Powered-Two-Wheelers kinematic characteristics and interactions during filtering and overtaking in urban arterials

Transportation Research Part F 24 (2014) 133–145

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Transportation Research Part F journal homepage: www.elsevier.com/locate/trf

Powered-Two-Wheelers kinematic characteristics and interactions during filtering and overtaking in urban arterials Eleni I. Vlahogianni ⇑ National Technical University of Athens, 5 Iroon Polytechniou Str, Zografou Campus, 157 73 Athens, Greece

a r t i c l e

i n f o

Article history: Received 8 September 2012 Received in revised form 4 January 2014 Accepted 8 April 2014

Keywords: Powered Two Wheelers Filtering Overtaking Virtual lanes Kinematic parameters PTW interactions Logit Neural networks

a b s t r a c t The present paper focuses on the Powered-Two-Wheelers (PTWs) kinematic characteristics and their interactions with the rest of traffic in urban arterials. The factors that may affect the likelihood of PTW drivers to accept critical spacing during filtering and overtaking are also investigated using trajectory data collected from video recordings. The distributional characteristics of the PTW kinematic parameters showed that the patterns of filtering and overtaking have several differences. Further results using Logit models show that PTW speed difference with the rest of traffic, spacing, the existence of heavy vehicles and the occurrence of platoon of moving PTWs (in which the leader is the reference PTW) are significant factors related to the probability of driving in critical spaces through traffic. The likelihood of accepting critical lateral distance from the vehicle being overtaken may be related to the adjacent lane spacing, the speed difference and the existence of a platoon of PTWs. A comparative study between Logit models and equivalent structures of neural networks showed that, in the specific application, neural networks were found to perform better than the Logit models in terms of the model’s discrimination power. Ó 2014 Elsevier Ltd. All rights reserved.

1. Introduction Differences in the structural, mechanical and driving dynamics between the Powered Two-Wheelers (PTWs) and the rest of the vehicles impose a unique maneuverability that is magnified in urban road networks due to the reduced free space in roads and the increase of the interactions with the rest of the traffic. Differences may also arise from the manner PTW users perceive driving when compared to the rest of road users. PTW unique characteristics also attract drivers who are risk-takers and may exhibit different hazard perception and behavior during driving from other vehicle drivers (Di Stasi, Contreras, Cándido, Cañas, & Catena, 2011). Usually PTW drivers are found to exhibit extreme behaviors on the road, such as speeding, disobeying traffic signals, give-way or stop sign, non-compliance to overtaking restrictions or pedestrian crossing, making illegal turns, maintaining short gaps with the following vehicles and so on (Broughton et al., 2009; Mannering & Grodsky, 1995, Vlahogianni, Karlaftis, & Orfanou, 2012). PTW drivers may show non-cooperative behavior with the rest of the traffic, especially in near to capacity traffic conditions. In such conditions PTW drivers will most likely attempt to position themselves in front of queues (e.g. in signalized intersections), avoid heavy vehicles involvement, change lane, or just maintain their speed when facing a downstream ⇑ Tel.: +30 210 772 1369; fax: +30 210 772 1454. E-mail address: [email protected] http://dx.doi.org/10.1016/j.trf.2014.04.004 1369-8478/Ó 2014 Elsevier Ltd. All rights reserved.

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bottleneck. This behavior may have significant effects on traffic conditions, such as speed reduction in the rest of the traffic, or increased risk of accident occurrence. The above are usually reflected to erratic driving patterns and trajectories that diverge from typical travel lanes. Especially in dense traffic, PTW drivers have been systematically observed to engage in complex maneuvers in order to filter through traffic by taking advantage of the lateral distances that the rest of the vehicles that move on typical travel lanes allow (Lan, Chiou, Lin, & Hsu, 2010; Nikias, Vlahogianni, Lee, & Golias, 2012). Literature has systematically underlined the differences between PTW flow and the rest of the traffic; these differences may be codified into the following categories (Lee, Polak, & Bell, 2009): (i) traveling alongside another vehicle in the same lane, (ii) Moving to the head of a queue, (iii) Filtering, (iv) Swerving or weaving, (v) tailgating, (vi) Oblique following, (vii) Maintaining a shorter headway when aligning to the lateral edge of the preceding vehicle, (viii) Traveling according to the virtual lanes formed dynamically by the vehicles in surroundings and (ix) Self-organization phenomena. On the modeling of PTW traffic, literature has underlined the inability of conventional theories to cope with such complex driving patterns (Lan et al., 2010; Lee et al., 2009). The focus has been mainly shifted to car following theories and the deployment of cellular automata models for inhomogeneous traffic (Lan & Chang, 2005; Meng, Dai, Donga, & Zhang, 2007; Nakatsuji & Nguyen, 2001; Lan et al., 2010). Regarding the road space accepted by the PTW drivers for maneuvering, most models adopt a static approach on the manner to describe the space that each PTW user occupy on the road (Lan & Chang, 2005), or refer to the behavior of PTW drivers at the stop line of a signalized intersection approach (Minh & Sano, 2005; Nakatsuji & Nguyen, 2001, Haque, Chin, & Huang, 2008) using, again, static width for the lanes dedicated to the PTW traffic. Meng et al. (2007) proposed a single-lane cellular automaton model to simulate mixed traffic with motorcycles based on fixed width virtual lanes; they used both automobile lanes of typical width and lanes of decreased width dedicated to PTW drivers. Recently, Lan et al. (2010) developed a cellular automaton model based on lanes with width equal to the PTW width; in this model the automobiles are to occupy more than one lane. These approaches have a conceptual shortcoming, as PTW trajectories may – more convincingly – be considered as complex and dynamically changing with respect to the space PTW drivers use to navigate; this space may define a path or a lane both virtual and dynamically changing with respect to its width depending on the manner the rest of the traffic is positioned on the actual travel lane. Arasan and Koshy (2005) and Dey, Chandra, and Gangopadhaya (2009) have emphasized on the need to take into consideration the space each vehicle category occupy on the road in order to improve the simulation of heterogeneous traffic. A previous study has related the physical width of a static motorcycle and the width of the operating space (Hussain, Radin, Ahmad, & Dadang, 2005). Recently, Lee et al. (2009) proposed an oblique and lateral headway model to describe the safety distance that a motorcyclist maintains when he/she follows another vehicle obliquely or laterally. Moreover, Lee (2008) and Minh, Sano, and Matsumoto (2010) provided linear relationships to describe the relation between the width of the virtual lane and the speed of the motorcycle. Nikias et al. (2012) underlined that filtering and overtaking from a free lane in an urban arterial with two lanes per direction of travel are the most frequently observed patterns and extended the approach of Lee (2008) and Minh et al. (2010) by introducing additional parameters in the linear regression, such as the speed difference with the rest of the traffic and the spacing, but with no clear-cut results due to the low performance of the models. With the utilization of enhanced video based data collection techniques, the present paper extends past research in investigating the determinants of PTW drivers’ behavior in urban arterials under the driving conditions of filtering and overtaking. Filtering – or else moving through the lateral clearances between slow moving or stationary vehicles – may be considered to create a virtual lane; its width should be dynamically changing and dependent on the traffic characteristics in both lanes. Overtaking is straightforward and requires that one of the two lanes is free of traffic; in this case, the distance of interest is the lateral distance from the vehicle being overtaken. The methodological framework uses both statistical and neural network techniques in order to provide answers to the following research questions:  Are filtering and overtaking similar patterns?  What affects a PTW driver decision to accept critical virtual lane widths when filtering and critical lateral distances when overtaking?  How the performance of classical statistical models compare to those of neural networks in predicting the probability of a PTW driver to accept critical spaces during filtering or overtaking? For the first, an attempt to evaluate the similarity of filtering and overtaking patterns with respect to the kinematic characteristics of the PTW and those of the rest of the traffic will be conducted. Emphasis will be given to the characteristics of the width of the virtual lane utilized by the PTW driver during filtering, as well as to the lateral distance the PTW driver positions itself from the vehicle he/she overtakes. This will enable the detection of those values of virtual lane width and lateral distance that are critical (lower than a certain threshold). The second question will be addressed by investigating the relationship between the kinematic characteristics and the probability of PTW driver engaging in extreme filtering and overtaking conditions using binary logistic regression models. The analysis aims at revealing which variables may be influential to the decision of a PTW driver to accept critical lane widths during filtering and critical lateral distances during overtaking. Finally, the third question will provide evidence on the performance of the models developed and their adequacy in terms of discrimination power when compared to neural networks. Neural networks are used as a typical example of computational intelligent techniques that are frequently met in transportation modeling.

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2. Methodological approach 2.1. Extracting trajectories from video recordings The study of the behavior of PTW drivers on urban roads requires detailed data on the trajectory they follow on the road and its relation to the rest of the traffic. Eventually, data on the basic kinematic parameters, such as speed, spacing etc., as well as the vehicular interactions, for example lateral distances from the rest of the vehicles, should be collected. In the present paper this is conducted via a semi-automatic approach to analyze video recordings and extract microscopic traffic variables and the positioning of vehicle on the study area. The procedure is as follows: first, video recording equipment is installed in a spot higher than the level of the road (e.g. 80–100 m). Second, videos are recorded in a resolution of up to 720 by 480 at a frame rate of approximately 29.97 fps. Then, video footage is converted to proper digital format and it is analyzed to extract the vehicular trajectories and the kinematic vehicle characteristics. Each vehicle in the video recordings is recognized and tracked every half a second. Following each vehicle tracking, the system records its location on the screen and the screen coordinates are transformed to real-world coordinates allowing for the system to derive and save the kinematic and other requested parameters. For the system calibration the screen coordinates need to be transformed to world coordinates. This is done by introducing four reference points in the area under study Coordinates conversion is done using the two simple equations (Mikhail, Bethel, & McGlone, 2001): þa2 yscreen þa3 xreal ¼ aa14xxscreen screen þa5 yscreen þ1

ð1Þ

þa7 yscreen þa8 yreal ¼ aa64xxscreen screen þa5 yscreen þ1

where (xreal, yscreen) is the real-world coordinate, (xscreen, yreal) is the video image coordinate and a1 to a8 are coefficients that are estimated based on the coordinates of four reference points. Based on the proposed approach for collected data, the traffic stream in the real world should be on a plane, i.e. not on a concave or convex slope. Moreover, the lens distortions need to be converted in advance (Lee, Polak, & Bell, 2008). 2.2. Neural networks as logistic regression models The problem of modeling the critical width of the PTW virtual lanes in arterials during filtering, as well as the critical lateral distances during overtaking is a typical classification problem that is usually dealt using the Logit models. The general form of the logistic regression that relates the probability of an outcome p to a set of independent variables (predictors) x1, . . . , xi is the following:



log

 p ¼ b0 þ b1 x1 þ . . . þ bi xi 1p

ð2Þ 



p is linearly where b1, . . . , bi are the coefficients of each predictor and b0 is the constant term. It is assumed that the log 1p related to the predictors. The model converges using the maximization of a likelihood function. However, there is currently an open debate on the use of advanced artificial intelligence techniques – mostly neural networks – in solving similar problems and how these approaches may perform in comparison to classical statistical models. These issues are introduced and extensively discussed in Karlaftis and Vlahogianni (2011). In this paper, Logit models will be compared to their equivalent Multilayer Perceptrons (MLPs). An MLP with one hidden layer and a logistic output activation function produces an output value yn of the n-th data example of the form (McNelis, 2005):

1 1 þ esj X sj ¼ wkj hk þ hj yn ¼

ð3Þ ð4Þ

k

where wkj is the connection weight between the kth neuron in the hidden layer and the jth neuron in the output layer and hj P is the bias term. The term hk presents the output of the hidden neuron and is given by: hk ¼ 1þe1sk , with sk ¼ i wik xi  hi , where wik is the connection weight between the kth neuron in the hidden layer and the ith input variable. hi is the bias term. Eq. (3) is a general case of a Logit model. The hidden layer, as opposed to the logistic regression, introduces the nonlinearity – the output hk is usually a nonlinear function of the input pattern – and, thus, adds flexibility to the model compared to the Logit models (Tu, 1996). ~i as the weighted average of the logsigmThe described structure of MLP provides for a discrete choice model probability p oid function for neurons bounded between 0 and 1 (McNelis, 2005):

~i ¼ p

X cj sj;i j

ð5Þ

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X cj ¼ 1; cj P 0

ð6Þ

j¼1

Both approaches – Logit and MLP – attempt to express a probability of an event to occur via a functional form and a vector of parameters. Literature tend to emphasize that the use of MLPs may result to more flexible and robust models when compared to similar statistical structures. Nevertheless, they encompass several shortcoming, such as their limited capability to extract causal relationships, overfitting etc. (Tu, 1996). Literature indicates that those shortcomings may be alleviated if synergies with classical statistics are established, a task rather difficult and cumbersome requiring to master both schools of thought. 3. Implementation and findings 3.1. Study area and data description The methodology is tested using data collected via the proposed video based trajectory extraction method from a highly visited urban arterial. As seen in Fig. 1 the specific arterial has two lanes per direction of travel. The section covered is approximately 100 m and is far from the upstream and downstream signalized intersections. Extended videos footage was recorded for selected weekdays during the May and June 2011. Recordings were made during morning peak periods (7:00–11:00). In all days selected, weather was clear and the visibility was good. A vast range of traffic conditions were included in the data sample ranging for unconstrained traffic to congested stopand-go conditions. Fig. 2 depicts the speed volume relationship in the arterial under study during a morning peak period. The video based analysis resulted in a vast dataset of PTW trajectories. For the purpose of the analysis, it was decided to leave out patterns observed in extreme traffic flow conditions (gray area on Fig. 2) and evaluate PTW drivers’ behavior in constrained but moving traffic flow. Moreover, any case with vehicle or other occlusions were excluded from the analysis. The resulting dataset consist of 1375 cases of PTW traffic patterns. These cases do not cover the entire spectrum of driver’s actions during overtaking maneuvers but the main driver’s kinematic characteristics at the time stamp where the PTW is adjacent to the vehicle(s) during filtering or overtaking. This time stamp was set by repeated visual inspection of the videos. The two main patterns observed in the study area, namely filtering and overtaking, are graphically depicted in Fig. 3. Evidently, the kinematic characteristics of all vehicles involved as well as the lateral distances of the adjacent vehicles from the subject PTW are of interest to the analysis. The video analyses provided a series of variables depicted on Table 1. The available variables involve the type of PTW (moped or motorcycle) under investigation, the existence of passenger car in the left (PCL) of right lane (PCR), the existence of platoon in which the leader is the PTW under investigation (PLATOON) and the heavy vehicle involvement in the left (HVL) and right (HVR) lane. Moreover, there exist variables defined according to whether filtering or overtaking is considered. For filtering, the spacing in the left (DL) and right (DR) lanes and speed of vehicles in the left (SL) and right (SR) lane are used. For the overtaking, the spacing in the reference lane (D) and in the adjacent lane (DA), as well as the respective speeds are introduced to the modeling. Finally, the speed difference (SD) is defined as the difference of speed of PTW from the average speed of the vehicles in the two lanes involved for filtering, whereas, for overtaking, as the difference of speed of PTW from the front vehicle that is being overtaken. Fig. 4 depicts the scatter plots of Lw versus PTW speed for both filtering and overtaking. As can be observed neither the width of the virtual lane in filtering or the lateral distance from the front vehicle during overtaking holds no linear relationship with PTW speed. This is indicative of a complex behavior that requires a larger number of parameters to be taken into consideration in order to be clarified. 3.2. Are filtering and overtaking similar patterns? In order to detect any similarities or differences between the filtering and overtaking the distributional characteristics of the width Lw, the spacing and speed difference are further evaluated. The Kolmogorov–Smirnov test is used to decide which

Fig. 1. The arterial section under study.

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Fig. 2. Indicative speed-speed volume graph for inhomogeneous traffic from the study area.

filtering

overtaking

Fig. 3. The 2 cases of PTW maneuvering in an urban arterial under study.

Table 1 Variables considered in the analysis of PTW traffic patterns. Variables

Description

PTW PCL PCR HVL HVR Lw

Motorcycle [1] or Moped [0] involvement Passenger Car in the left lane [0/1] Passenger Car in the right lane [0/1] Heavy vehicle in the left lane [0/1] Heavy vehicle in the right lane [0/1] Width of the virtual lane (filtering) Lateral width of overtaking (overtaking) (m) Spacing in the reference lane (overtaking) (m) Spacing in the adjacent lane (overtaking) (m) Spacing between vehicles in the left lane (filtering) (m) Spacing between vehicles in the right lane (filtering) (m) Speed of the PTW (km/h) Speed of the front vehicle (the one that is being overtaken) (km/h) Average Speed of vehicle in the adjacent lane (km/h) Speed of the vehicle in the left lane (filtering) (km/h) Speed of the vehicle in the right lane(filtering) (km/h) Existence of platoon of PTWs [0/1] Difference of speed of PTW from the average speed of the vehicles in the two lanes involved (filtering) Difference of speed of PTW from the front vehicle that is being overtaken (overtaking) (km/h)

D DA DL DR S SF SA SL SR Platoon SD

theoretical distribution fits best the available data; based on the empirical cumulative distribution function, the test decides whether a sample comes from a hypothesized continuous distribution. With the null hypothesis that the data follow the specified distribution, the Kolmogorov–Smirnov statistic (K–S D statistic) estimates the largest vertical difference between the theoretical and the empirical cumulative distribution function (Washington, Karlaftis, & Mannering, 2010); the hypothesis regarding the distributional form is rejected at the chosen significance level if the test statistic is greater than the certain critical value. The Kolmogorov–Smirnov test results are seen in Table 2, along with the type and parameters of the best fitted theoretical distribution. As can be observed, in the case of PTW filtering, the lognormal distribution may efficiently describe the selected variables. In the case of overtaking, similar distributional characteristics were not observed. A 3-parameter Gamma distribution fits the spacing in the reference lane D during overtaking, whereas speed difference SD is described by a Weibull

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2

Lw (m)

1.5

1.5

.5

.5

1

1

Lw (m)

2

2.5

3

2.5

138

0

20

40

60

80

100

0

50

PTW Speed (km/h)

100

150

PTW Speed (km/h)

Fig. 4. Scatter plots of Lw versus PTW speed for the Case 1 (filtering) and Case 2 (overtaking from free lane) of traffic patterns.

0.26

Probability Density Function

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 0.8

0.9

1

1.1

1.2

1.3

1.4

1.5

1.6

1.7

1.8

1.9

2

2.1

2.2

2.3

5.6

6

Lw (m) Histogram

Lognormal

0.56 0.52

Probability Density Function

0.48 0.44 0.4 0.36 0.32 0.28 0.24 0.2 0.16 0.12 0.08 0.04 0 0.8

1.2

1.6

2

2.4

2.8

3.2

3.6

4

4.4

4.8

5.2

Lw (m) Histogram

Lognormal

Fig. 5. Empirical and theoretical distributions for the width of the virtual lane for filtering (top) and the lateral distance from the front vehicle when overtaking (bottom).

distribution. It is to note that a successful fit for the Spacing in the adjacent lane DA was not possible. Moreover, for Lw, 10% of values of the distribution for filtering is below 1.2 m, whereas the same percentage in overtaking is below 0.9 m.

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E.I. Vlahogianni / Transportation Research Part F 24 (2014) 133–145 Table 2 Kolmogorov–Smirnov D test results.

*

Variables

Distribution

Parameters

K–S D statistic

Filtering Lw DL DR SD

Lognormal Lognormal Lognormal Lognormal

s = 0.169, s = 1.014, s = 1.023, s = 0.377,

0.022 0.029 0.038 0.067

Overtaking Lw D DA SD

Lognormal Gamma (3P) Weibull Weibull

s = 0.262, m = 0.305 a = 0.972, b = 13.213, g = 0.3 a = 1.161, b = 12.576 a = 2.043, b = 25.3

m = 0.395 m = 1.798 m = 1.692 m = 3.330

0.027 0.040 0.062* 0.034

Reject at 1%.

0.8

Probability Density Function

0.72 0.64 0.56 0.48 0.4 0.32 0.24 0.16 0.08 0 0

20

40

60

80

100

120

140

Spacing - LL (m) Histogram

Lognormal

0.56 0.52

Probability Density Function

0.48 0.44 0.4 0.36 0.32 0.28 0.24 0.2 0.16 0.12 0.08 0.04 0 0

4

8

12

16

20

24

28

32

36

40

44

48

52

56

Spacing - RL (m) Histogram

Lognormal

Fig. 6. Empirical and theoretical distributions for left lane (top) and right lane (bottom) spacings for filtering.

Figs. 5–8 depict the empirical and theoretical distributions for the selected variables for both filtering and overtaking. In both driving patterns, the PTW driver accepts larger spacing from the left and adjacent lane. Moreover, in filtering, greater speed difference between the PTW and the rest of the traffic is observed when compared to overtaking.

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Probability Density Function

0.8 0.72 0.64 0.56 0.48 0.4 0.32 0.24 0.16 0.08 0 0

20

40

60

80

100

120

140

160

Spacing (m) Histogram

Gamma (3P)

0.48

Probability Density Function

0.44 0.4 0.36 0.32 0.28 0.24 0.2 0.16 0.12 0.08 0.04 0

20

40

60

80

100

120

140

160

180

Spacing - Adjacent Lane (m) Histogram Weibull

Fig. 7. Empirical and theoretical distributions for spacing in the reference lane (top) and the adjacent lane (bottom) for the case of overtaking.

To further investigate the differences observed, a series of two-sample test of equal means –assuming unpaired data – with unequal variables is conducted. Results are seen in Table 3 and depicts that the mean values of all variables considered are statistically different between samples for both filtering and overtaking. Consequently, the manner a PTW driver behaves during filtering and overtaking may present distinct characteristics that should be separately studied. 3.3. What affects PTW driver decision to accept critical virtual lane widths when filtering? A binary logistic model is used in order to evaluate which determinants may be related to the PTW driver decision to drive through traffic at critical values of virtual lane width. Based on the distributional characteristics seen in Fig. 5, the Lw = 1.2 m was considered as the cut-off point separating the critical widths (marked as 1 in the binary output of the logistic model) from the rest of the values of Lw (marked as 0 in the binary output of the logistic model). Prior to the modeling, a correlation analysis was conducted to exclude correlated variables from further analysis. Results from the best fitted Logit model (r2 = 0.38) with respect to the coefficients and the marginal effects are seen in Table 4. As can be observed, the type of PTW, the existence of heavy vehicle at the left lane and the spacing in the right lane were not found to be significant variables. The difference in the speed SD of the PTW with the rest of traffic is a significant factor negatively related to the probability of driving in critical spaces through traffic. Moreover, the increase in left lane spacing DL leads to increased likelihood of the PTW driver accepting smaller virtual lane widths. The existence of heavy vehicles in the right lane HVR acts negatively to the increase of the above probability. Interestingly, results show that when the reference PTW is the leader of a platoon of moving PTWs, the likelihood of accepting narrower virtual lanes is higher. Further, the marginal effects – depicted in parentheses on Table 4 – that account for the amount of change in the dependent variable

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E.I. Vlahogianni / Transportation Research Part F 24 (2014) 133–145 0.24 0.22

Probability Density Function

0.2 0.18 0.16 0.14 0.12 0.1 0.08 0.06 0.04 0.02 0 8

12

16

20

24

28

32

36

40

44

48

52

56

60

Speed Difference (km/h) Histogram

Lognormal (3P)

0.26

Probability Density Function

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 0

8

16

24

32

40

48

56

64

72

80

Speed Difference (km/h) Histogram Weibull

Fig. 8. Empirical and theoretical distributions for speed difference for filtering (top) and overtaking (bottom).

that will be produced by a 1-unit change in each independent variable reveal increased sensitivity for changes occurring in the HVR and PLATOON variables. Overall, the model may predict the probability of driving through traffic in virtual lanes of critical width with % accuracy estimated to be 65.6%. 3.4. What affects PTW driver decision to accept critical lateral distances when overtaking? A similar approach is adopted in order to investigate the relationships of the independent variables to the decision of a PTW driver to accept small lateral distances from the vehicle been overtaken in urban arterials. Critical lateral distances Lw are considered to be below 0.9 m, based on the distributional characteristics revealed in a previous section of the analysis (Fig. 5). Prior to modeling, correlated independent variables have been detected and excluded. As seen in Table 4, the best fitted Logit model (r2 = 0.42) for the case of accepting critical lateral distances in overtaking relates the likelihood of accepting critical lateral distance from the vehicle overtaken with the spacing of vehicles at the adjacent lane DA, the speed different SD and the existence of a platoon of PTWs. The spacing and speed difference variables are negatively related to the likelihood of accepting critical lateral distances, whereas, as opposed to filtering, the existence of a Platoon of PTWs is positively related to the same likelihood. This difference may be attributed to the fact that the PTW driver, when leading a platoon and overtaking, want to avoid further conflicts with other PTW drivers coming from the same platoon. As in the case of filtering, the changes occurring in the platoon of PTW may impose changes in the likelihood of critical lateral distances with larger sensitivity compared to the rest of significant independent variables. Interestingly, the heavy vehicle involvement plays no significant role in overtaking, an issue that may considered to contradict intuition which indicates that in higher speeds the turbulent wind flow at heavy vehicle’s side should significantly

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Table 3 Results of the test for comparing continuous variables for PTW filtering and overtaking basic kinematic parameters. Variable

Std. Err.

Std. Dev.

95% Conf. Interval

Lw Filtering 1.51 Overtaking 1.31 Diff* 0.19 Ho: no difference in mean t = 8.998**

Mean

0.01 0.02 0.02

0.25 0.39

1.49 1.28 0.15

1.53 1.35 0.23

DL/DA Filtering 9.86 Overtaking 42.37 Diff* 32.51 H0: no difference in mean t = 17.187**

0.48 1.83 1.89

12.48 37.36

8.92 38.78 36.23

10.81 45.97 28.79

DR/D Filtering 8.78 Overtaking 28.10 * Diff 19.32 H0: no difference in mean t = 11.863**

0.35 1.59 1.63

9.04 32.48

8.10 24.97 22.52

9.47 31.23 16.12

0.39 0.60

10.02 12.20

29.03 18.74

30.55 21.09

SD Filtering 29.79 Overtaking 19.91 Diff* H0: no difference in mean t = 13.896** * **

Diff = mean (Variable in Filtering) – mean (Variable in Overtaking). Significant in 1% level of significance.

Table 4 Estimation results of the binary logistic regression model for filtering. Filtering

*

Overtaking

Independent variables

Coefficient estimates

Independent variables

Coefficient estimates

PTW HVL HVR DL DR SD PLATOON a

0.297 0.290 0.196* 0.033* 0.001 0.065* 0.239* 0.91

PTW HVL HVR DA D SD PLATOON a

0.036 0.381 0.075 0.002 0.040* (0.004) 0.031* (0.007) 0.701* (0.072) 1.95*

(0.015) (0.005) (0.007) (0.037)

Significant at 1% level (marginal effects in parentheses).

effect the overtaking critical lateral distances acceptance. It is to note that only 9.8% of the overtaking cases involved a heavy vehicle pointing to suggest that drivers in high speed conditions may choose not to overtake and adopt a tailgating behavior. Nevertheless, the effect of the involvement of heavy vehicles in overtaking anuevers in urban arterials is an issue of further research. Moreover, as in the case of filtering, the type of PTW and the spacing in the reference lane are found not to be significant. Overall the accuracy of modeling equals to 70.7%. 3.5. How accurate are the statistical models compared to the equivalent neural networks? The accuracy in predicting the likelihood of a PTW driver to move through traffic and maneuver using the Logit models may be considered as fair, but raises questions on whether there exists a more robust model with better discrimination capabilities. Therefore, a comparative study is deemed necessary. For the sake of the comparison, MLP classifiers with structural properties similar to binary logistic (Logit) models are developed and trained. The MLP classifier predicts the probability of accepting narrower distances from the vehicle overtaken or narrower widths for filtering using as input variables (independent variables) those already utilized in the Logit models. The network consists of the input layer, one hidden layer and the output layer. The activation functions are tan h in hidden and output layers. The MLP classifiers are trained with the Back-propagation learning rule and the cross-validation criterion is used as stopping criterion for learning. The network’s learning is genetically optimized with respect to the learning rate and momentum rate. For the genetic optimization, the preference is given to the fittest chromosome (survival of the fittest) (roulette selection) (Goldberg, 1989). Moreover, the probabilities of the two points cross-over and the mutation equal to 0.9 and 0.02 respectively. The population size and generation are 20 and 100 respectively. Finally, the data used are divided into three subsets: the training set (60%) that will be used in the training, cross-validation set (15%) that will be used in the validation

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E.I. Vlahogianni / Transportation Research Part F 24 (2014) 133–145 Table 5 Neural network classification model structural, learning and optimization specifications. Parameter

Value

Architecture Input space Hidden layers Output space Activation Preprocessing Normalization

7 GA optimized 2 [0/1] tan h [1, +1]

Learning Rule Learning rate and momentum

Back-propagation GA Optimized

GA Optimization Population Generation Selection Cross-over Mutation probability

20 100 Roulette Two points: 0.9 0.02

Table 6 Classification results for the Logit and Neural Network models for filtering and overtaking. Filtering

Overtaking

Logit Output/desired Typical Lw Critical Lw Average accuracy: 65.6%

Typical Lw 98.4% 1.6%

Critical Lw 67.2% 32.8%

Output/desired Typical Lw Critical Lw Average accuracy: 70.7%

Typical Lw 99.5% 0.5%

Critical Lw 58.0% 42.0%

Neural networks Output/desired Typical Lw Critical Lw Average accuracy: 81.9%

Typical Lw 97.6% 2.4%

Critical Lw 33.8% 66.2%

Output/desired Typical LwQ Critical Lw Average accuracy: 86.9%

Typical Lw 98.5% 1.5%

Critical Lw 24.7% 75.3%

Fig. 9. Receiver Operating Characteristic (ROC) curves for the logistic regression models for filtering (left) and overtaking (right).

of the training and the testing set (25%) that will be used for the testing of the performance of neural network. The model specifications with regards to its structural, learning and optimization parameters are presented in Table 5. Classification results are seen in Table 6 for all models considered in the comparative study. It seems that neural networks outperform the Logit models. In order to compare the models in terms of their discriminating power, the Receiver Operation Characteristic (ROC) curves are constructed. ROC curve is the plot of sensitivity (true positive rate) versus 1-specificity (false positive rate) and provides a useful tool for assessing the discrimination power of a model or comparing different models. The ROC curves for both overtaking and filtering are seen in Fig. 9, along with the calculation of the Area Under the ROC curve (AUROC); a large value close to 1 indicates that is an indication of very accurate prediction whereas a value close to 0.5 indicates a random guess.

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Table 7 Comparison results of testing equality of Areas under ROC curves. Model

ROC AUROC

Asymptotic Normal Std. Err.

[95% Conf. Interval]

Filtering MLP Classifier 0.893 Logit 0.838 Ho: areas are equal chi2(1) = 4.98 Prob > chi2 = 0.025

0.024 0.032

0.846 0.940 0.775 0.901

Overtaking MLP Classifier 0.941 Logit 0.816 Ho: areas are equal chi2(1) = 11.53 Prob > chi2 = 0.001

0.024 0.038

0.894 0.987 0.742 0.890

As can be observed, in the case of filtering, the ROC curves are close, whereas the ROC curves of Logit and NN exhibit differences in overtaking. To compare the ROC curves a confidence interval for the difference between ROC summary indices is calculated and a Wald statistic is compared to the standard normal distribution in order to report a p-value (Pepe, Longton, & Janes, 2000); results seen in Table 7 demonstrate that the two models provide marginally different results in terms of discrimination power for filtering. This is not the case of overtaking, where the neural networks significantly outperform the prediction provided by the Logit model. Although the MLP classifiers may seem more accurate in predicting the probability of the PTW driver accepting critical spaces in filtering and overtaking, comparing to Logit models, they may be less useful in the present application, as they do not provide any specific information on the manner each factor (e.g. kinematic parameters) taken into consideration may affect the above probability. On the contrary Logit models provide a solid inference ground for evaluating the observed relationships between dependent and independent variables. Extracting the statistical significance of input variables fro NNs has been largely disregarded in transportation literature, but is feasible through synergies with statistics before (e.g. principal components analysis or entropy based methods) or after the training (e.g. partial derivatives and bootstrapping) of NNs (Vlahogianni, Yannis, & Golias, 2012). 4. Conclusions The present paper attempted to compare the manner PTW drivers navigate through traffic in urban arterials with two lanes per direction of travel under high demand conditions. Using powerful video based techniques, detailed data were collected for two basic PTW driving patterns: (i) filtering and (ii) overtaking. The methodological framework compared statistical and neural networks approaches to answer three distinct modeling questions: first, what are the similarities of filtering and overtaking in terms of the kinematic characteristics and observed vehicular interactions, second, how these characteristics and interactions are related to the probability of accepting narrow free spaces when filtering and overtaking using Logit models and, third, how the performance of the Logit models may be compared to other neural network approaches that bare structural similarities with the Logit. In the first question, analyses on the distributional characteristics of the kinematic parameters showed that filtering and overtaking from the free lane are different patterns, occurring in different traffic conditions. The distributional analysis of the accepted virtual lane widths for filtering and lateral distances for overtaking resulted in detecting the critical cut-off values for both patterns of PTW driving. In the second research question, different Logit models were developed for filtering and overtaking and resulted in a set of PTW driving parameters that were significant in determining the likelihood to accept critical values of virtual lane widths for filtering or lateral distances for the vehicle been overtaken. For filtering, the difference in the speed of the PTW with the rest of traffic, the left lane spacing, the existence of heavy vehicles in the right lane and the occurrence of platoon of moving PTWs (in which the leader is the reference PTW) are significant factors related to the probability of driving in critical virtual lane widths. For overtaking, the likelihood of accepting critical lateral distance from the vehicle overtaken may be related to the spacing of vehicles at the adjacent lane, the speed difference and the existence of a platoon of PTWs. Finally, in the third question, the comparative study showed that, in the specific application, neural networks were found to perform better than the Logit models in terms of the model’s discrimination power. However, there is a trade-off between the model that performs best and the model that may be used to explain the phenomenon. The neural networks as presented, may outperform the classical statistical modeling, but were deprived from any explanatory power, whereas the Logit models succeeded in providing a set of kinematic parameters that may be influential to filtering and overtaking and, thus, provide some level of perception on the PTW maneuvering in urban arterials. As opposed to current thinking in transportation analyses, neural networks and statistics should be seen as complementary rather than competing methodologies for data analysis. The trade-off between performance and explanatory power should be addressed by introducing statistical inference concepts to neural network models; this is an open issue in transportation science.

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Evidently, the reduced performance in modeling may hint the need to address factors involving the cognitive and behavioral aspects of PTW driving in dense urban road networks, aspects highly discussed, but difficult to monitor and quantify. In order for the results to be transferable, future work should focus on comparing PTW driving patterns between different countries, cultural contexts or traffic environments. Monitoring and statistically evaluating PTW drivers’ maneuvers on urban networks may improve on the representational power of existing simulation models, or help to macroscopically define a PTW specific level of service. Findings may be also used in PTW safety for the development of countermeasures focusing on alleviating those factors that may influence the likelihood of criticalities during filtering or overtaking in urban arterials. 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