 2 vehicles; and l 1 is the length of the leading vehicle. Assume that a2 equals the maximum deceleration, determined by the product of wheel–road adhesive coefficient (ϕ) and gravity acceleration (g); the value of ϕ is 0.80 when the road surface is dry according to the Roadway Design Code (2006), and g is 9.8 m/s2; thus, the maximum deceleration equals 7.84 m/s2. Considering the worst situation, we get the critical acceleration (deceleration) of the leading vehicle: 2(V2 − V1 )Tc + 7.84(Tc − Tb  )2 + 2l1 − 2V2 th − V2 tb . Tc2 (14) Note that Tb  = tr + tb + tb  , and Tc = Tb  + tc , as shown in Figure 3. ac =

Fig. 2b. Final positions of 2 adjacent vehicles after the leading vehicle brakes.

(10)

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Ni and Li

Overall Model and Monte Carlo Simulation Based on the previous work, the overall model can be written as follows:

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 P = 1−

 · −Logi t( p) 1

1+e

max(ar, ac )

−∞



1 2π σ

e

−(x−μ)2 2σ 2

d x. (15)

It is complicated to calculate the P value directly; therefore, a Monte Carlo simulation approach was adopted using MATLAB software. The Monte Carlo simulation technique produces samples generated from given probability distributions. The average of the output variable (rear-end collision probability in this article) can be used as an estimator of system evaluation. A total of 20,000 pairs of vehicles (one leading vehicle and one following vehicle) were simulated for GSCD and NGSCD intersections. Each vehicle was randomly assigned a distance, an entering time, a speed, and a headway according to the following rules. • Distance from stop line. The leading vehicle was randomly assigned a distance from 0 to 90 m at 0.5-m intervals, and the following vehicle’s distance was set by adding the result of multiplying its current speed and headway by the leading vehicle’s distance. • Time. The leading and following vehicles entered at the same time; the entering time was 0 to 6 s at 0.1-s intervals. • Speed. The leading vehicle’s speed was normally distributed according to the parameters listed in Table 1. The following vehicle’s speed was related to the speed of the leading vehicle and an adjusting factor following normal distribution N (1.0, 0.3) was adopted according to the statistical results of observed data. • Headway. Headways followed a second-order Erlang distribution; the curves of the probability density function are shown in Figure 1.

Results and Discussion Results Based on the results of Monte Carlo simulation, diagrams indicating the correlation between rear-end probability, time, and distance for GSCD and NGSCD intersections are shown in Figurea 4a and 4b. Dots on the curves are the average probability values for the first (consisting of 10 “0.1 s”) second, and third second of the flashing green interval (namely, FG1, FG2, FG3) and yellow interval (namely, Y1, Y2, Y3). Rear-end collision probability has the lowest value near the stop line at the onset of the flashing green and rises with the passage of time and the increase in distance from the stop line, which is common at both GSCD and NGSCD intersections. The difference lies in the following: (1) rear-end collision probability increases more sharply during the FG interval at GSCD intersections with the increase in distance; (2) rearend collision probability increases steadily from FG1 to Y3 at NGSCD intersections, and the probability jumps to a higher value from FG3 to Y1 at GSCD intersections.

Fig. 4a. Probability of rear-end collisions at GSCD intersections.

To explore how GSCD devices affect the rear-end collision potential, a comparison of rear-end accident probabilities between GSCD and NGSCD intersections was carried out, given the relative difference of rear-end accident probability between two intersections as R: R=

PG SC D − PNG SC D × 100%. PNG SC D

(16)

If R > 0, GSCDs result in higher probability of rear-end accidents; otherwise, GSCDs help to reduce such accidents. The distribution of R during FG and Y intervals is shown in Appendixes 6 and 7 (see online supplement). R > 0 appears during almost the whole FG interval. The R value is extremely high at the onset of the flashing green and decreases from FG1 to FG3. The R value is lower at 2 ends of the X-axis (distance axis) than in the middle. Rearend collision probability is almost 3–5 times higher at GSCD intersections than at NGSCD intersections in a zone ranging from 15 to 70 m during FG1. R < 0 occurs from the start of FG3 in a zone from 0 to 20 m. The situation is different during the Y interval. R has the highest value of ca. 50 percent during Y1 in a zone ranging

Fig. 4b. Probability of rear-end collisions at NGSCD intersections.

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from 30 to 80 m and decreases from Y1 to Y3. The zone with R > 0 shrinks to 50–90 m in the end of Y3. Meanwhile, R < 0 occurs in a zone from 0 to 10 m at the onset of yellow, which increases from Y1 to Y3 and finally covers an area of 0–50 m from the stop line. The closer a vehicle is to the stop line, the lower the R value is. The lowest R value is around −70 percent, occurring in an area ca. 10 m from the stop line during Y3. The results suggest that, on the one hand, GSCD devices cause significantly negative safety effects during the flashing green interval, especially for vehicles in a zone ranging from 15 to 70 m. On the other hand, GSCD devices are helpful to reduce rear-end accidents during the yellow interval, especially in a zone from 0 to 50 m. Discussion In this section, how GSCD devices influence car-following behavior and dilemma zone distribution will be further discussed, because they are the most important factors contributing to the above results. Car-Following Behavior Car-following headway, which is headway less than 3 s as defined previously, was analyzed. Mean car-following headway at GSCD and NGSCD intersections is 1.05 and 1.81 s with standard deviations of 0.32 and 0.65 s, respectively. Independent sample t test reveals that car-following headways at GSCD intersections are significantly smaller than those at NGSCD intersections (t = −10.029, P < .0001). Scatterplots of vehicle speed and car-following headway of GSCD and NGSCD intersections are shown in Figures 5a and 5b. Given the common speed range (40 and 60 km/h), carfollowing headways at NGSCD intersections range from 0.5 to 3.0 s, but the dots are more assembled around 0.5 to 1.5 s at GSCD intersections. It shows that drivers at GSCD intersections are prone to accept smaller headways, whereas at NGSCD intersections drivers adopt safer headways depending on the current speeds. Thus, the availability of information

Fig. 5a. Scatterplots of vehicle speed and car-following headway of GSCD intersections.

Fig. 5b. b. Scatterplots of vehicle speed and car-following headway of NGSCD intersections.

on remaining green time stimulates risky car-following behavior and results in a high probability of rear-end collisions in indecision zones. Dilemma Zone Distribution The dilemma zone distribution has always been regarded as the most critical indicator for intersection safety. In other words, vehicles in dilemma zones are more likely to be involved in rear-end collisions. According to previous studies, there are 2 types of dilemma zones: (1) Type I was first referenced in the literature by Gazis et al. (1960), who described the situation of a driver who, when presented with a yellow when approaching a signalized intersection, would be unable to safely pass through the intersection or stop prior to the stop bar. According to the theoretic definition and calculating model of the Type I dilemma zone, there were no differences between 2 adjacent intersections, proposed in Homburger (1985), because they had similar traffic compositions, traffic pattern, signal timings, and speed limits. (2) Type II describes the area in which the driver experienced difficulty making the correct stop/go decision, which was typically defined by Zegeer and Deen (1978) as the area upstream from the stop line between which 10 and 90 percent of the drivers would stop in response to the yellow light. In the study, a Type II dilemma zone, also called the indecision zone, was studied, and we considered it for both yellow and flashing green indications. Given a vehicle speed of 50 km/h, the probability curves of drivers making a stop decision during the flashing green and yellow intervals at GSCD and NGSCD intersections were established considering whether a vehicle is in a car-following status or not, as shown in Appendixes 8–11; the Type II dilemma zones (indecision zones) are listed in Table 2. It can be seen that indecision zones at GSCD intersections are shorter and farther from the stop line than those at NGSCD intersections during both flashing green and yellow intervals. Furthermore, the car-following situation has different impacts on indecision zones: indecision zones move toward the stop line at NGSCD intersections when vehicles are in

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Table 2. Type II dilemma zone (indecision zone) distribution Flashing green indication

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GSCD intersections NGSCD intersections

Yellow indication

Car-following (m)

Non-car-following (m)

Car-following (m)

Non-car-following (m)

50–90 30–90

40–85 40–90

35–80 10–60

25–70 10–75

car-following situations, whereas they move toward the upstream direction at GSCD intersections. Drivers are less likely to make a stop decision at GSCD intersections during the flashing green interval and accept very small car-following headways, which increase the probability of rear-end collisions at indecision zones than at NGSCD intersections. Concerning the yellow interval, more than 90 percent of drivers make a go decision when they are within 45 m of the stop line (at a speed of 50 km/h) at GSCD intersections; however, this area is exactly the indecision zone for vehicles at NGSCD intersections and therefore, NGSCD intersections have higher probability of rear-end collisions in this area during the yellow interval than GSCD intersections. This study proposed a microscopic modeling approach to estimate rear-end accident probability during the phase transition interval at signalized intersections and investigated the effects of GSCD devices on rear-end collision potential. The results indicated that GSCD devices helped shorten indecision zones and reduce rear-end collisions near the stop line during the yellow interval, but they easily evoked risky car-following behavior that resulted in much higher rear-end collision probability at indecision zones during both flashing green and yellow intervals. Based on the above research findings, we recommend that (1) GSCD devices should be cautiously installed, considering their negative effects on rear-end accidents; (2) car-following headways must be controlled at a safe level; (3) more attention should be paid to traffic education, especially to educate drivers with regard to phase transitions interval and reducing their dependence on countdown devices.

Funding This research was carried out with support of the National High Technology Research and Development Program of China (Project No. 2011AA110305).

Supplemental Material Supplemental data for this article can be accessed on the publisher’s website.

References Abdel-Aty M, Abdelwahab H. Modeling rear-end collisions including the role of driver’s visibility and light truck vehicles using a nested logit structure. Accid Anal Prev. 2004;36:447–456. Akcelik R, Chung E, Besley M. Performance of roundabouts under heavy demand conditions. Road Transp Res. 1996;5:36–50. Al-Ghamdi AS. Analysis of time headways on urban roads: case study from Riyadh. J Transp Eng. 2001;127:289–294.

Brill E. A car-following model relating reaction times and temporal headways to accident frequency. Transp Sci. 1972;6:343–353. Chen IC, Chang KK, Chang CC, Lai CH. The Impact Evaluation of Vehicular Signal Countdown Displays. Taiwan: Institute of Transportation, Ministry of Transportation and Communications; 2007. Chiou YC, Chang CH. Driver responses to green and red vehicular signal countdown displays: safety and efficiency aspects. Accid Anal Prev. 2010;42:1057–1065. Gazis D, Herman R, Maradudin A. The problem with the amber signal light in traffic flow. Oper Res. 1960;8:112–132. Hamed MM, Jaber SA. Modeling vehicle–time headways in urban multilane highways. Road Transp Res. 1997;6:32–44. Highway Capacity Manual. Washington, DC: Transportation Research Board; 2000. Homburger WS, ed. Transportation and Traffic Engineering Handbook. 2nd ed. Englewood Cliffs, NJ: Prentice Hall; 1985. Koll H, Bader M, Axhausen KW. Driver behavior during flashing green before amber: a comparative study. Accid Anal Prev. 2004;36:273–280. Kostyniuk L, Eby D. Exploring Rear-End Roadway Crashes From the Driver’s Perspective. Ann Arbor, MI: Human Factors Division, Transportation Research Institute; 1998. Limanond T, Prabjabok P, Tippayawong K. Exploring impacts of countdown timers on traffic operations and driver behavior at a signalized intersection in Bangkok. Transp Policy. 2010;17:420–427. Long KJ, Han LD, Yang Q. Effects of countdown timers on driver behavior after the yellow onset at Chinese intersections. Traffic Inj Prev. 2011;12:538–544. Lu SW, Zhang LF, Fang SE. Probabilistic analysis and risk evaluation of highway rear-end collision. J Tongji Univ (Nat Sci). 2011;39:1150–1154. Lum KM, Halim H. A before-and-after study on green signal countdown device installation. Transp Res Part F Traffic Psychol Behav. 2006;9:29–41. Ma WJ, Liu Y, Yang X. Investigating the impacts of green signal countdown devices: empirical approach and case study in China. J Transp Eng. 2010;136:1049–1055. Mitra S, Chin HC, Quddus MA. Study of intersection accidents by maneuver type. Transp Res Rec. 2002;1784:43–50. Newton C, Mussa RN, Sadalla EK, Burns EK, Matthias J. Evaluation of an alternative traffic light change anticipation system. Accid Anal Prev. 1997;29:201–209. Oh C, Kim T. Estimation of rear-end crash potential using vehicle trajectory data. Accid Anal Prev. 2010;42:1888–1893. Roadway Design Code. Beijing, China: China Communication Press; 2006. JTG D20-2006. Wang Y. Modeling Vehicle-to-Vehicle Accident Risks Considering the Occurrence Mechanism at Four-Legged Signalized Intersections [dissertation]. Tokyo, Japan: University of Tokyo; 1998. Wang Y, Ieda H, Mannering F. Estimating rear-end accident probability at signalized intersections: occurrence-mechanism approach. J Transp Eng. 2003;129:377–384. Yan X, Radwan E, Abdel-Aty M. Characteristics of rear-end accidents at signalized intersections using multiple logistic regression model. Accid Anal Prev. 2005;37:983–995. Yu Q, Liu J, Rong J. A car-following criteria at a signalized intersections in Beijing. Paper presented at: ICCTP 2009: Critical Issues In Tran sportation Systems Planning, Development, and Management; 2009. Zegeer CV, Deen RC. Green-extension systems at high-speed intersections. ITE J. 1978;48:19–24.

Estimating rear-end accident probabilities at signalized intersections: a comparison study of intersections with and without green signal countdown devices.

Rear-end accidents are the most common accident type at signalized intersections, because the diversity of actions taken increases due to signal chang...
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