IATSS Research 37 (2013) 61–67
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IATSS Research
Modeling drivers' passing duration and distance in a virtual environment Haneen Farah ⁎ Department of Transport Sciences, KTH-Royal Institute of Technology, Teknikringen 72, SE-100 44 Stockholm, Sweden
a r t i c l e
i n f o
Article history: Received 7 June 2012 Received in revised form 20 December 2012 Accepted 28 March 2013 Keywords: Passing duration Passing distance Driver behavior modeling Two-lane highways Driving simulator
a b s t r a c t In many countries two-lane rural highways constitute a large proportion of the road network. One of the most fatal crash types is head-on collisions. Some of these head-on collisions are caused by failed passing maneuvers, when a driver does not succeed to complete the pass safely. Detailed observation of drivers' passing behavior in reality is difficult and complex. This study uses a driving simulator to collect detailed data on drivers' passing behavior. Using this data, empirical models explaining passing duration and distance were developed and estimated. These models take into account the impact of the traffic conditions, geometric design, and drivers' socio-demographic characteristics. The results revealed that the passing duration and distance of older drivers are significantly higher than younger drivers. The passing duration and distance are significantly affected by the traffic related variables of the subject, front, and opposing vehicles. The duration and passing distance increase when drivers initiate the passing maneuvers from a larger following distance from the front vehicle. Driver gender, road curvature, and types of front and opposing vehicles were not found to have a statistically significant impact on the passing duration and distance. The time that takes the driver to arrive to the critical position, or the point of no return, from the moment of start passing is equal to 41.7% of the time needed to complete the passing maneuver, higher compared to the value suggested by AASHTO (33%). This has important implications on safety. The main contribution of this paper is in the empirical models developed for passing duration and distance which highlights the factors that affect drivers' passing behavior and can be used to enhance the passing models in simulation programs. © 2013 International Association of Traffic and Safety Sciences. Production and hosting by Elsevier Ltd. All rights reserved.
1. Introduction Two-lane, two-way roads constitute a major part of the road network in most countries [1]. A fast traveling vehicle overtakes a lead slower vehicle, on this type of roads, by traveling on the traffic lane designated for the opposing traffic. Thus, this maneuver involves a risk of a head-on collision with opposing traffic, and therefore has a direct impact on safety. About 20% of the fatal crashes that occurred on two-lane rural highways in the US are head-on collisions, in which passing is one main leading cause to this type of crashes [2]. In the OECD (Organization for Economic Co-operation and Development) European countries this percentage is even higher, reaching 25% [3]. This maneuver is considered as one of the most complex maneuvers on this type of roads [4] because the passing vehicle needs to ⁎ Tel.: +46 8 790 79 77; fax: +46 8 21 28 99. E-mail address:
[email protected]. Peer review under responsibility of International Association of Traffic and Safety Sciences.
adapt its speed and position so that it could complete the passing maneuver safely. A road segment which provides few opportunities for passing could lead to the causation of platoons and to a reduction in road capacity and its level of service. This has also implications on fuel consumption. Therefore, the design of passing sight distances is a very important element of two-lane highways. This topic has been dealt with extensively by safety and traffic operational researchers as discussed in the following paragraphs. According to AASHTO [1] the passing sight distance is composed of four elements: the distance the passing driver travels during the perception and reaction time and the initial acceleration to the point of encroachment on the left lane (d1), the distance traveled on the opposing lane (d2), the distance at the end of the passing maneuver between the passing and opposing vehicle (d3), and the distance traveled by the opposing vehicle for two-thirds of the time the passing vehicle occupies the left lane (d4). Many other analytical models for passing sight distance were developed in the last four decades. Harwood et al. [5] conducted a comprehensive review of passing sight distance models developed between 1971 and 1998 summarized in a report for the National Cooperative Highway Research Program (NCHRP). The main purpose was to examine the adequacy of the AASHTO Green Book models knowing that they are based on old
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H. Farah / IATSS Research 37 (2013) 61–67
data and have not been revised for many years. The authors reviewed more than 12 models and highlighted for each model the conceptual approach used, the analytical models that have been developed, the assumed values of the model parameters, and a critique of each model. The authors found that the two models developed by Glennon [6] and Hassan et al. [7] were the most appropriate alternatives to the AASHTO models. These models recognize that drivers might abort a passing maneuver at an early stage of passing, before reaching the critical position. Glennon [6] defined the critical position as the location where the sight distance needed to continue the passing is equal to the sight distance needed to abort the passing. Hassan et al. [7] proposed a broader definition of the critical position accounting for situations where the critical position, as defined by Glennon, occurs beyond the abreast position. The abreast position is defined as when the passing vehicle is at a position alongside the front vehicle. In these cases, the authors suggested that the critical position be defined as the location where the two vehicles are abreast because it is unlikely that a passing driver would abort a passing maneuver when the front bumper of his vehicle is ahead of the front bumper of the front vehicle. Hegeman [3] analyzed 26 accelerative and 6 flying passing maneuvers on two-lane rural roads using an instrumented vehicle and found that the average duration of accelerative passing is 7.9 s with a standard deviation of 1.5 s, and the average duration of flying passing maneuvers is 6.8 s with a standard deviation of 1.4 s However, the author did not develop models that explain the duration or distance of passing maneuvers. Polus et al. [8] studied completed passing maneuvers to determine the required sight distances for diverse combinations of design speeds and traffic conditions based on estimates of passing distances. They found that passing distances depend on the speed of the vehicle in front. The mean passing distance was found to be 254 m with a standard deviation of 80.9 m. Harwood et al. [5], in the same report prepared for the NCHRP, also present their results of a field study on passing maneuvers on two-lane highways at seven sites in Missouri including 12 passing zones, and eight sites in Pennsylvania including 16 passing zones. The data collection was conducted under daytime and off-peak conditions. They analyzed 153 passing maneuvers in Missouri and 149 in Pennsylvania, in long passing zones (300 m. or more), and 45 passing maneuvers in Missouri and 20 in Pennsylvania, in short passing zones (between 120 and 240 m.). They also analyzed 7 aborted passing maneuvers. The authors reached several conclusions that have direct implications on the design criteria according to AASHTO. For example, AASHTO design criteria are based on the assumption that the speed differential between the subject and front vehicles is equal to 16 km/h, while the authors found that this value is closer to 19 km/h. Moreover, AASHTO assumes that the travel time on the left lane is between 9.3 and 11.3 s and that it increases with higher driving speeds, while the authors found that the mean is 9.9 s, and that there is no correlation between the travel time on the left lane and the driving speed. Therefore, the authors suggest modifying AASHTO Green Book according to their findings. They also found that the mean passing duration is 10 s with a standard deviation of 2.8 s, and the mean passing distance is 282 m with a standard deviation of 75 m. A recent study by Llorca and Garcia [9] included detailed registration of the trajectories of passing and passed vehicles using 6 fixed video recording cameras, installed next to 4 passing sections in the surrounding of Valencia, Spain in 2010. 234 passing maneuvers were observed, however full trajectories of vehicles were complete for only 58 maneuvers. The authors developed multiple linear regression models for explaining passing time durations and distances. The explanatory variables that were found to have a significant impact on the time of travel on the left lane included the type of the impeding vehicle, the passing zone length, and the speed differential between the passing and the impeding vehicle. The distance traveled
on the left lane on the other hand was found to be a function of the vehicle type, the passing zone length and the speed of the impeding vehicle. As can be seen most of the models developed for passing sight distance were analytical models based on equations of motion, or studies that collected field data on passing maneuvers and analyzed their duration and distance as a function of mainly traffic related variables. Very few studies modeled passing duration and distance as a function of traffic, geometric, and drivers' characteristics simultaneously. The rest of the paper is organized as follows; Section 2 presents the research methodology which describes the experiment, data collection and model formulation. This is followed by Section 3 which presents the results, and finally Section 4 concludes the study, presents the limitations and suggests further directions for research. 2. Research methodology The main objective of this study is to model the passing duration and passing distance on two-lane highways as a function of driver, geometric and traffic characteristics. The following paragraphs describe the research methodology adopted in this study. 2.1. Experiment design Collecting detailed data of passing maneuvers, including the trajectories of the passing, passed, and opposing vehicles, in real life is a difficult, complex, and tedious task. Also, it would require a relatively long period of time to capture enough observations for a firm analysis to be conducted. There are multiple advantages for using simulators in driving behavior research, mainly, the safe environment and the ability to control the factors that can affect the study results. Driving simulators enable the investigation of effects of non-existent road elements, and risky situations, and drivers can be repeatedly confronted with events that infrequently occur in reality. In the context of passing behavior, data collected with driving simulators have been used by several authors. For example, Jenkins and Rilett [10] used simulator data to develop a classification of passing maneuvers, Bar-Gera and Shinar [11] evaluated the impact of speed difference between the lead and subject vehicle on drivers' desire to pass, Farah et al. [12] developed a passing gap acceptance model that takes into account the impact of the road geometry, traffic conditions and drivers' characteristics, Bella and D'Agostini [13] used interactive fixed-base driving simulator to analyze rear-end collision risk under various traffic and road geometric conditions, and Vlahogianni and Golias [14] studied the overtaking behavior of
Fig. 1. Snapshot from the driving simulator scenario.
H. Farah / IATSS Research 37 (2013) 61–67 Table 1 Factors included in the Experimental design. Factor
Level High
Geometric design Gaps in the opposing lane
Speed of front vehicle
Speed of opposing vehicle
Low
Lane width: 3.75 m., shoulder width: 2.25 m. Curve radius: 1500–2500 m. Curve radius: 300–400 m. Drawn from truncated negative exponential distributions Mean: 10.3 s Mean: 18.0 s Min: 5.0 s, max: 25.0 s Min: 9.0 s, max: 31.0 s Drawn from uniform distributions 67% between 80 and 33% between 80 and 120 km/h 120 km/h 33% between 40 and 80 km/h 67% between 40 and 80 km/h Drawn from uniform distributions 67% between 80 and 33% between 80 and 120 km/h 120 km/h 33% between 40 and 80 km/h 67% between 40 and 80 km/h
young drivers in two-lane highways and the factors influencing their decisions to overtake. Therefore, in this study it was decided to utilize the STISIM [15], a low-cost fixed-base, interactive driving simulator. The STISIM has a 60° horizontal and 40° vertical display of a simulated driving scene projected onto a wall 3.5 m in front of the driver. The image was continually updated at a rate of 30 frames per second. Different simulator scenarios with different combinations of geometric and traffic conditions were designed for the experiment. All designed segments were two-lane highway segments, each segment of a total length of 7.5 km, with no intersections, and on a level terrain. The scenarios were designed with good weather conditions and good visibility (day time) as shown in Fig. 1. Previous studies [8,11,12,16] showed that passing maneuvers are affected by the speeds of vehicles, mainly the lead and opposing vehicles, by the gaps available for passing on the opposing lane, and by the road geometric design. Therefore, these variables were considered as the main factors in the experimental design. Thus, a full factorial design with 4 factors in 2 levels (High, Low), as shown in Table 1, which produces 16 different scenarios, was applied. However, following Farah et al. [12] and Farah and Toledo [16], it was decided that each participant will complete only 4 scenarios in order to limit the experiment duration to be less than one hour. A useful method for cases where the number of total scenarios (16 in this case) is more than the number of scenario runs in each block for each driver (4 in this case) is named the partial confounding method [17] where some effects have to be confounded. In the current experiment, third level interactions were confounded. A detailed discussion of the partial confounding method and the design of experiments can be found in Hicks and Turner [17] and Brown and
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Melamed [18]. Following this method, the scenarios that each participant completed were determined. The order of scenarios presented to the participants was also randomized to eliminate any impact of the scenario ordering on the results. In addition to these factors, the type of lead and opposing vehicles (truck or passenger cars) were considered in order to facilitate their inclusion in the passing duration and distance models. The vehicle type was randomly set for each vehicle in each scenario run, and so participants in the experiment encountered both types of vehicles. Participating drivers were instructed to drive as they would normally do in real world and completed a familiarization scenario (~ 10 min) to get used to the simulator. No instructions were given regarding their driving speed, distance from other vehicles, or passing other vehicles.
2.2. Participants One hundred Israeli drivers (64 males, 36 females) who drove on a regular basis and already established their driving style (driving license for at least five years) participated in the experiment on a voluntary basis. The age of participating drivers ranged between 22 and 70 years old, with an average of 32.7 years old and a standard deviation of 9.8 years. Drivers were also been asked for their driving experience. A strong and significant correlation was found between drivers' age and years of driving experience (R = 0.935, p-value b 0.001).
2.3. Data collection & definitions The driving simulator collects data about speeds, positions, and acceleration of the subject vehicle and all other vehicles in the scenario, at a resolution of 0.1 s. From this raw data other variables of interest, such as relative speeds and distances between vehicles can be calculated. These variables are then used to calculate important measures such as the following gap between the subject vehicle (SV) and the front vehicle (FV) at the moment of start passing and the time-to-collision between the subject vehicle (SV) and the opposing vehicle (OV) at the end of a passing maneuver (see Fig. 2). The start of a passing maneuver (P1) was defined as when the subject vehicle's left front wheel touches the center line. The end of a passing maneuver (P2) was defined as when the subject vehicle's rear left wheel touches the center line (see Fig. 2). These definitions are consistent with previous definitions adopted in other studies [3,19]. Hegeman [3] indicates that the real start of a passing maneuver begins when drivers start to change their lateral position to get prepared for passing. However, since this positioning differs from one driver to another, it is difficult to measure the real starting moment. Therefore, it is important to have a clear and consistent definition of the start position for all observed passing maneuvers.
Fig. 2. Illustration of a passing maneuver process.
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H. Farah / IATSS Research 37 (2013) 61–67
2.4. Model formulation
Table 2 Summary of several related overtaking measures.
Several previous studies examined the relationship between passing duration and passing distance, as dependent variables, with individual explanatory variables such as the average front vehicle speed and average differential speed between front and subject vehicles [8,9], including AASHTO [1]. However, few studies examined the impact of all of these variables simultaneously (traffic, geometric and drivers' characteristics) on the passing duration and distance. Furthermore, drivers' characteristics, such as age, gender and driving experience were rarely included. Therefore, the objective of this study is to explore the impact of these variables as potential explanatory variables of passing duration and distance. Each driver had several measurements and therefore the errors for those measurements most probably are correlated. To account for this correlation, each driver is set to have an individual intercept which randomly deviate from the mean intercept of the group. Therefore, random effect for the intercept of the model is introduced to account for individual heterogeneity within the model. The approach is to estimate a single variance parameter which represents how spread out the random intercepts is around the common intercept (following a Normal distribution). Multiple regression type model was used with logarithmic transformation to guarantee only positive values for passing duration and passing distance. The formulation is shown in Eq. (1): lnðdnÞ ¼ βX n þ þb0i þ εn
εn i n
Units Mean
Passing duration Passing distance Subject vehicle driving speeda Following distancea Relative speed between subject vehicle and front vehicle a, (front speed– subject speed) Relative distance between subject vehicle and opposing vehiclea Relative speed between subject vehicle and opposing vehicle a (opposing speed–subject speed) Time gap between the subject vehicle and the front vehicleb Time gap between the subject vehicle and opposing vehicleb
s m km/h
a b
7.1 175.5 75.6
Median Std. 6.9 168.0 75.2
m 13.5 10.3 km/h −15.1 −11.2
m
480.4
466.3
km/h
−0.3
s
s
2.2 56.3 21.2
Min
Max
2.8 68.5 40.7
19.4 403.0 145.4
10.2 1.4 13.3 −83.9
83.0 2.2
203.6
3.2
1006.7
0.9
8.2 −23.9
17.9
1.6
1.3
1.3
0.2
11.1
3.9
2.6
4.1
−0.06
25.7
At moment of start passing (P1). At moment of end passing (P3).
ð1Þ
where; dn Xn β b0i
Variable
passing duration or passing distance (dependent variable), vector of explanatory variables (independent variables), vector of corresponding parameters to be estimated, random effect parameter for the intercept, assumed to follow a normal distribution with mean 0 and standard deviation of σb0, error term, the index i represents the driver number, observation number.
3. Results 3.1. General statistics A total of 455 completed passing maneuvers were recorded and analyzed. Table 2 summarizes initial processed data observed from the simulator experiment with respect to different measures that will be used in further analysis including the development of passing duration and passing distance models. Some of these measures were calculated at the moment of start passing and some at the moment of end passing, as defined earlier in Fig. 1 above. The passing duration is defined as the time the subject vehicle needs to arrive from point P1 to point P3 as illustrated in Fig. 1. The distance between those two points (P1 and P3) is considered as the passing distance. Several measures are calculated at point P1, appearing in Table 2, including the driving speed of the subject vehicle, relative distance or following distance (front to rear) and relative speed between the subject and the front vehicle, and also the relative distance and speed between the subject and opposing vehicles (front to front). At point P3, two measures were calculated which are related to the safety level of the passing maneuver, these are the time gap between the subject vehicle and the front vehicle, calculated as the distance separation between the vehicles divided by the speed of the lead vehicle, and the time gap between the subject vehicle and opposing vehicle, calculated as the distance separation between the vehicles divided by the sum of their speeds. The min value of the
time gap between the subject vehicle and opposing vehicle in Table 2 is negative indicating that some of the passing maneuvers resulted in accidents. In the data base collected three accidents occurred. These cases were excluded from the database used for the development of the models. Prior to modeling the duration and distance of passing maneuvers, histograms of the observed duration and distance were plotted as shown in Fig. 3. It can be seen that both distributions are rightly skewed. Log-normal probability density functions were found to best fit the data. To examine the appropriateness of the log-normal distribution to the sample data in each case (passing duration and passing distance) the Kolmogorov Smirnov test (non-parametric test) was conducted. The test results showed that the null hypothesis, that the sample data are drawn from the hypothesized log-normal distribution, cannot be rejected at the 95% confidence level (p-Values = 0.366; 0.908 for passing duration and passing distance, respectively). This distribution (log-normal) was previously used to fit lane-changing duration of vehicles on freeways [20]. 3.2. Passing duration and distance Table 3 presents the estimation results of the passing duration and passing distance models. The ‘glmmADMB’ package in R statistical program for fitting generalized linear mixed models (GLMMs) was used to estimate the model parameters (Bolker et al., [21]). Pearson correlations among the independent variables in Table 3 were examined before the estimation of the models and found to be low to moderate (correlations less than 0.65). The estimation results in Table 3 show that all of the variables are statistically significant at the 95% confidence level. It is interesting to note that not only the traffic related variables but also the drivers' age significantly impact the duration and distance of passing maneuvers. Driver age was found to have a significant high correlation (R = 0.935, p-value b 0.001) with the number of years of actual driving experience. Fig. 4 illustrates the impact of the different variables on the passing duration and distance. To examine the impact of a certain variable on the passing duration and distance, the value of the variable of interest was changed while keeping the values of all other variables fixed. Unless specified,
H. Farah / IATSS Research 37 (2013) 61–67
Probability Density Function
a) 0.4 0.36 0.32 0.28 0.24 0.2 0.16 0.12 0.08 0.04 0
4
6
8
10
12
14
16
18
Passing Duration (sec) Histogram
Lognormal
Probability Density Function
b) 0.3 0.28 0.26 0.24 0.22 0.2 0.18 0.16 0.14 0.12 0.1 0.08 0.06 0.04 0.02 0
80
120
160
200
240
280
320
360
400
Passing Distance (m) Histogram
Lognormal
Fig. 3. Probability density functions of passing duration (a) and passing distance (b).
it was assumed that the driver is 30 years old, the driving speed at the start of the maneuver is 72 km/h (20 m/s), with a following distance of 10 m from the front vehicle, the relative speed (front speed minus subject speed) is − 18 km/h (− 5 m/s), and the relative speed from the opposing vehicle is 0 m/s (opposing speed minus subject speed). The relative distance from the opposing vehicle at the beginning of the passing maneuver is 480 m., and the gap from the opposing vehicle at end of passing is 3 s. These values were chosen to be close to the average conditions of the observed maneuvers. The results shown in Fig. 4(a) indicate that the passing duration and passing distance increase as the driver age increases. In other words, older drivers need more time to complete a passing maneuver than
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younger drivers. This could be because younger drivers accelerate faster and return faster to their lane, maintaining shorter gaps from the overtaken vehicle. This is supported by the results of the study by Farah [22] where it was found that older drivers maintain larger gaps from the overtaken vehicle at the end of the overtaking maneuver than younger drivers. The passing duration and distance are significantly affected by the traffic related variables of the subject, front, and opposing vehicles. As shown in Fig. 4(b), the passing duration significantly (95% confidence level) decreases with higher driving speeds of the passing vehicle at the beginning of the maneuver. AASHTO [1] assumes that the time spent in the opposing lane increases with higher speeds of the passing vehicle, while Harwood et al. [5] found a very weak correlation between the two parameters (the speed is measured at the abreast position) and recommended to use a constant value of the passing duration independent of the passing speed. Higher relative speeds between the front and subject vehicles (front vehicle speed minus subject vehicle speed) increases the passing duration, as shown in Fig. 4(c). Higher relative speeds from opposing vehicles (opposing vehicle speed minus passing vehicle speed) were found to decrease the passing duration (Fig. 4(d)), probably because passing drivers try to complete the passing faster in order to avoid conflicts with opposing vehicles. The passing distance increases with higher driving speeds of the passing vehicle at the beginning of the maneuver (Fig. 4(b)) and with higher relative speeds between the front and subject vehicles, and decreases with higher relative opposing vehicles' speeds (Fig. 4(c), (d), respectively). The following distance between the subject and front vehicles, at the moment of start passing, has also a significant positive impact on the duration and distance of passing (Fig. 4(e)). In other words, the duration and passing distance increase when drivers initiate the passing maneuvers from a larger following distance from the lead vehicle. Similar results were found with respect to the relative distance between the passing and opposing vehicles (Fig. 4(f)). It is found that when drivers have larger available gap they allow themselves to perform the passing maneuver in a more relaxed manner and as a result their passing duration and passing distance increase. Interesting to notice is the fact that in order to assure a larger gap from the opposing vehicle at the end of a passing maneuver, a passing driver should attempt to complete the passing maneuver faster, and with shorter passing distance (see Fig. 4(g)). Driver gender, road curvature, and types of front and opposing vehicles were not found to have a statistically significant impact on the passing duration and distance. The critical position or the point of no return [23,24] is defined as the location where beyond it drivers are recommended to complete
Table 3 Estimation results of passing duration and passing distance. Variable
Constant Subject speed Following distance (subject–front) Relative speed (front–subject) Relative speed (opposing–subject) Relative distance (opposing–subject) Gap from opposing vehicle (end of passing) Age Random effect variance Residual variance Number of observations Number of drivers Log-likelihood ⁎ p-Value b 0.05. ⁎⁎⁎ p-Value b 0.001.
Units
– km/h m km/h km/h m s years
Passing duration (s)
Passing distance (m)
Estimate (Std. error)
z value
Estimate (Std. error)
z value
1.74 (0.077) −0.006(6.4e–04) 0.011(0.001) 0.007(7.70e–04) −0.003(3.53e–04) 0.001(5.84e–05) −0.026(0.003) 0.007(0.002) 0.015 (Std. dev.: 0.122) 0.146 (Std. err.: 0.006) 430 73 163.37
22.47⁎⁎⁎ −9.28⁎⁎⁎ 10.51⁎⁎⁎ 9.58⁎⁎⁎ −7.60⁎⁎⁎ 17.66⁎⁎⁎ −9.13⁎⁎⁎ 3.83⁎⁎⁎
4.30(0.076) 0.003(6.88e–04) 0.012(0.001) 0.009(8.33e–04) −0.003(3.81e–04) 0.001(6.17e–05) −0.032(0.003) 0.004(0.002) 0.011 (Std. dev.: 0.107) 0.159 (Std. err.: 0.006) 430 73 138.14
55.92⁎⁎⁎ 4.86⁎⁎⁎ 10.77⁎⁎⁎ 11.35⁎⁎⁎ −7.59⁎⁎⁎ 18.77⁎⁎⁎ −10.38⁎⁎⁎ 2.46⁎
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H. Farah / IATSS Research 37 (2013) 61–67
Passing Duration Passing Distance
9
Passing Duration (s)
165 160
8
155
7
150 145
6 5 20
140 135 30
40
50
10
120 80
6
40
5
50
60
70
80
90
100 110
0
Speed of Subject Vehicle (km/h)
-20
0
20
40
320 240 160 80
f)
Passing Distance (m)
400 Passing Duration Passing Distance
0
0
20
40
60
Passing Duration (s)
10 9
120 80
7
40
6
0 5 -50 -40 -30 -20 -10 0 10 20 30 40 50
11 10 9 8 7 6 5 4
200 Passing Duration Passing Distance
80 40 0
200
170 Passing Distance
160
8
150 7
140 130
6 2
3
400
600
0 800
Relative Distance between Subject and Opposing Vehicles (m)
Passing Duration
1
160 120
9
0
160
8
80
Following Distance between Subject Vehicle and Front Vehicle (m)
g)
Passing Duration Passing Distance
Relative Speed between Subject and Opposing Vehicles (km/h)
e) 19 17 15 13 11 9 7 5
200
11
Passing Distance (m)
Passing Distance
Passing Duration (s)
Passing Duration
Passing Duration (s)
280 240 200 160 120 80 40 0
Passing Distance (m)
d) 12 11 10 9 8 7 6 5 -40
Passing Distance (m)
Passing Duration (s)
160
7
60
Relative Speed between Subject and FrontVehicles (km/h) Passing Duration (s)
200
8
Driver Age (years)
c)
Passing Duration Passing Distance
9
4
5
Passing Distance (m)
Passing Duration (s)
170
10
Passing Distance (m)
b)
a)
6
Time Gap between Subject and Opposing Vehicles at the end of a Passing Maneuver (km/h) Fig. 4. Impact of different variables on passing duration and passing distance.
the passing maneuver rather than aborting it. According to AASHTO [1] the critical position is when the subject vehicle is abreast to the leading vehicle. The time that takes the driver to arrive to the critical position from the moment of start passing is, according to AASHTO, equal to third of the time needed to complete the passing maneuver (1/3d2). Calculating the same ratio based on the data from the driving simulator, it was found that this ratio is equal to 41.7% of d2, higher than the one proposed by AASHTO, but almost identical to the result by Harwood et al. [5] who found it to be 41%. This result has also implication on the calculation of d4, which according to ASSHTO is the distance that the opposing vehicle travels for two-third of the time the passing vehicle occupies the left lane. In other words, it is the
distance that the opposing vehicle travels, from the time the passing vehicle is at abreast position to the front vehicle till the point it completes the pass. Fig. 5 presents a comparison between d4 calculated according to AASHTO (2/3 t2 ∗ opposing vehicle speed) to d4 calculated from the trajectories of the vehicles, from the time the passing vehicle was at an abreast position with the front vehicle till the point it completed the pass. A significant correlation (R = 0.63, p-value b 0.001) was found between the calculated d4 and the d4 according to AASHTO. It can be seen that AASHTO underestimates the distance traveled by the opposing vehicle. This result suggests the need for further examination of the definition of this parameter (d4) since it has implications on safety.
H. Farah / IATSS Research 37 (2013) 61–67
250
References
d4 -AASHTO (m)
200 150 100 50 0
0
67
50
100
150
200
250
d4 -Calculated (m) Fig. 5. Comparison of the traveled distance by the opposing vehicle.
4. Conclusions This study modeled the duration and distance of passing maneuvers as a function of the traffic conditions and drivers' characteristics on two-lane rural highways. Detailed data of passing maneuvers were collected using a driving simulator. The results of the developed and estimated models showed that, beside the traffic related variables, drivers' characteristics captured by drivers' age has a significant impact on passing duration and passing distance. The detailed observation of passing maneuvers enhances our understanding of how drivers perform passing maneuvers. This in turn has significant practical implications on passing sight distance design and traffic safety. The results can also guide the development of solutions to improve the safety on two-lane highways. Moreover, the developed models can be used to enhance the passing models in simulation programs. In spite of these useful conclusions, this study has some limitations. The main limitation of this study is that the data were collected using a low-cost driving simulator. The estimated and perceived distances and speeds by drivers might be affected by the resolution and frequency of the displayed images, and by the fact that the images are displayed on a flat screen and not in a 3D (three-dimensional) environment. Also, by its nature driving in a simulator does not involve the risks associated with real-world driving. Thus, this might bias the results, and therefore it is recommended that future studies use actual real data collected from the field to validate these models. Miles et al. [25] and Harwood et al. [5] describe methods to observe and collect data on actual passing maneuvers from the field. Future research should also examine the impact of other geometric characteristics on the duration and distance of passing maneuvers, such as vertical alignment, quality of the pavement, sight distances, and road side features. Some of these characteristics are difficult to model and capture in virtual environment, such as quality of the pavement and sight distances. Therefore, real world data is needed.
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