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Modeling lateral placement and movement of vehicles on urban undivided roads in mixed traffic: A case study of India
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Original Research Paper
Modeling lateral placement and movement of vehicles on urban undivided roads in mixed traffic: A case study of India Punith B. Kotagi a, Pooja Raj b, Gowri Asaithambi c,* a
Department of Civil Engineering, The National Institute of Engineering Mysuru, Mysuru 570008, India Department of Civil Engineering, National Institute of Technology Karnataka, Mangalore 575025, India c Department of Civil and Environmental Engineering, Indian Institute of Technology Tirupati, Tirupati 517506, India b
highlights Lateral placement and movement of vehicles on urban undivided roads are analyzed and modelled. Lateral separation of vehicle decreases with increase in subject vehicle size. Lateral separation of vehicle increases with increase in the speed of opposing vehicle. Multiple linear regression model was developed to predict lateral placement of subject vehicle. Multinomial logistic regression model was developed to study the choice of path of lateral movements.
article info
abstract
Article history:
In India, the majority of urban roads are undivided where the behavior of flows in a
Received 12 January 2018
particular direction is predominantly influenced by the opposing traffic. Due to lack of lane
Received in revised form
segregation, the vehicles in ongoing direction occupy the opposing lane, which increases
7 June 2018
the lateral interactions between vehicles. These lateral interactions are influenced by
Accepted 8 June 2018
various parameters such as vehicle types, driver behavior and vehicular speeds. Study of
Available online xxx
such complex interactions plays an important role in evaluating various management measures using microscopic simulation models. The lateral characteristics of vehicles,
Keywords:
such as placement, separation and movement, act as necessary input for simulation
Transportation
models. The present study aims to analyze and model the lateral characteristics of vehicles
Urban undivided road
on two-lane urban undivided roads. To achieve this, traffic flow data were collected from
Mixed traffic
an urban undivided mid-block section in Bangalore City, India, using video graphic tech-
Lateral placement
nique. Multiple linear regression model was developed for predicting the lateral placement
Lateral separation
of subject vehicle and it was found that lateral placement of subject vehicle is influenced
Lateral movement
by types and speeds of subject and opposing vehicles. Lateral separation for different types of ongoing (subject) and opposing pairs was also analyzed. The results show that both the ongoing and opposing vehicles have less freedom to move laterally when their sizes increase and hence, lateral separation decreases. The choice of path of vehicles' lateral shifts (left, current and right) on urban undivided roads was modeled using multinomial logistic regression. Lateral shift of a vehicle is influenced by speeds of subject vehicle and leader
* Corresponding author. Tel.: þ91 824 2473366. E-mail addresses: [email protected] (P.B. Kotagi), [email protected] (P. Raj), [email protected] (G. Asaithambi). Peer review under responsibility of Periodical Offices of Chang'an University. https://doi.org/10.1016/j.jtte.2018.06.008 2095-7564/© 2019 Periodical Offices of Chang'an University. Publishing services by Elsevier B.V. on behalf of Owner. This is an open access article under the CC BY-NC-ND license (http://creativecommons.org/licenses/by-nc-nd/4.0/).
Please cite this article as: Kotagi, P.B et al., Modeling lateral placement and movement of vehicles on urban undivided roads in mixed traffic: A case study of India, Journal of Traffic and Transportation Engineering (English Edition), https://doi.org/10.1016/ j.jtte.2018.06.008
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J. Traffic Transp. Eng. (Engl. Ed.) xxxx; xxx (xxx): xxx
vehicle in current path, speed of leader vehicle in target path, and lateral gap between leader vehicles in current path and target path. © 2019 Periodical Offices of Chang'an University. Publishing services by Elsevier B.V. on behalf of Owner. This is an open access article under the CC BY-NC-ND license (http:// creativecommons.org/licenses/by-nc-nd/4.0/).
1.
Introduction
The study of lateral placement and movement of vehicles finds important applications in traffic control and management measures, geometric design of roads, accident analysis, and estimation of level of service and roadway capacity. In most of the developing economies like India, traffic flow is mixed in nature consisting of vehicles with varying static and dynamic characteristics. In such traffic conditions, due to weak lane discipline, vehicles tend to utilize any lateral position available on the road and also interact both in lateral and longitudinal directions. Most of the roads in urban cities of India are undivided in nature where the vehicles travelling in ongoing direction often use the opposing lanes as well. Hence, the lateral interaction of vehicles on undivided roads is significantly higher when compared to vehicles travelling on divided roads. Generally, the lateral interactions are influenced by various parameters such as vehicle types, vehicular speeds and driver behaviour. Lateral placement and movement of vehicles are also influenced by the opposing vehicles due to lack of lane segregation. The earlier studies which focused on lateral characteristics of vehicles in homogeneous and mixed traffic conditions were limited to divided roads. Moreover, all these studies focused on longitudinal movement of vehicles and lateral movement behaviour of vehicles has received less attention. Also, only limited studies focused on analysis of various factors which influence lateral placement and movement of vehicles on urban undivided roads. Based on the above research motivation, overall objective of present study is to analyse and model the lateral placement and movement of vehicles on urban undivided roads under mixed traffic conditions and the specific objectives are: (1) to analyze and model the lateral placement of different types of vehicles, (2) to study and analyze lateral separation between different types of subject and opposing vehicles, (3) to analyze and model lateral movement behavior of vehicles. To investigate above objectives, traffic data were collected from an urban mid-block section of an undivided road in Bangalore City, India, using video graphic technique. To achieve the first objective, lateral placement and speed of different vehicle types in ongoing and opposing directions were extracted from the video data. Multiple linear regression (MLR) model was developed for predicting the lateral placement of ongoing vehicles considering types and speeds of ongoing and opposing vehicles as influencing variables. To attain the second objective, lateral separation between different types of ongoing and opposing vehicles were obtained. For achieving the third objective, lateral movements performed by different types of vehicles were analysed. A
multinomial logistic regression model was developed to study the choice of path of lateral movements performed by different types of vehicles. The rest of the paper is organised as follows. Section 2 discusses review of the literature focusing on studies related to lateral placement and movement of vehicles on both divided and undivided roads under mixed traffic conditions in developing nations as well as under homogeneous traffic conditions in developed nations. The process of data collection and extraction is discussed in Section 3. Section 4 presents the results of lateral placement and separation of vehicles. In Section 5, discussion on lateral movement behaviour of vehicles and model development is presented. Finally, the summary and conclusions of the study are presented in Section 6.
2.
Literature review
In this section, the studies focusing on the lateral placement and movement of vehicles under mixed traffic conditions in developing countries such as India are presented. Studies carried out in advanced countries with homogenous traffic cannot be used to analyse lateral placement and movement of vehicles in mixed traffic due to presence of varying vehicle type and weak lane discipline. However, a few studies carried out in developed nations with homogeneous traffic have also been reported.
2.1. Studies carried out for mixed traffic conditions in developing countries Dey et al. (2006) analysed lateral position of vehicles under mixed traffic conditions and found that the lateral position of vehicles followed unimodal or a bimodal curve depending on proportion of slow and fast moving vehicles. They introduced two parameters including placement factor (PF) and skewness range (SR) to describe the placement of vehicles and they concluded that the lateral placement follows unimodal curve if PF and SR are lower than 1.30 and 0.54, respectively. Chunchu et al. (2010) collected microscopic traffic data under mixed traffic conditions with the help of image processing technique. The traffic data such as vehicular composition, lateral placements of vehicles, longitudinal and lateral gaps were extracted. Authors studied the gap maintaining behaviour of different vehicle types when exposed to varying traffic conditions. An empirical relationship between lateral gap and area occupancy for different combinations of vehicles were developed. Balaji et al. (2013) studied the relation of
Please cite this article as: Kotagi, P.B et al., Modeling lateral placement and movement of vehicles on urban undivided roads in mixed traffic: A case study of India, Journal of Traffic and Transportation Engineering (English Edition), https://doi.org/10.1016/ j.jtte.2018.06.008
J. Traffic Transp. Eng. (Engl. Ed.) xxxx; xxx (xxx): xxx
placement and speed of different vehicles on two lane state highways. The analysis showed that three-wheelers, heavy vehicles and slow-moving vehicles follow a linear relation, while two-wheelers and cars follow a second-degree polynomial relation. The vehicles as a whole followed a second-degree polynomial relation. Mahapatra and Maurya (2013) analysed the impact of lane positions of vehicles on average travel speed, time headway and lateral clearances for four-lane, six-lane and eight-lane divided highways. They concluded that there exists a wide variation in the lane-specific vehicular speed, traffic composition, time headway and lateral gap in mixed traffic condition of Indian highways. Munigety et al. (2014) presented lateral movement tactical decision and choice making using vehicle type variant models for Eastern Express Highway, Mumbai city. They studied the motivation behind a driver to perform a lateral shift by comparing the speeds of the subject vehicle and that of the leader vehicle in the current lane. In the selection of a target path, speeds of the leader vehicle and the lead space gaps of the immediate left and right paths were analysed. Mahapatra and Maurya (2015) analysed lateral and longitudinal behaviour of vehicles in mixed traffic condition on Indian highways. It was observed that there exists an inverse relationship between the speed and the lateral characteristics. Mahapatra et al. (2016) studied lateral movements of vehicles over different types of roads in three metropolitan cities of India (Kolkata, Mumbai and Pune) under moderate traffic conditions. Lateral acceleration variation of five different types of vehicles and its relationship with vehicle longitudinal characteristics (i.e., longitudinal speed) were analysed. Lateral acceleration values rise quickly with initial increase in speed. Afterward, lateral acceleration values reduce with further increase in longitudinal speed of vehicles. Asaithambi and Shravani (2017) mathematically modelled the overtaking behaviour of different vehicle types under mixed traffic condition. Moving car observer method and vehicle registration plate method were adopted to collect the overtaking data from a two-lane two-way undivided highway. From the study, it was observed that the number of overtaking increases with increase in ongoing direction flow and decreases with increase in opposing direction flow.
2.2. Studies carried out for homogeneous traffic conditions in developed countries Miller and Steuart (1982) analysed vehicle lateral placements at five different locations in Toronto metropolitan area. Influences of lateral placement along with lane width and lane type on speeds of vehicle were studied. Results showed that there is no explicit relationship between lateral placement of vehicle and its speed. Armour (1985) identified that the main factors influencing lateral placement are shoulder type and lane width. Vehicles travelled further from the centre line as lane width increased. Lennie and Bunker (2005) compared the behavioural characteristics of passenger car drivers surrounding multi-combination vehicles using lateral position characteristics. They observed that the behaviour of a passenger car changes when a heavy vehicle approaches it closer than a passenger car does. It
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was also seen that there is no significant change in passenger car behaviour when they are nearer semi-trailers than B-doubles. Bunker and Parajuli (2006) made an attempt to study the lateral placement of cars and heavy vehicles (HV) on a two-way two-lane road in Port of Brisbane. It was seen that presence of opposing vehicle and its length influenced the lateral placement of cars, utility vehicles, and semi-trailers statistically. According to Stodart and Donnell (2008), the restrictive nature of road geometry does not produce significant variation in lane position among the vehicles. Also, curve direction and horizontal curve radius were found to have the major relationship with the change in vehicle lane position. Thiemann et al. (2008) studied realworld trajectory data with different mathematical techniques to examine acceleration and lane-changing dynamics. Arai et al. (2015) studied the effect of drivers' awareness on the lane-changing manoeuver. This study simplifies relations between scope awareness parameter and the lane-changing behaviour of drivers. Most of the previous studies focused only on lateral characteristics of vehicles on divided roads. However, only limited attempts have been made to study the lateral placement and movement of vehicles on urban undivided roads in mixed traffic conditions. There are no such studies in the development of model for lateral placement of vehicles. Also, very few attempts have been made to study the choice of path of lateral movement. These research gaps highlight the necessity for studying the lateral placement and movement of vehicles on urban undivided roads under non-lane based mixed traffic conditions.
3.
Data collection and extraction
The data for the present study were collected using video graphic technique during morning peak hours (8:30 a.m.e9:30 a.m.) for two weekdays on a mid-block section of a 12 m wide two-way urban undivided road located in Bangalore City, India. The road section of 30 m long which is free from the influence of intersections, crossroads, bus stops, roadside parking and pedestrians was considered for the study. Fig. 1 shows the layout of the study section. The disaggregate data were extracted from the video images using an image processing software, IrfanView, which was developed by Irfan Skiljan (2007). This software enables to extract 25 frames for one second video data. Gridlines with
Fig. 1 e Layout of the study section.
Please cite this article as: Kotagi, P.B et al., Modeling lateral placement and movement of vehicles on urban undivided roads in mixed traffic: A case study of India, Journal of Traffic and Transportation Engineering (English Edition), https://doi.org/10.1016/ j.jtte.2018.06.008
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J. Traffic Transp. Eng. (Engl. Ed.) xxxx; xxx (xxx): xxx
sufficient scale were plotted in AutoCAD with obtained (x, y) image coordinates and then overlaid on video by using Ulead Video Studio 10.0 editor (Fig. 2). In order to remove the
Fig. 2 e Gridlines overlaid on video image of the study section.
parallax effect due to camera angle, certain correction factors were used (Gowri et al., 2009). These factors were calculated for each grid block using the known distance on the ground and corresponding coordinates on the screen. The data, such as lateral placement of vehicles in ongoing direction, lateral separation between vehicles in ongoing direction and opposing direction, and lateral movement of vehicles, were obtained from frame by frame analysis. The road width was divided into lateral blocks of each 1 m wide and longitudinal blocks of each 2 m long. The volume counts of vehicles during peak hours in ongoing and opposing directions were obtained from the video data. The vehicular composition of the study section is shown in Fig. 3. The ongoing traffic at the section moving towards Central Power Research Institute (CPRI) comprises about 3541 motorized vehicles per hour, where twowheelers (TW) accounted for the largest share of 63.7% and heavy vehicles (comprising of light commercial vehicles and buses) with the least share of 1.9%. The traffic in the opposing direction (towards MSR Hospital) at the section comprises about 908 motorized vehicles per hour, where two-wheelers accounted for the largest share of 57.6% and heavy vehicles with the least share of 4.4%.
Fig. 3 e Vehicular composition in the study section. (a) Ongoing direction (towards CPRI). (b) Opposing direction (towards MSR Hospital).
Fig. 4 e Schematic representation of lateral placement and separation of vehicles. Please cite this article as: Kotagi, P.B et al., Modeling lateral placement and movement of vehicles on urban undivided roads in mixed traffic: A case study of India, Journal of Traffic and Transportation Engineering (English Edition), https://doi.org/10.1016/ j.jtte.2018.06.008
J. Traffic Transp. Eng. (Engl. Ed.) xxxx; xxx (xxx): xxx
4.
Lateral behaviour of vehicles
Lateral placement of a vehicle is defined as the closest lateral position of the vehicle from the edge of the pavement when the vehicle is in motion as shown in Fig. 4. To extract this data, the carriageway width was divided into segments of 50 cm with reference line at the middle of the road section. When the vehicle touches the reference line, the closest lateral position of each vehicle from the edge of the pavement was noted down. The entry time and exit time of each vehicle are obtained from the video frames and with known distance (length of study stretch), the speed of each vehicle is calculated. When subject vehicle (SV) and opposing vehicle (OV) oppose each other and if they overlap each other longitudinally within the stretch, the closest distance between the vehicles was recorded as the lateral separation (Fig. 4). Lateral movement is defined as the movement of a vehicle to the next lane in homogeneous and lane discipline traffic conditions which is represented by lane-changing process. In non-lane discipline traffic conditions, vehicles perform lateral movement by shifting its lateral movement to its sides. Hence, in this study lateral shift is referred as lateral movement. When the subject vehicle (SV) initiates lateral shift at time t and moves its lateral position equal to its width at time t þ T
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under the influence of leader vehicle (LV), it is called lateral shift (Fig. 5).
4.1.
Lateral placement of vehicles
Fig. 6 shows the frequency distribution for lateral placement of vehicles in ongoing direction. It is found that the majority of the vehicles (70.9%) preferred to travel in the middle of the road, with a lateral placement of 3e7 m. Two-wheelers (TW) and auto-rickshaws occupy almost the entire width of the road as they have a tendency to occupy every lateral gap available on the road due to their smaller sizes and higher manoeuvrability. Most of the cars (78.8%) prefer to travel near the middle of the road compared to two-wheelers (63.7%) and auto-rickshaws (76.1%) so as to maintain higher speeds. All the heavy vehicles (HV) are concentrated near the middle of the road, with a lateral placement of 3e7 m, so as to avoid side interferences from other vehicles. Descriptive statistics for lateral placement and speed of each type of vehicle is shown in Table 1. The mean speed of two-wheelers (12.7 m/s) and cars (12.6 m/s) are both higher when compared to heavy vehicles which travel at lower mean speed (11.2 m/s) due to their larger size and lower manoeuvrability. It is also found that the mean lateral placement of all types of vehicles is in the range of 4e5 m
Fig. 5 e Schematic representation of lateral movement of vehicles.
Fig. 6 e Frequency distribution for lateral placement of different types of vehicle. Please cite this article as: Kotagi, P.B et al., Modeling lateral placement and movement of vehicles on urban undivided roads in mixed traffic: A case study of India, Journal of Traffic and Transportation Engineering (English Edition), https://doi.org/10.1016/ j.jtte.2018.06.008
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J. Traffic Transp. Eng. (Engl. Ed.) xxxx; xxx (xxx): xxx
Table 1 e Descriptive statistics of lateral placement and speed of vehicles. Vehicle type
Aggregate Two-wheeler Auto-rickshaw Car Heavy vehicle
Sample size
1849 980 197 619 53
Lateral placement (m)
Speed (m/s)
Mean
SD
Min
Max
Mean
SD
Min
Max
4.5 4.4 4.4 4.8 4.6
1.8 1.9 1.6 1.7 1.3
1.3 1.3 1.3 1.3 3.1
11.8 11.5 9.6 11.8 7.1
12.0 12.7 11.5 12.6 11.2
2.5 1.9 1.6 2.2 2.7
2.1 2.1 5.1 4.7 7.4
16.7 16.7 16.3 16.7 16.3
Note: SD is the standard deviation.
from the edge of the pavement, which indicates that most of the vehicles prefer to travel near the middle of the road. The one-way analysis of variance (ANOVA) test indicates that the lateral placement of different vehicle types is significantly different (the observed value of F (Fobs ¼ 8.61), the critical value of F (Fcrit ¼ 2.61), degrees of freedom (dof ¼ 1848)) from each other at a significance level of 5%. Graphs were plotted between lateral placement and speed of subject vehicles in ongoing direction as shown in Fig. 7. Regression analysis was done and its goodness was checked by the value of coefficient of correlation. 75% of the data were considered for development of the model and the remaining 25% were used for validation. These graphs show that all the four types of vehicles (TW, cars, auto-rickshaws and HV) followed a second-degree polynomial relation. Most of the two-wheelers have higher speeds near the middle of the road because of their tendency for overtaking and also, they are not much influenced by the opposing vehicles due to their higher manoeuvrability. The speeds of auto-rickshaws and cars do not vary much up to the middle of the road and then start decreasing when they move towards the opposing lane due to the influence of opposing vehicles. Heavy vehicles generally travel at lower
speeds and their motion is not disturbed by the presence of other vehicles. It is believed that speed of the opposing vehicle will also influence the lateral position of subject vehicle and hence, speeds of opposing vehicles were also extracted. Fig. 8 shows the relationship between the lateral placement of ongoing vehicle and speed of opposing vehicles. The results indicate that when the ongoing vehicles are travelling in their corresponding lanes, speed of the opposing vehicles will not have much influence on the lateral positions of ongoing vehicles. When the ongoing vehicles (particularly TW and cars) are shifting towards the opposing lane, the speeds of opposing vehicles are reduced. The predicted speed values from the model were compared with the speed values observed from the field for different lateral placements. Mean absolute percentage error (MAPE) was calculated for each lateral placement and they were found to be less than 15% for all the vehicle types, which conformed the limits (15%) as proposed by Mathew and Radhakrishnan (2010) and Gowri and Sivanandan (2015). This shows that the model replicates the field conditions reasonably. Lateral placement of vehicles on an undivided road cannot be explained only by studying the distribution of vehicles and
Fig. 7 e Relationship between lateral placement and speed of ongoing vehicles. (a) Two-wheelers. (b) Cars. (c) Autorickshaws. (d) Heavy vehicles. Please cite this article as: Kotagi, P.B et al., Modeling lateral placement and movement of vehicles on urban undivided roads in mixed traffic: A case study of India, Journal of Traffic and Transportation Engineering (English Edition), https://doi.org/10.1016/ j.jtte.2018.06.008
J. Traffic Transp. Eng. (Engl. Ed.) xxxx; xxx (xxx): xxx
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Fig. 8 e Relationship between lateral placement of ongoing vehicles and speed of opposing vehicles. (a) Two-wheelers. (b) Cars. (c) Auto-rickshaws. (d) Heavy vehicles.
Table 2 e ANOVA tests comparing unopposed against opposed lateral placements. Distributions compared Twoewheelers unopposed against opposed Auto-rickshaws unopposed against opposed Cars unopposed against opposed Heavy vehicles unopposed against opposed
Sample Fobs Fcrit p value size 1710
4.4
3.8
0.04
250
4.8
3.9
0.04
998 66
4.8 0.5
3.9 4.0
0.04 0.52
hence, lateral placement was also examined by considering the lateral position of subject vehicle when opposed by other vehicles and also when unopposed. The one-way ANOVA test was performed to check whether there is any significant difference in lateral placement of different types of ongoing vehicles when they are opposed and also when they are unopposed. ANOVA test results show that these two distributions are statistically different for TW, cars and auto-rickshaws as shown in Table 2. These vehicles alter their lateral placement under the influence of opposing vehicles. However, lateral placements of heavy vehicles do not differ significantly when opposed than when unopposed. It shows that heavy vehicles are not much influenced by opposing vehicles. Frequency distributions for lateral placements of twowheelers, cars, auto-rickshaws and heavy vehicles when opposed and unopposed are shown in Fig. 9. It can also be observed that two-wheelers are laterally distributed almost on the entire road width due to smaller sizes and higher manoeuvrability. They are not much influenced by opposing vehicles and try to squeeze in between the vehicles. In case
of cars and auto-rickshaws when opposed by other vehicles, most of them occupy the home lane, maintaining a safe lateral distance with the opposing vehicles as they have larger sizes compared to two-wheelers. Most of the heavy vehicles are concentrated near the middle of the road, with a lateral placement of 3e6 m, even if they are opposed by other vehicles as they are not disturbed by any other vehicles due to their larger sizes (other vehicles move away from the path of heavy vehicles). A model was developed using regression analysis to predict the lateral placement of subject vehicles on undivided roads. This regression model can be used in vehicle placement logics to develop traffic simulation models (Kotagi et al., 2018). In building microscopic simulation model, vehicle placement is an important logic. The generated vehicles are placed in the starting point of the simulation road stretch based on some assumptions and observations from field. The placement of vehicles is unpredictable and also depends on many factors such as types and speeds of subject and opposing vehicles. Hence, it is necessary to develop a model to predict the lateral placement of vehicles. The variables considered for model development includes presence of each category of vehicle (two-wheeler, car, auto-rickshaw, heavy vehicle), and speed of each category of vehicle (both as subject vehicle and opposing vehicle). Correlation analysis was carried out to select the most influencing variables and to eliminate the irrelevant variables. It was found that presence of two-wheeler, car and auto-rickshaw as subject and opposing vehicle type and their speeds are the most influencing variables and hence, they are considered for developing the model. The model was developed using 75% of the total data and the remaining 25% was used for validation. The developed
Please cite this article as: Kotagi, P.B et al., Modeling lateral placement and movement of vehicles on urban undivided roads in mixed traffic: A case study of India, Journal of Traffic and Transportation Engineering (English Edition), https://doi.org/10.1016/ j.jtte.2018.06.008
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J. Traffic Transp. Eng. (Engl. Ed.) xxxx; xxx (xxx): xxx
Fig. 9 e Frequency distributions of lateral placements of different types of vehicles when opposed and unopposed. (a) Twowheelers. (b) Cars. (c) Auto-rickshaws. (d) Heavy vehicles.
model, which can be used to predict the lateral placement of subject vehicle (Y), is shown in Eq. (1). Y ¼ b0 þ b1 X1 þ b2 X2 þ b3 X3 þ b4 X4 þ b5 X5 þ b6 X6 þ b7 X7 þ b8 X8 (1) where b0 is a constant, b1eb8 are the coefficients of independent variables X1eX8. X1eX3 represent presence or absence of two-wheelers, cars and auto-rickshaws as ongoing vehicle types. Similarly, X5 e X7 represent presence or absence of twowheelers, cars and auto-rickshaws as opposing vehicle types. X4 represents speed of ongoing vehicle. X8 represents speed of opposing vehicle. The significance of overall model and the significance of independent variables were tested using goodness of fit. The R2 value of the model is obtained as 0.55. The model has an Fobserved value which is greater than the critical value (Fobs ¼ 19.42, Fcrit ¼ 2.42, dof ¼ 889), implying that the model is statistically significant. The parameter estimation signifies that for every unit increment in independent variable, there is
an average change in dependent variable provided that other variables are held constant. The values of coefficients, t-statistics (tstat) and p value for the developed model were investigated to identify the significant variables. After checking for significance, regression analysis was repeated by using those variables which are significant and the model coefficients were estimated for the revised model (Table 3). When the speed of the subject vehicle (ongoing vehicle) increases, it will move towards the middle of the road or to the opposing lane when there is no opposing vehicle mainly for the purpose of overtaking. Subject vehicle shifts towards the left side of the road when speed of opposing vehicle increases in order to avoid collision with the opposing vehicles. Twowheelers and auto-rickshaws as ongoing vehicles has significant influence on lateral placement as they occupy almost entire road width due to their smaller sizes and higher manoeuvrability. The MAPE values were calculated by comparing predicted and observed values and it was found to
Table 3 e Estimation of coefficients for MLR model. Explanatory variable Constant Presence of two-wheeler (ongoing) Presence of auto-rickshaw (ongoing) Speed of ongoing vehicle Speed of opposing vehicle
Coefficient (b)
Standard error
tstat
p value
11.95 3.84 3.62 0.34 1.12
1.26 0.56 0.51 0.09 0.10
9.49 6.86 7.07 3.73 11.73
0.00 0.00 0.00 0.00 0.00
Please cite this article as: Kotagi, P.B et al., Modeling lateral placement and movement of vehicles on urban undivided roads in mixed traffic: A case study of India, Journal of Traffic and Transportation Engineering (English Edition), https://doi.org/10.1016/ j.jtte.2018.06.008
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J. Traffic Transp. Eng. (Engl. Ed.) xxxx; xxx (xxx): xxx
be less than 15%, which shows that the model replicates the field conditions reasonably.
4.2.
Speed of opposing vehicle (km/h)
Lateral separation of vehicles
Table 4 shows the descriptive statistics for lateral separation of different types of vehicles. It is observed that lateral separation of a vehicle decreases as the size of the subject vehicle increases. It is also observed that vehicles travelling at higher speeds, such as two-wheelers, maintain higher mean lateral separation (4.7 m) with opposing vehicles when compared to slow moving vehicles such as heavy vehicles (2.7 m). Table 5 shows the lateral separation values for different ongoing and opposing vehicle pairs. It is found that ongoing and opposing vehicles have less freedom to move laterally when the size of either vehicle increases and hence, lateral separation decreases. The one-way ANOVA test was performed to check whether there is any significant difference in the lateral separation of vehicles. The result indicates that the lateral separation of vehicles is significantly different (Fobs ¼ 90.08, Fcrit ¼ 2.62, dof ¼ 1216) for different types of vehicles at a significance level of 5%. Lateral separation also depends on the speeds of ongoing (subject) and opposing vehicles. From Table 6, it is clear that lateral gap maintained by the ongoing vehicle with opposing vehicle is greater when the speed of the opposing vehicle is higher. Table 7 shows the relationship between lateral separation and speed of opposing vehicles for varying speed ranges of subject vehicles. It indicates that lateral separation between subject and opposing vehicles increases with the increase in speed of the opposing vehicles.
Table 4 e Descriptive statistics for lateral separation of different type of vehicles. Vehicle type
Aggregate Two-wheeler Auto-rickshaw Car Heavy vehicle
Sample size
1217 598 152 384 83
Table 6 e Lateral separation depending on speed of subject and opposing vehicles.
Lateral separation (m) Mean
SD
Min
Max
3.6 4.7 4.2 2.9 2.7
1.6 1.8 1.2 1.4 1.4
0.6 0.9 0.9 0.6 1.4
8.6 8.6 7.8 8.0 6.7
20e30 30e40 40e50 50e60
5.
Speed of subject vehicle (km/h) 20e30
30e40
40e50
50e60
e 4.07 3.79 5.01
3.97 3.97 3.87 4.38
3.80 3.71 3.78 3.93
e 3.62 3.56 3.80
Analysis of lateral movement of vehicles
Lateral movement is defined as the movement of a vehicle to the next lane in homogeneous and lane discipline traffic conditions which is represented by lane-changing process. In non-lane discipline traffic conditions, vehicles perform lateral movement by shifting its lateral movement to its sides. Hence, in this study lateral shift is referred as lateral movement. Lateral shift is defined as the type of lateral movement in which the subject vehicle moves its lateral position equal to its width under the influence of the leader vehicle. Lateral shift can be either to the left or to the right depending upon the leader vehicle behaviour. Any front vehicle, whose width completely or partially overlaps with the width of subject vehicle is called a leader vehicle. In this study, total number of lateral shifts obtained are 294 including left shift (16.32%) and right shift (83.67%), out of which 76.8% of lateral shifts are performed by two-wheelers (Munigety et al., 2014). Lateral shift can be classified into three stages including the motivation to change current path, selection of alternate path (left or right lateral shift) to change into and execution of lateral shift. In this study, the first two stages were examined. In undivided roads, since the ongoing traffic is predominantly influenced by opposing traffic, the effect of opposing vehicle on motivation for lateral shift and selection of the path of lateral shifts was also studied. The factors such as speed of subject vehicle, speed of leader vehicle in target path and alternate path, and lateral gaps in target path and alternate path were considered to study and model the lateral shifts.
5.1.
Motivation for lateral movement
In this study, the traffic characteristics such as speeds of leader vehicles in current, target and alternate paths, which
Table 5 e Summary statistics for lateral separation of ongoing and opposing vehicle pairs. Ongoing and opposing vehicle pair
Two-wheeler and two-wheeler Two-wheeler and auto-rickshaw Two-wheeler and car Auto-rickshaw and two-wheeler Auto-rickshaw and car Car and two-wheeler Car and auto-rickshaw Car and car
Sample size
129 51 137 24 28 109 43 43
Lateral separation (m) Mean
SD
Min
Max
5.5 4.6 4.1 5.0 3.3 3.7 3.1 3.0
1.6 1.2 1.3 1.0 1.1 1.1 1.1 1.1
1.7 1.9 0.6 3.2 0.9 1.3 0.5 0.5
8.8 7.7 7.4 7.4 5.5 6.6 4.9 4.9
Please cite this article as: Kotagi, P.B et al., Modeling lateral placement and movement of vehicles on urban undivided roads in mixed traffic: A case study of India, Journal of Traffic and Transportation Engineering (English Edition), https://doi.org/10.1016/ j.jtte.2018.06.008
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Table 7 e Relationship between lateral separation and speed of opposing vehicles. Case
Sample size
Speed of opposing vehicle > speed of subject vehicle Speed of opposing vehicle ¼ speed of subject vehicle Speed of opposing vehicle < speed of subject vehicle
408 22 315
motivate the subject vehicle to perform discretionary lanechanging (DLC) manoeuvres, were investigated. The relationship between speed of subject vehicle and speed of front vehicle in current path is shown in Fig. 10. The results show that speed of subject vehicle is higher than speed of leader vehicle for 60.2% cases when considering all vehicles. When the subject vehicle is TW, its speed is found to be greater than the leader vehicle in current path for 70.6% cases. These greater speed values of subject vehicles when compared to leader vehicles may encourage the drivers to perform a lateral shift. To test whether the subject vehicle speeds differ significantly with leader speeds, a t-test assuming unequal variances was conducted on the null hypothesis that their speeds do not differ significantly. The mean speed of subject vehicle (13.27 m/s) is found to be greater than the mean speed of leader vehicle (12.19 m/s) in case of all vehicles (aggregate) which shows that null hypothesis is rejected (tstat ¼ 5.86, t-critical (tcrit) ¼ 1.96).
5.2.
Lateral separation (m)
Selection of the target path
In DLC manoeuvers, drivers prefer either left or right adjacent path as their target path. The traffic flow characteristics in both left and right adjacent paths were studied and influence of these characteristics on selection of target path was investigated.
Speeds of leader vehicles in current path are compared to speeds of leader vehicles in target and alternate paths. Fig. 11 shows the relationship between speeds of leader vehicles in current path and target path. For all vehicles (aggregate), the leader vehicle speed in target path is greater than the leader vehicle speed in current path for 73.3% cases. However, there are only 27.7% cases where the leader vehicle speed in alternate path is greater than the leader vehicle speed in
SD
Min
Max
3.9 3.8 3.7
1.7 1.8 1.6
0.5 1.4 0.6
8.9 7.4 7.9
current path in case of all vehicles (Fig. 12(a)). In case of TWs, the speed of leader vehicle in alternate path is greater than the speed of leader vehicle in current path for 15.3% cases (Fig. 12(b)). This shows that the speed of leader vehicle in target path plays an important role in making the decision of lateral shift of subject vehicles. The t-test conducted enhances these arguments and the results indicate that the mean speed of leader vehicle in current path (11.23 m/s) is significantly lower than the mean speed of leader vehicle in target path (12.55 m/s) (tstat ¼ 2.54, tcrit ¼ 1.96). On the other hand, the speed of leader vehicle in current path (12.3 m/s) is significantly greater than the speed in alternate path (11.7 m/s), which was shown by t-test results (tstat ¼ 1.98, tcrit ¼ 1.96).
5.2.2.
Longitudinal gaps in target and alternate paths
The relationship between longitudinal gaps in target path and alternate path shown in Fig. 13 indicates that only for 31.1% cases of all vehicles and only for 27.3% cases of TWs, longitudinal gap is greater in target path than in alternate path. Hence, the result reveals that longitudinal space gap is not an influential variable for choosing paths. The t-test results show that the longitudinal gap in target path (18.5 m) is significantly shorter than the longitudinal gap in alternate path (21.1 m) in case of all vehicles (tstat ¼ 3.65, tcrit ¼ 1.00).
5.2.3. 5.2.1. Speeds of leader vehicles in current path, target path and alternate path
Mean
Lateral gaps in target and alternate paths
Lateral gap in target path is greater than that in the alternate path for 83.2% cases of aggregate and for 81.0% cases of TWs, which shows that lateral gap is an influential factor in the selection of paths (Fig. 14). Thus, the subject vehicle has a tendency to choose the correct target path. To test whether the lateral gaps in target and alternate paths are significantly different, a t-test assuming unequal variances was conducted on the null hypothesis that their lateral gaps do not differ significantly. It is found that the mean lateral gap in target path (7.0 m) is greater than that in alternate
Fig. 10 e Relationship between speeds of subject vehicle and leader vehicle in current path. (a) Aggregate. (b) Two-wheelers. Please cite this article as: Kotagi, P.B et al., Modeling lateral placement and movement of vehicles on urban undivided roads in mixed traffic: A case study of India, Journal of Traffic and Transportation Engineering (English Edition), https://doi.org/10.1016/ j.jtte.2018.06.008
J. Traffic Transp. Eng. (Engl. Ed.) xxxx; xxx (xxx): xxx
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Fig. 11 e Relationship between speeds of leader vehicles in current and target paths. (a) Aggregate. (b) Two-wheelers.
Fig. 12 e Relationship between speeds of leader vehicles in current and alternate paths. (a) Aggregate. (b) Two-wheelers.
path (4.1 m) in case of all vehicles, which shows that null hypothesis is thus rejected (tstat ¼ 16.4, tcrit ¼ 1.96).
5.2.4.
Influence of opposing vehicles on lateral movement
The influence of opposing vehicles on the lateral movement of a subject vehicle was also investigated. Lateral placement of the leader vehicle in current path is compared with lateral separation between leader vehicle in current path and opposing vehicle. Lateral gap in the target path is found to be greater in 72.2% cases of all vehicles (Fig. 15(a)) and 65.1% cases of TWs (Fig. 15(b)). Thus, vehicles freely shift towards the target path. The lateral gap in the target path (5.6 m) is significantly greater than the lateral gap in the alternate path (4.2 m) in case of all vehicles (tstat ¼ 8.42, tcrit ¼ 1.96).
5.3.
using statistical package for the social science (SPSS) (IBM, Corp., 2012). These regression models assume that log-odd of each choice of path followed a linear model as given in Eq. (2).
Multinomial logistic regression model
Multinomial logistic regression is used to model the choices of path of lateral shift (left, current, right) made by all vehicles
hiq ¼ ln
piq ¼ aq þ Xi bq piQ
(2)
where h is the log-odd of choice of lateral shift, p is the choice of lateral shift. aq is a constant and bq is a vector of regression coefficients (q ¼ 1, 2,$$$ Q1). An appropriate category Q is fixed as reference. Interpretation of the estimates are similar to that of linear regression model in Eq. (1). Dependent variable is the choice of lateral shift (left, right and current) and the significant independent variables are sizes of subject vehicle (X1) and leader vehicle (X2), lateral gap between leader vehicle and right adjacent leader vehicle (X3), lateral gap between leader vehicle and left adjacent leader vehicle (X4), relative speed between subject vehicle and leader vehicle (X5), relative speed between leader vehicle and right adjacent leader vehicle (X6), relative speed between leader
Fig. 13 e Relationship between longitudinal gaps in target path and alternate path. (a) Aggregate. (b) Two-wheelers. Please cite this article as: Kotagi, P.B et al., Modeling lateral placement and movement of vehicles on urban undivided roads in mixed traffic: A case study of India, Journal of Traffic and Transportation Engineering (English Edition), https://doi.org/10.1016/ j.jtte.2018.06.008
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Fig. 14 e Relationship between lateral gaps in target path and alternate path (without the influence of opposing vehicles). (a) Aggregate. (b) Two-wheelers.
Fig. 15 e Relationship between lateral gaps in target and alternate path (under the influence of opposing vehicles). (a) Aggregate. (b) Two-wheelers.
vehicle and left adjacent leader vehicle (X7), and lateral gap between leader vehicle and opposing vehicle (X8). The speeds of leader vehicles and lateral gaps in the target and alternate paths turned out to be the influential variables for the choice of path. 75% of data were used for model development and remaining 25% for validation. A log likelihood ratio chi-square test was performed to determine the statistical significance of the overall model. The result shows that the overall model is statistically significant at a significance level of 5% (p value ¼ 0.000). Hence, there exists a relationship between the independent and dependent variables. The estimated results of the model include coefficient values, value of standard error, Wald test and significance value. Current path is considered as a reference category in the model and hence, the coefficients obtained are the values indicating the ratios of left shift to the current path and right shift to the current path. The significance of each independent variable is checked by the value of standard error (which should be less than 2) and the significance value (p value should be less than the significance level of 5%). Parameter estimates of the target path choice model are presented in Table 8. The goodness of fit of the developed model is determined using McFadden pseudo R2 value (0.452). The model results show that the decrease in subject vehicle size and increase in leader vehicle size increases the probability of a subject vehicle choosing either left or right shift compared to the probability of travelling in current path. The increase in lateral gap between leader vehicles in current path and target path increases the probability of a subject vehicle shifting either to the left or to the right compared to the probability of travelling
in current path. When the relative speed between the subject vehicle and leader vehicle gives a negative sign, the probability of a subject vehicle shifting either to the left or to the right increases compared to the probability of travelling in current path. The increase in relative speed between leader vehicle in current path and adjacent leader vehicle increases or decreases the probability of a subject vehicle shifting to the left or to the right compared to the probability of travelling in current path. Since the road section is undivided, lateral gap between leader vehicle in current path and opposing vehicle also influences the lateral movement. The increase in lateral gap between leader vehicle in current path and opposing vehicle increases the probability of a subject vehicle shifting to the right and decreases the probability of shifting to the left compared to the probability of travelling in current path. In India (left hand drive rule is followed), drivers prefer to move at higher speed near the right side due to the absence of roadside frictions like parking, pedestrians, encroachments, etc. (Kanagaraj et al., 2015). Thus, drivers prefer right side path generally. Earlier studies also reported that drivers are more willing to perform right shift compared to left shift (Mallikarjuna and Rao, 2011; Mathew et al., 2014; Munigety et al., 2014). The same was observed from the real world traffic data collected from Bangalore, India. A total of 294 lateral shifts were observed, out of which 48 are left shifts and remaining 246 are right shifts. Hence, the prediction success for right shifts (83.2%) is greater than the left shifts (60.1%). The model was validated using 25% data and the coefficients of the developed and validated model were compared. The results show that the mean absolute percentage error obtained is less than 3%.
Please cite this article as: Kotagi, P.B et al., Modeling lateral placement and movement of vehicles on urban undivided roads in mixed traffic: A case study of India, Journal of Traffic and Transportation Engineering (English Edition), https://doi.org/10.1016/ j.jtte.2018.06.008
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J. Traffic Transp. Eng. (Engl. Ed.) xxxx; xxx (xxx): xxx
Table 8 e Parameter estimates of the model. Lateral shifta Left lateral shift
Right lateral shift
Variable
Coefficient (b)
Standard error
Wald
p value
Intercept Subject vehicle size Leader vehicle size Lateral gap between leader vehicle and right adjacent leader vehicle Lateral gap between leader vehicle and left adjacent leader vehicle Relative speed between subject vehicle and leader vehicle Relative speed between leader vehicle and right adjacent leader vehicle Relative speed between leader vehicle and left adjacent leader vehicle Lateral gap between leader vehicle and opposing vehicle Intercept Subject vehicle size Leader vehicle size Lateral gap between leader vehicle and right adjacent leader vehicle Lateral gap between leader vehicle and left adjacent leader vehicle Relative speed between subject vehicle and leader vehicle Relative speed between leader vehicle and right adjacent leader vehicle Relative speed between leader vehicle and left adjacent leader vehicle Lateral gap between leader vehicle and opposing vehicle
0.486 3.116 1.741 0.082 0.659 0.230 0.195 0.264 0.093 1.545 1.714 0.019 0.432 0.871 0.196 0.079 0.407 0.317
1.455 0.702 0.487 0.165 0.191 0.119 0.071 0.087 0.142 1.438 0.432 0.395 0.172 0.181 0.099 0.066 0.081 0.120
0.111 19.680 12.760 2.251 11.870 3.725 7.577 9.208 3.428 1.155 15.740 2.002 6.317 23.140 3.869 2.412 25.420 6.992
0.73 0.00 0.00 0.00 0.00 0.04 0.00 0.00 0.00 0.28 0.00 0.01 0.01 0.00 0.04 0.02 0.00 0.00
Note: a means the reference category is current path, where the number of observations for current path is 126, prediction success for current path is 84.1%, number of observations for right shift is 101, prediction success for right shift is 83.2%, number of observations for left shift is 40, and prediction success for left shift is 60.1%.
6.
Summary and conclusion
The present study aims to analyse and model the lateral placement and movement of vehicles on urban undivided roads in mixed traffic conditions. For this purpose, traffic data collected from an urban undivided road in Bangalore city, India, was used. The lateral placement and separation of different types of vehicles were extracted and investigated to study the effect of speed of ongoing and opposing vehicles on lateral placement and separation of vehicles. Multiple linear regression model was developed for predicting the lateral placement of subject vehicle and it was found that lateral placement of a subject vehicle was influenced by types and speeds of subject and opposing vehicles. The various factors which motivate the lateral shift of vehicles were analysed. Also, the selection of path of vehicles during lateral shifts were also analysed and modelled using multinomial logistic regression. The key conclusions arising from this study are as follows. It was found that the majority of the vehicles (70.9%) preferred to travel in the middle of the road, with a lateral placement of 3e7 m. Two-wheelers, cars and auto-rickshaws adjust their lateral placement when opposed by vehicles. Heavy vehicles are not much influenced by opposing vehicles due to their larger sizes and thus, lateral placements do not vary significantly when opposed than when unopposed. Lateral separation of vehicles decreases with increase in subject vehicle size and increases with increase in the speed of opposing vehicle. The probability of a subject vehicle choosing either left or right lateral shift increases with decrease in subject vehicle size and increases with leader vehicle size. The increase in lateral gap between leader vehicle in current path and opposing vehicle increases the probability of
a subject vehicle shifting to the right and decreases the probability of shifting to the left. This study finds interesting applications in development of traffic simulation models to carry out various traffic control and management measures. MLR model developed for lateral placement can be used in traffic simulation model (vehicle placement logic) to assign the lateral position of vehicles in the starting point of simulation road stretch. The path choice model developed for lateral shifts can be used in microscopic traffic simulation to model the lateral movements of vehicles. The factors such as road width, road type, driver characteristics, weather conditions, time of day, etc., can be considered in the models for better results. The model for lateral placement and movement can be further improved by developing class-wise model. In the study of lateral movement, only lateral shift was taken into consideration for analysis and modelling due to limited field of view of study section. In the future, the execution of lateral movements (i.e., overtaking behaviour of vehicles) can also be studied and modelled. The findings of the study can be generalized by collecting and analysing large amount of data.
Conflict of interest The authors do not have any conflict of interest with other entities or researchers.
Acknowledgements The authors are thankful to Additional Commissioner, Bangalore Traffic Police, India, for permitting us to record the traffic data necessary for present study. Authors also thank
Please cite this article as: Kotagi, P.B et al., Modeling lateral placement and movement of vehicles on urban undivided roads in mixed traffic: A case study of India, Journal of Traffic and Transportation Engineering (English Edition), https://doi.org/10.1016/ j.jtte.2018.06.008
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J. Traffic Transp. Eng. (Engl. Ed.) xxxx; xxx (xxx): xxx
the editor and the reviewers for their valuable comments and suggestions which helped us in refining and improving this paper.
references
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Punith B. Kotagi is an assistant professor at Department of Civil Engineering in The National Institute of Engineering Mysuru, Mysuru, India. He completed his PhD from National Institute of Technology Karnataka, Surathkal, India, and master of technology in highway technology from Resource Centre for Asphalt and Soil Training Academy (RASTA), Bangalore, India. His research area includes development of traffic simulation model and its application in various traffic operations and management measures under mixed traffic conditions.
Pooja Raj completed her master of technology (research) from the Department of Civil Engineering in National Institute of Technology Karnataka, Surathkal, India, in 2016. Presently, she is pursuing her PhD in the same organization. Her research interests include traffic flow modelling and simulation, pedestrian studies, PCU and capacity estimation under mixed traffic conditions.
Dr. Gowri Asaithambi is currently working as an assistant professor in the Department of Civil and Environmental Engineering at Indian Institute of Technology (IIT) Tirupati, India. Prior to joining the IIT Tirupati, she was an assistant professor at the Department of Civil Engineering in National Institute of Technology (NIT) Karnataka, Surathkal, India. She received her PhD from Indian Institute of Technology (IIT) Madras, India, in 2011. Her main research interests are traffic flow modelling and simulation, traffic operations and management, capacity of traffic facilities, pedestrian safety, and intelligent transportation systems.
Please cite this article as: Kotagi, P.B et al., Modeling lateral placement and movement of vehicles on urban undivided roads in mixed traffic: A case study of India, Journal of Traffic and Transportation Engineering (English Edition), https://doi.org/10.1016/ j.jtte.2018.06.008
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Original Research Paper
Modeling lateral placement and movement of vehicles on urban undivided roads in mixed traffic: A case study of India Punith B. Kotagi a, Pooja Raj b, Gowri Asaithambi c,* a
Department of Civil Engineering, The National Institute of Engineering Mysuru, Mysuru 570008, India Department of Civil Engineering, National Institute of Technology Karnataka, Mangalore 575025, India c Department of Civil and Environmental Engineering, Indian Institute of Technology Tirupati, Tirupati 517506, India b
highlights Lateral placement and movement of vehicles on urban undivided roads are analyzed and modelled. Lateral separation of vehicle decreases with increase in subject vehicle size. Lateral separation of vehicle increases with increase in the speed of opposing vehicle. Multiple linear regression model was developed to predict lateral placement of subject vehicle. Multinomial logistic regression model was developed to study the choice of path of lateral movements.
article info
abstract
Article history:
In India, the majority of urban roads are undivided where the behavior of flows in a
Received 12 January 2018
particular direction is predominantly influenced by the opposing traffic. Due to lack of lane
Received in revised form
segregation, the vehicles in ongoing direction occupy the opposing lane, which increases
7 June 2018
the lateral interactions between vehicles. These lateral interactions are influenced by
Accepted 8 June 2018
various parameters such as vehicle types, driver behavior and vehicular speeds. Study of
Available online xxx
such complex interactions plays an important role in evaluating various management measures using microscopic simulation models. The lateral characteristics of vehicles,
Keywords:
such as placement, separation and movement, act as necessary input for simulation
Transportation
models. The present study aims to analyze and model the lateral characteristics of vehicles
Urban undivided road
on two-lane urban undivided roads. To achieve this, traffic flow data were collected from
Mixed traffic
an urban undivided mid-block section in Bangalore City, India, using video graphic tech-
Lateral placement
nique. Multiple linear regression model was developed for predicting the lateral placement
Lateral separation
of subject vehicle and it was found that lateral placement of subject vehicle is influenced
Lateral movement
by types and speeds of subject and opposing vehicles. Lateral separation for different types of ongoing (subject) and opposing pairs was also analyzed. The results show that both the ongoing and opposing vehicles have less freedom to move laterally when their sizes increase and hence, lateral separation decreases. The choice of path of vehicles' lateral shifts (left, current and right) on urban undivided roads was modeled using multinomial logistic regression. Lateral shift of a vehicle is influenced by speeds of subject vehicle and leader
* Corresponding author. Tel.: þ91 824 2473366. E-mail addresses: [email protected] (P.B. Kotagi), [email protected] (P. Raj), [email protected] (G. Asaithambi). Peer review under responsibility of Periodical Offices of Chang'an University. https://doi.org/10.1016/j.jtte.2018.06.008 2095-7564/© 2019 Periodical Offices of Chang'an University. Publishing services by Elsevier B.V. on behalf of Owner. This is an open access article under the CC BY-NC-ND license (http://creativecommons.org/licenses/by-nc-nd/4.0/).
Please cite this article as: Kotagi, P.B et al., Modeling lateral placement and movement of vehicles on urban undivided roads in mixed traffic: A case study of India, Journal of Traffic and Transportation Engineering (English Edition), https://doi.org/10.1016/ j.jtte.2018.06.008
2
J. Traffic Transp. Eng. (Engl. Ed.) xxxx; xxx (xxx): xxx
vehicle in current path, speed of leader vehicle in target path, and lateral gap between leader vehicles in current path and target path. © 2019 Periodical Offices of Chang'an University. Publishing services by Elsevier B.V. on behalf of Owner. This is an open access article under the CC BY-NC-ND license (http:// creativecommons.org/licenses/by-nc-nd/4.0/).
1.
Introduction
The study of lateral placement and movement of vehicles finds important applications in traffic control and management measures, geometric design of roads, accident analysis, and estimation of level of service and roadway capacity. In most of the developing economies like India, traffic flow is mixed in nature consisting of vehicles with varying static and dynamic characteristics. In such traffic conditions, due to weak lane discipline, vehicles tend to utilize any lateral position available on the road and also interact both in lateral and longitudinal directions. Most of the roads in urban cities of India are undivided in nature where the vehicles travelling in ongoing direction often use the opposing lanes as well. Hence, the lateral interaction of vehicles on undivided roads is significantly higher when compared to vehicles travelling on divided roads. Generally, the lateral interactions are influenced by various parameters such as vehicle types, vehicular speeds and driver behaviour. Lateral placement and movement of vehicles are also influenced by the opposing vehicles due to lack of lane segregation. The earlier studies which focused on lateral characteristics of vehicles in homogeneous and mixed traffic conditions were limited to divided roads. Moreover, all these studies focused on longitudinal movement of vehicles and lateral movement behaviour of vehicles has received less attention. Also, only limited studies focused on analysis of various factors which influence lateral placement and movement of vehicles on urban undivided roads. Based on the above research motivation, overall objective of present study is to analyse and model the lateral placement and movement of vehicles on urban undivided roads under mixed traffic conditions and the specific objectives are: (1) to analyze and model the lateral placement of different types of vehicles, (2) to study and analyze lateral separation between different types of subject and opposing vehicles, (3) to analyze and model lateral movement behavior of vehicles. To investigate above objectives, traffic data were collected from an urban mid-block section of an undivided road in Bangalore City, India, using video graphic technique. To achieve the first objective, lateral placement and speed of different vehicle types in ongoing and opposing directions were extracted from the video data. Multiple linear regression (MLR) model was developed for predicting the lateral placement of ongoing vehicles considering types and speeds of ongoing and opposing vehicles as influencing variables. To attain the second objective, lateral separation between different types of ongoing and opposing vehicles were obtained. For achieving the third objective, lateral movements performed by different types of vehicles were analysed. A
multinomial logistic regression model was developed to study the choice of path of lateral movements performed by different types of vehicles. The rest of the paper is organised as follows. Section 2 discusses review of the literature focusing on studies related to lateral placement and movement of vehicles on both divided and undivided roads under mixed traffic conditions in developing nations as well as under homogeneous traffic conditions in developed nations. The process of data collection and extraction is discussed in Section 3. Section 4 presents the results of lateral placement and separation of vehicles. In Section 5, discussion on lateral movement behaviour of vehicles and model development is presented. Finally, the summary and conclusions of the study are presented in Section 6.
2.
Literature review
In this section, the studies focusing on the lateral placement and movement of vehicles under mixed traffic conditions in developing countries such as India are presented. Studies carried out in advanced countries with homogenous traffic cannot be used to analyse lateral placement and movement of vehicles in mixed traffic due to presence of varying vehicle type and weak lane discipline. However, a few studies carried out in developed nations with homogeneous traffic have also been reported.
2.1. Studies carried out for mixed traffic conditions in developing countries Dey et al. (2006) analysed lateral position of vehicles under mixed traffic conditions and found that the lateral position of vehicles followed unimodal or a bimodal curve depending on proportion of slow and fast moving vehicles. They introduced two parameters including placement factor (PF) and skewness range (SR) to describe the placement of vehicles and they concluded that the lateral placement follows unimodal curve if PF and SR are lower than 1.30 and 0.54, respectively. Chunchu et al. (2010) collected microscopic traffic data under mixed traffic conditions with the help of image processing technique. The traffic data such as vehicular composition, lateral placements of vehicles, longitudinal and lateral gaps were extracted. Authors studied the gap maintaining behaviour of different vehicle types when exposed to varying traffic conditions. An empirical relationship between lateral gap and area occupancy for different combinations of vehicles were developed. Balaji et al. (2013) studied the relation of
Please cite this article as: Kotagi, P.B et al., Modeling lateral placement and movement of vehicles on urban undivided roads in mixed traffic: A case study of India, Journal of Traffic and Transportation Engineering (English Edition), https://doi.org/10.1016/ j.jtte.2018.06.008
J. Traffic Transp. Eng. (Engl. Ed.) xxxx; xxx (xxx): xxx
placement and speed of different vehicles on two lane state highways. The analysis showed that three-wheelers, heavy vehicles and slow-moving vehicles follow a linear relation, while two-wheelers and cars follow a second-degree polynomial relation. The vehicles as a whole followed a second-degree polynomial relation. Mahapatra and Maurya (2013) analysed the impact of lane positions of vehicles on average travel speed, time headway and lateral clearances for four-lane, six-lane and eight-lane divided highways. They concluded that there exists a wide variation in the lane-specific vehicular speed, traffic composition, time headway and lateral gap in mixed traffic condition of Indian highways. Munigety et al. (2014) presented lateral movement tactical decision and choice making using vehicle type variant models for Eastern Express Highway, Mumbai city. They studied the motivation behind a driver to perform a lateral shift by comparing the speeds of the subject vehicle and that of the leader vehicle in the current lane. In the selection of a target path, speeds of the leader vehicle and the lead space gaps of the immediate left and right paths were analysed. Mahapatra and Maurya (2015) analysed lateral and longitudinal behaviour of vehicles in mixed traffic condition on Indian highways. It was observed that there exists an inverse relationship between the speed and the lateral characteristics. Mahapatra et al. (2016) studied lateral movements of vehicles over different types of roads in three metropolitan cities of India (Kolkata, Mumbai and Pune) under moderate traffic conditions. Lateral acceleration variation of five different types of vehicles and its relationship with vehicle longitudinal characteristics (i.e., longitudinal speed) were analysed. Lateral acceleration values rise quickly with initial increase in speed. Afterward, lateral acceleration values reduce with further increase in longitudinal speed of vehicles. Asaithambi and Shravani (2017) mathematically modelled the overtaking behaviour of different vehicle types under mixed traffic condition. Moving car observer method and vehicle registration plate method were adopted to collect the overtaking data from a two-lane two-way undivided highway. From the study, it was observed that the number of overtaking increases with increase in ongoing direction flow and decreases with increase in opposing direction flow.
2.2. Studies carried out for homogeneous traffic conditions in developed countries Miller and Steuart (1982) analysed vehicle lateral placements at five different locations in Toronto metropolitan area. Influences of lateral placement along with lane width and lane type on speeds of vehicle were studied. Results showed that there is no explicit relationship between lateral placement of vehicle and its speed. Armour (1985) identified that the main factors influencing lateral placement are shoulder type and lane width. Vehicles travelled further from the centre line as lane width increased. Lennie and Bunker (2005) compared the behavioural characteristics of passenger car drivers surrounding multi-combination vehicles using lateral position characteristics. They observed that the behaviour of a passenger car changes when a heavy vehicle approaches it closer than a passenger car does. It
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was also seen that there is no significant change in passenger car behaviour when they are nearer semi-trailers than B-doubles. Bunker and Parajuli (2006) made an attempt to study the lateral placement of cars and heavy vehicles (HV) on a two-way two-lane road in Port of Brisbane. It was seen that presence of opposing vehicle and its length influenced the lateral placement of cars, utility vehicles, and semi-trailers statistically. According to Stodart and Donnell (2008), the restrictive nature of road geometry does not produce significant variation in lane position among the vehicles. Also, curve direction and horizontal curve radius were found to have the major relationship with the change in vehicle lane position. Thiemann et al. (2008) studied realworld trajectory data with different mathematical techniques to examine acceleration and lane-changing dynamics. Arai et al. (2015) studied the effect of drivers' awareness on the lane-changing manoeuver. This study simplifies relations between scope awareness parameter and the lane-changing behaviour of drivers. Most of the previous studies focused only on lateral characteristics of vehicles on divided roads. However, only limited attempts have been made to study the lateral placement and movement of vehicles on urban undivided roads in mixed traffic conditions. There are no such studies in the development of model for lateral placement of vehicles. Also, very few attempts have been made to study the choice of path of lateral movement. These research gaps highlight the necessity for studying the lateral placement and movement of vehicles on urban undivided roads under non-lane based mixed traffic conditions.
3.
Data collection and extraction
The data for the present study were collected using video graphic technique during morning peak hours (8:30 a.m.e9:30 a.m.) for two weekdays on a mid-block section of a 12 m wide two-way urban undivided road located in Bangalore City, India. The road section of 30 m long which is free from the influence of intersections, crossroads, bus stops, roadside parking and pedestrians was considered for the study. Fig. 1 shows the layout of the study section. The disaggregate data were extracted from the video images using an image processing software, IrfanView, which was developed by Irfan Skiljan (2007). This software enables to extract 25 frames for one second video data. Gridlines with
Fig. 1 e Layout of the study section.
Please cite this article as: Kotagi, P.B et al., Modeling lateral placement and movement of vehicles on urban undivided roads in mixed traffic: A case study of India, Journal of Traffic and Transportation Engineering (English Edition), https://doi.org/10.1016/ j.jtte.2018.06.008
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sufficient scale were plotted in AutoCAD with obtained (x, y) image coordinates and then overlaid on video by using Ulead Video Studio 10.0 editor (Fig. 2). In order to remove the
Fig. 2 e Gridlines overlaid on video image of the study section.
parallax effect due to camera angle, certain correction factors were used (Gowri et al., 2009). These factors were calculated for each grid block using the known distance on the ground and corresponding coordinates on the screen. The data, such as lateral placement of vehicles in ongoing direction, lateral separation between vehicles in ongoing direction and opposing direction, and lateral movement of vehicles, were obtained from frame by frame analysis. The road width was divided into lateral blocks of each 1 m wide and longitudinal blocks of each 2 m long. The volume counts of vehicles during peak hours in ongoing and opposing directions were obtained from the video data. The vehicular composition of the study section is shown in Fig. 3. The ongoing traffic at the section moving towards Central Power Research Institute (CPRI) comprises about 3541 motorized vehicles per hour, where twowheelers (TW) accounted for the largest share of 63.7% and heavy vehicles (comprising of light commercial vehicles and buses) with the least share of 1.9%. The traffic in the opposing direction (towards MSR Hospital) at the section comprises about 908 motorized vehicles per hour, where two-wheelers accounted for the largest share of 57.6% and heavy vehicles with the least share of 4.4%.
Fig. 3 e Vehicular composition in the study section. (a) Ongoing direction (towards CPRI). (b) Opposing direction (towards MSR Hospital).
Fig. 4 e Schematic representation of lateral placement and separation of vehicles. Please cite this article as: Kotagi, P.B et al., Modeling lateral placement and movement of vehicles on urban undivided roads in mixed traffic: A case study of India, Journal of Traffic and Transportation Engineering (English Edition), https://doi.org/10.1016/ j.jtte.2018.06.008
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4.
Lateral behaviour of vehicles
Lateral placement of a vehicle is defined as the closest lateral position of the vehicle from the edge of the pavement when the vehicle is in motion as shown in Fig. 4. To extract this data, the carriageway width was divided into segments of 50 cm with reference line at the middle of the road section. When the vehicle touches the reference line, the closest lateral position of each vehicle from the edge of the pavement was noted down. The entry time and exit time of each vehicle are obtained from the video frames and with known distance (length of study stretch), the speed of each vehicle is calculated. When subject vehicle (SV) and opposing vehicle (OV) oppose each other and if they overlap each other longitudinally within the stretch, the closest distance between the vehicles was recorded as the lateral separation (Fig. 4). Lateral movement is defined as the movement of a vehicle to the next lane in homogeneous and lane discipline traffic conditions which is represented by lane-changing process. In non-lane discipline traffic conditions, vehicles perform lateral movement by shifting its lateral movement to its sides. Hence, in this study lateral shift is referred as lateral movement. When the subject vehicle (SV) initiates lateral shift at time t and moves its lateral position equal to its width at time t þ T
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under the influence of leader vehicle (LV), it is called lateral shift (Fig. 5).
4.1.
Lateral placement of vehicles
Fig. 6 shows the frequency distribution for lateral placement of vehicles in ongoing direction. It is found that the majority of the vehicles (70.9%) preferred to travel in the middle of the road, with a lateral placement of 3e7 m. Two-wheelers (TW) and auto-rickshaws occupy almost the entire width of the road as they have a tendency to occupy every lateral gap available on the road due to their smaller sizes and higher manoeuvrability. Most of the cars (78.8%) prefer to travel near the middle of the road compared to two-wheelers (63.7%) and auto-rickshaws (76.1%) so as to maintain higher speeds. All the heavy vehicles (HV) are concentrated near the middle of the road, with a lateral placement of 3e7 m, so as to avoid side interferences from other vehicles. Descriptive statistics for lateral placement and speed of each type of vehicle is shown in Table 1. The mean speed of two-wheelers (12.7 m/s) and cars (12.6 m/s) are both higher when compared to heavy vehicles which travel at lower mean speed (11.2 m/s) due to their larger size and lower manoeuvrability. It is also found that the mean lateral placement of all types of vehicles is in the range of 4e5 m
Fig. 5 e Schematic representation of lateral movement of vehicles.
Fig. 6 e Frequency distribution for lateral placement of different types of vehicle. Please cite this article as: Kotagi, P.B et al., Modeling lateral placement and movement of vehicles on urban undivided roads in mixed traffic: A case study of India, Journal of Traffic and Transportation Engineering (English Edition), https://doi.org/10.1016/ j.jtte.2018.06.008
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Table 1 e Descriptive statistics of lateral placement and speed of vehicles. Vehicle type
Aggregate Two-wheeler Auto-rickshaw Car Heavy vehicle
Sample size
1849 980 197 619 53
Lateral placement (m)
Speed (m/s)
Mean
SD
Min
Max
Mean
SD
Min
Max
4.5 4.4 4.4 4.8 4.6
1.8 1.9 1.6 1.7 1.3
1.3 1.3 1.3 1.3 3.1
11.8 11.5 9.6 11.8 7.1
12.0 12.7 11.5 12.6 11.2
2.5 1.9 1.6 2.2 2.7
2.1 2.1 5.1 4.7 7.4
16.7 16.7 16.3 16.7 16.3
Note: SD is the standard deviation.
from the edge of the pavement, which indicates that most of the vehicles prefer to travel near the middle of the road. The one-way analysis of variance (ANOVA) test indicates that the lateral placement of different vehicle types is significantly different (the observed value of F (Fobs ¼ 8.61), the critical value of F (Fcrit ¼ 2.61), degrees of freedom (dof ¼ 1848)) from each other at a significance level of 5%. Graphs were plotted between lateral placement and speed of subject vehicles in ongoing direction as shown in Fig. 7. Regression analysis was done and its goodness was checked by the value of coefficient of correlation. 75% of the data were considered for development of the model and the remaining 25% were used for validation. These graphs show that all the four types of vehicles (TW, cars, auto-rickshaws and HV) followed a second-degree polynomial relation. Most of the two-wheelers have higher speeds near the middle of the road because of their tendency for overtaking and also, they are not much influenced by the opposing vehicles due to their higher manoeuvrability. The speeds of auto-rickshaws and cars do not vary much up to the middle of the road and then start decreasing when they move towards the opposing lane due to the influence of opposing vehicles. Heavy vehicles generally travel at lower
speeds and their motion is not disturbed by the presence of other vehicles. It is believed that speed of the opposing vehicle will also influence the lateral position of subject vehicle and hence, speeds of opposing vehicles were also extracted. Fig. 8 shows the relationship between the lateral placement of ongoing vehicle and speed of opposing vehicles. The results indicate that when the ongoing vehicles are travelling in their corresponding lanes, speed of the opposing vehicles will not have much influence on the lateral positions of ongoing vehicles. When the ongoing vehicles (particularly TW and cars) are shifting towards the opposing lane, the speeds of opposing vehicles are reduced. The predicted speed values from the model were compared with the speed values observed from the field for different lateral placements. Mean absolute percentage error (MAPE) was calculated for each lateral placement and they were found to be less than 15% for all the vehicle types, which conformed the limits (15%) as proposed by Mathew and Radhakrishnan (2010) and Gowri and Sivanandan (2015). This shows that the model replicates the field conditions reasonably. Lateral placement of vehicles on an undivided road cannot be explained only by studying the distribution of vehicles and
Fig. 7 e Relationship between lateral placement and speed of ongoing vehicles. (a) Two-wheelers. (b) Cars. (c) Autorickshaws. (d) Heavy vehicles. Please cite this article as: Kotagi, P.B et al., Modeling lateral placement and movement of vehicles on urban undivided roads in mixed traffic: A case study of India, Journal of Traffic and Transportation Engineering (English Edition), https://doi.org/10.1016/ j.jtte.2018.06.008
J. Traffic Transp. Eng. (Engl. Ed.) xxxx; xxx (xxx): xxx
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Fig. 8 e Relationship between lateral placement of ongoing vehicles and speed of opposing vehicles. (a) Two-wheelers. (b) Cars. (c) Auto-rickshaws. (d) Heavy vehicles.
Table 2 e ANOVA tests comparing unopposed against opposed lateral placements. Distributions compared Twoewheelers unopposed against opposed Auto-rickshaws unopposed against opposed Cars unopposed against opposed Heavy vehicles unopposed against opposed
Sample Fobs Fcrit p value size 1710
4.4
3.8
0.04
250
4.8
3.9
0.04
998 66
4.8 0.5
3.9 4.0
0.04 0.52
hence, lateral placement was also examined by considering the lateral position of subject vehicle when opposed by other vehicles and also when unopposed. The one-way ANOVA test was performed to check whether there is any significant difference in lateral placement of different types of ongoing vehicles when they are opposed and also when they are unopposed. ANOVA test results show that these two distributions are statistically different for TW, cars and auto-rickshaws as shown in Table 2. These vehicles alter their lateral placement under the influence of opposing vehicles. However, lateral placements of heavy vehicles do not differ significantly when opposed than when unopposed. It shows that heavy vehicles are not much influenced by opposing vehicles. Frequency distributions for lateral placements of twowheelers, cars, auto-rickshaws and heavy vehicles when opposed and unopposed are shown in Fig. 9. It can also be observed that two-wheelers are laterally distributed almost on the entire road width due to smaller sizes and higher manoeuvrability. They are not much influenced by opposing vehicles and try to squeeze in between the vehicles. In case
of cars and auto-rickshaws when opposed by other vehicles, most of them occupy the home lane, maintaining a safe lateral distance with the opposing vehicles as they have larger sizes compared to two-wheelers. Most of the heavy vehicles are concentrated near the middle of the road, with a lateral placement of 3e6 m, even if they are opposed by other vehicles as they are not disturbed by any other vehicles due to their larger sizes (other vehicles move away from the path of heavy vehicles). A model was developed using regression analysis to predict the lateral placement of subject vehicles on undivided roads. This regression model can be used in vehicle placement logics to develop traffic simulation models (Kotagi et al., 2018). In building microscopic simulation model, vehicle placement is an important logic. The generated vehicles are placed in the starting point of the simulation road stretch based on some assumptions and observations from field. The placement of vehicles is unpredictable and also depends on many factors such as types and speeds of subject and opposing vehicles. Hence, it is necessary to develop a model to predict the lateral placement of vehicles. The variables considered for model development includes presence of each category of vehicle (two-wheeler, car, auto-rickshaw, heavy vehicle), and speed of each category of vehicle (both as subject vehicle and opposing vehicle). Correlation analysis was carried out to select the most influencing variables and to eliminate the irrelevant variables. It was found that presence of two-wheeler, car and auto-rickshaw as subject and opposing vehicle type and their speeds are the most influencing variables and hence, they are considered for developing the model. The model was developed using 75% of the total data and the remaining 25% was used for validation. The developed
Please cite this article as: Kotagi, P.B et al., Modeling lateral placement and movement of vehicles on urban undivided roads in mixed traffic: A case study of India, Journal of Traffic and Transportation Engineering (English Edition), https://doi.org/10.1016/ j.jtte.2018.06.008
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Fig. 9 e Frequency distributions of lateral placements of different types of vehicles when opposed and unopposed. (a) Twowheelers. (b) Cars. (c) Auto-rickshaws. (d) Heavy vehicles.
model, which can be used to predict the lateral placement of subject vehicle (Y), is shown in Eq. (1). Y ¼ b0 þ b1 X1 þ b2 X2 þ b3 X3 þ b4 X4 þ b5 X5 þ b6 X6 þ b7 X7 þ b8 X8 (1) where b0 is a constant, b1eb8 are the coefficients of independent variables X1eX8. X1eX3 represent presence or absence of two-wheelers, cars and auto-rickshaws as ongoing vehicle types. Similarly, X5 e X7 represent presence or absence of twowheelers, cars and auto-rickshaws as opposing vehicle types. X4 represents speed of ongoing vehicle. X8 represents speed of opposing vehicle. The significance of overall model and the significance of independent variables were tested using goodness of fit. The R2 value of the model is obtained as 0.55. The model has an Fobserved value which is greater than the critical value (Fobs ¼ 19.42, Fcrit ¼ 2.42, dof ¼ 889), implying that the model is statistically significant. The parameter estimation signifies that for every unit increment in independent variable, there is
an average change in dependent variable provided that other variables are held constant. The values of coefficients, t-statistics (tstat) and p value for the developed model were investigated to identify the significant variables. After checking for significance, regression analysis was repeated by using those variables which are significant and the model coefficients were estimated for the revised model (Table 3). When the speed of the subject vehicle (ongoing vehicle) increases, it will move towards the middle of the road or to the opposing lane when there is no opposing vehicle mainly for the purpose of overtaking. Subject vehicle shifts towards the left side of the road when speed of opposing vehicle increases in order to avoid collision with the opposing vehicles. Twowheelers and auto-rickshaws as ongoing vehicles has significant influence on lateral placement as they occupy almost entire road width due to their smaller sizes and higher manoeuvrability. The MAPE values were calculated by comparing predicted and observed values and it was found to
Table 3 e Estimation of coefficients for MLR model. Explanatory variable Constant Presence of two-wheeler (ongoing) Presence of auto-rickshaw (ongoing) Speed of ongoing vehicle Speed of opposing vehicle
Coefficient (b)
Standard error
tstat
p value
11.95 3.84 3.62 0.34 1.12
1.26 0.56 0.51 0.09 0.10
9.49 6.86 7.07 3.73 11.73
0.00 0.00 0.00 0.00 0.00
Please cite this article as: Kotagi, P.B et al., Modeling lateral placement and movement of vehicles on urban undivided roads in mixed traffic: A case study of India, Journal of Traffic and Transportation Engineering (English Edition), https://doi.org/10.1016/ j.jtte.2018.06.008
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be less than 15%, which shows that the model replicates the field conditions reasonably.
4.2.
Speed of opposing vehicle (km/h)
Lateral separation of vehicles
Table 4 shows the descriptive statistics for lateral separation of different types of vehicles. It is observed that lateral separation of a vehicle decreases as the size of the subject vehicle increases. It is also observed that vehicles travelling at higher speeds, such as two-wheelers, maintain higher mean lateral separation (4.7 m) with opposing vehicles when compared to slow moving vehicles such as heavy vehicles (2.7 m). Table 5 shows the lateral separation values for different ongoing and opposing vehicle pairs. It is found that ongoing and opposing vehicles have less freedom to move laterally when the size of either vehicle increases and hence, lateral separation decreases. The one-way ANOVA test was performed to check whether there is any significant difference in the lateral separation of vehicles. The result indicates that the lateral separation of vehicles is significantly different (Fobs ¼ 90.08, Fcrit ¼ 2.62, dof ¼ 1216) for different types of vehicles at a significance level of 5%. Lateral separation also depends on the speeds of ongoing (subject) and opposing vehicles. From Table 6, it is clear that lateral gap maintained by the ongoing vehicle with opposing vehicle is greater when the speed of the opposing vehicle is higher. Table 7 shows the relationship between lateral separation and speed of opposing vehicles for varying speed ranges of subject vehicles. It indicates that lateral separation between subject and opposing vehicles increases with the increase in speed of the opposing vehicles.
Table 4 e Descriptive statistics for lateral separation of different type of vehicles. Vehicle type
Aggregate Two-wheeler Auto-rickshaw Car Heavy vehicle
Sample size
1217 598 152 384 83
Table 6 e Lateral separation depending on speed of subject and opposing vehicles.
Lateral separation (m) Mean
SD
Min
Max
3.6 4.7 4.2 2.9 2.7
1.6 1.8 1.2 1.4 1.4
0.6 0.9 0.9 0.6 1.4
8.6 8.6 7.8 8.0 6.7
20e30 30e40 40e50 50e60
5.
Speed of subject vehicle (km/h) 20e30
30e40
40e50
50e60
e 4.07 3.79 5.01
3.97 3.97 3.87 4.38
3.80 3.71 3.78 3.93
e 3.62 3.56 3.80
Analysis of lateral movement of vehicles
Lateral movement is defined as the movement of a vehicle to the next lane in homogeneous and lane discipline traffic conditions which is represented by lane-changing process. In non-lane discipline traffic conditions, vehicles perform lateral movement by shifting its lateral movement to its sides. Hence, in this study lateral shift is referred as lateral movement. Lateral shift is defined as the type of lateral movement in which the subject vehicle moves its lateral position equal to its width under the influence of the leader vehicle. Lateral shift can be either to the left or to the right depending upon the leader vehicle behaviour. Any front vehicle, whose width completely or partially overlaps with the width of subject vehicle is called a leader vehicle. In this study, total number of lateral shifts obtained are 294 including left shift (16.32%) and right shift (83.67%), out of which 76.8% of lateral shifts are performed by two-wheelers (Munigety et al., 2014). Lateral shift can be classified into three stages including the motivation to change current path, selection of alternate path (left or right lateral shift) to change into and execution of lateral shift. In this study, the first two stages were examined. In undivided roads, since the ongoing traffic is predominantly influenced by opposing traffic, the effect of opposing vehicle on motivation for lateral shift and selection of the path of lateral shifts was also studied. The factors such as speed of subject vehicle, speed of leader vehicle in target path and alternate path, and lateral gaps in target path and alternate path were considered to study and model the lateral shifts.
5.1.
Motivation for lateral movement
In this study, the traffic characteristics such as speeds of leader vehicles in current, target and alternate paths, which
Table 5 e Summary statistics for lateral separation of ongoing and opposing vehicle pairs. Ongoing and opposing vehicle pair
Two-wheeler and two-wheeler Two-wheeler and auto-rickshaw Two-wheeler and car Auto-rickshaw and two-wheeler Auto-rickshaw and car Car and two-wheeler Car and auto-rickshaw Car and car
Sample size
129 51 137 24 28 109 43 43
Lateral separation (m) Mean
SD
Min
Max
5.5 4.6 4.1 5.0 3.3 3.7 3.1 3.0
1.6 1.2 1.3 1.0 1.1 1.1 1.1 1.1
1.7 1.9 0.6 3.2 0.9 1.3 0.5 0.5
8.8 7.7 7.4 7.4 5.5 6.6 4.9 4.9
Please cite this article as: Kotagi, P.B et al., Modeling lateral placement and movement of vehicles on urban undivided roads in mixed traffic: A case study of India, Journal of Traffic and Transportation Engineering (English Edition), https://doi.org/10.1016/ j.jtte.2018.06.008
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Table 7 e Relationship between lateral separation and speed of opposing vehicles. Case
Sample size
Speed of opposing vehicle > speed of subject vehicle Speed of opposing vehicle ¼ speed of subject vehicle Speed of opposing vehicle < speed of subject vehicle
408 22 315
motivate the subject vehicle to perform discretionary lanechanging (DLC) manoeuvres, were investigated. The relationship between speed of subject vehicle and speed of front vehicle in current path is shown in Fig. 10. The results show that speed of subject vehicle is higher than speed of leader vehicle for 60.2% cases when considering all vehicles. When the subject vehicle is TW, its speed is found to be greater than the leader vehicle in current path for 70.6% cases. These greater speed values of subject vehicles when compared to leader vehicles may encourage the drivers to perform a lateral shift. To test whether the subject vehicle speeds differ significantly with leader speeds, a t-test assuming unequal variances was conducted on the null hypothesis that their speeds do not differ significantly. The mean speed of subject vehicle (13.27 m/s) is found to be greater than the mean speed of leader vehicle (12.19 m/s) in case of all vehicles (aggregate) which shows that null hypothesis is rejected (tstat ¼ 5.86, t-critical (tcrit) ¼ 1.96).
5.2.
Lateral separation (m)
Selection of the target path
In DLC manoeuvers, drivers prefer either left or right adjacent path as their target path. The traffic flow characteristics in both left and right adjacent paths were studied and influence of these characteristics on selection of target path was investigated.
Speeds of leader vehicles in current path are compared to speeds of leader vehicles in target and alternate paths. Fig. 11 shows the relationship between speeds of leader vehicles in current path and target path. For all vehicles (aggregate), the leader vehicle speed in target path is greater than the leader vehicle speed in current path for 73.3% cases. However, there are only 27.7% cases where the leader vehicle speed in alternate path is greater than the leader vehicle speed in
SD
Min
Max
3.9 3.8 3.7
1.7 1.8 1.6
0.5 1.4 0.6
8.9 7.4 7.9
current path in case of all vehicles (Fig. 12(a)). In case of TWs, the speed of leader vehicle in alternate path is greater than the speed of leader vehicle in current path for 15.3% cases (Fig. 12(b)). This shows that the speed of leader vehicle in target path plays an important role in making the decision of lateral shift of subject vehicles. The t-test conducted enhances these arguments and the results indicate that the mean speed of leader vehicle in current path (11.23 m/s) is significantly lower than the mean speed of leader vehicle in target path (12.55 m/s) (tstat ¼ 2.54, tcrit ¼ 1.96). On the other hand, the speed of leader vehicle in current path (12.3 m/s) is significantly greater than the speed in alternate path (11.7 m/s), which was shown by t-test results (tstat ¼ 1.98, tcrit ¼ 1.96).
5.2.2.
Longitudinal gaps in target and alternate paths
The relationship between longitudinal gaps in target path and alternate path shown in Fig. 13 indicates that only for 31.1% cases of all vehicles and only for 27.3% cases of TWs, longitudinal gap is greater in target path than in alternate path. Hence, the result reveals that longitudinal space gap is not an influential variable for choosing paths. The t-test results show that the longitudinal gap in target path (18.5 m) is significantly shorter than the longitudinal gap in alternate path (21.1 m) in case of all vehicles (tstat ¼ 3.65, tcrit ¼ 1.00).
5.2.3. 5.2.1. Speeds of leader vehicles in current path, target path and alternate path
Mean
Lateral gaps in target and alternate paths
Lateral gap in target path is greater than that in the alternate path for 83.2% cases of aggregate and for 81.0% cases of TWs, which shows that lateral gap is an influential factor in the selection of paths (Fig. 14). Thus, the subject vehicle has a tendency to choose the correct target path. To test whether the lateral gaps in target and alternate paths are significantly different, a t-test assuming unequal variances was conducted on the null hypothesis that their lateral gaps do not differ significantly. It is found that the mean lateral gap in target path (7.0 m) is greater than that in alternate
Fig. 10 e Relationship between speeds of subject vehicle and leader vehicle in current path. (a) Aggregate. (b) Two-wheelers. Please cite this article as: Kotagi, P.B et al., Modeling lateral placement and movement of vehicles on urban undivided roads in mixed traffic: A case study of India, Journal of Traffic and Transportation Engineering (English Edition), https://doi.org/10.1016/ j.jtte.2018.06.008
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Fig. 11 e Relationship between speeds of leader vehicles in current and target paths. (a) Aggregate. (b) Two-wheelers.
Fig. 12 e Relationship between speeds of leader vehicles in current and alternate paths. (a) Aggregate. (b) Two-wheelers.
path (4.1 m) in case of all vehicles, which shows that null hypothesis is thus rejected (tstat ¼ 16.4, tcrit ¼ 1.96).
5.2.4.
Influence of opposing vehicles on lateral movement
The influence of opposing vehicles on the lateral movement of a subject vehicle was also investigated. Lateral placement of the leader vehicle in current path is compared with lateral separation between leader vehicle in current path and opposing vehicle. Lateral gap in the target path is found to be greater in 72.2% cases of all vehicles (Fig. 15(a)) and 65.1% cases of TWs (Fig. 15(b)). Thus, vehicles freely shift towards the target path. The lateral gap in the target path (5.6 m) is significantly greater than the lateral gap in the alternate path (4.2 m) in case of all vehicles (tstat ¼ 8.42, tcrit ¼ 1.96).
5.3.
using statistical package for the social science (SPSS) (IBM, Corp., 2012). These regression models assume that log-odd of each choice of path followed a linear model as given in Eq. (2).
Multinomial logistic regression model
Multinomial logistic regression is used to model the choices of path of lateral shift (left, current, right) made by all vehicles
hiq ¼ ln
piq ¼ aq þ Xi bq piQ
(2)
where h is the log-odd of choice of lateral shift, p is the choice of lateral shift. aq is a constant and bq is a vector of regression coefficients (q ¼ 1, 2,$$$ Q1). An appropriate category Q is fixed as reference. Interpretation of the estimates are similar to that of linear regression model in Eq. (1). Dependent variable is the choice of lateral shift (left, right and current) and the significant independent variables are sizes of subject vehicle (X1) and leader vehicle (X2), lateral gap between leader vehicle and right adjacent leader vehicle (X3), lateral gap between leader vehicle and left adjacent leader vehicle (X4), relative speed between subject vehicle and leader vehicle (X5), relative speed between leader vehicle and right adjacent leader vehicle (X6), relative speed between leader
Fig. 13 e Relationship between longitudinal gaps in target path and alternate path. (a) Aggregate. (b) Two-wheelers. Please cite this article as: Kotagi, P.B et al., Modeling lateral placement and movement of vehicles on urban undivided roads in mixed traffic: A case study of India, Journal of Traffic and Transportation Engineering (English Edition), https://doi.org/10.1016/ j.jtte.2018.06.008
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Fig. 14 e Relationship between lateral gaps in target path and alternate path (without the influence of opposing vehicles). (a) Aggregate. (b) Two-wheelers.
Fig. 15 e Relationship between lateral gaps in target and alternate path (under the influence of opposing vehicles). (a) Aggregate. (b) Two-wheelers.
vehicle and left adjacent leader vehicle (X7), and lateral gap between leader vehicle and opposing vehicle (X8). The speeds of leader vehicles and lateral gaps in the target and alternate paths turned out to be the influential variables for the choice of path. 75% of data were used for model development and remaining 25% for validation. A log likelihood ratio chi-square test was performed to determine the statistical significance of the overall model. The result shows that the overall model is statistically significant at a significance level of 5% (p value ¼ 0.000). Hence, there exists a relationship between the independent and dependent variables. The estimated results of the model include coefficient values, value of standard error, Wald test and significance value. Current path is considered as a reference category in the model and hence, the coefficients obtained are the values indicating the ratios of left shift to the current path and right shift to the current path. The significance of each independent variable is checked by the value of standard error (which should be less than 2) and the significance value (p value should be less than the significance level of 5%). Parameter estimates of the target path choice model are presented in Table 8. The goodness of fit of the developed model is determined using McFadden pseudo R2 value (0.452). The model results show that the decrease in subject vehicle size and increase in leader vehicle size increases the probability of a subject vehicle choosing either left or right shift compared to the probability of travelling in current path. The increase in lateral gap between leader vehicles in current path and target path increases the probability of a subject vehicle shifting either to the left or to the right compared to the probability of travelling
in current path. When the relative speed between the subject vehicle and leader vehicle gives a negative sign, the probability of a subject vehicle shifting either to the left or to the right increases compared to the probability of travelling in current path. The increase in relative speed between leader vehicle in current path and adjacent leader vehicle increases or decreases the probability of a subject vehicle shifting to the left or to the right compared to the probability of travelling in current path. Since the road section is undivided, lateral gap between leader vehicle in current path and opposing vehicle also influences the lateral movement. The increase in lateral gap between leader vehicle in current path and opposing vehicle increases the probability of a subject vehicle shifting to the right and decreases the probability of shifting to the left compared to the probability of travelling in current path. In India (left hand drive rule is followed), drivers prefer to move at higher speed near the right side due to the absence of roadside frictions like parking, pedestrians, encroachments, etc. (Kanagaraj et al., 2015). Thus, drivers prefer right side path generally. Earlier studies also reported that drivers are more willing to perform right shift compared to left shift (Mallikarjuna and Rao, 2011; Mathew et al., 2014; Munigety et al., 2014). The same was observed from the real world traffic data collected from Bangalore, India. A total of 294 lateral shifts were observed, out of which 48 are left shifts and remaining 246 are right shifts. Hence, the prediction success for right shifts (83.2%) is greater than the left shifts (60.1%). The model was validated using 25% data and the coefficients of the developed and validated model were compared. The results show that the mean absolute percentage error obtained is less than 3%.
Please cite this article as: Kotagi, P.B et al., Modeling lateral placement and movement of vehicles on urban undivided roads in mixed traffic: A case study of India, Journal of Traffic and Transportation Engineering (English Edition), https://doi.org/10.1016/ j.jtte.2018.06.008
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J. Traffic Transp. Eng. (Engl. Ed.) xxxx; xxx (xxx): xxx
Table 8 e Parameter estimates of the model. Lateral shifta Left lateral shift
Right lateral shift
Variable
Coefficient (b)
Standard error
Wald
p value
Intercept Subject vehicle size Leader vehicle size Lateral gap between leader vehicle and right adjacent leader vehicle Lateral gap between leader vehicle and left adjacent leader vehicle Relative speed between subject vehicle and leader vehicle Relative speed between leader vehicle and right adjacent leader vehicle Relative speed between leader vehicle and left adjacent leader vehicle Lateral gap between leader vehicle and opposing vehicle Intercept Subject vehicle size Leader vehicle size Lateral gap between leader vehicle and right adjacent leader vehicle Lateral gap between leader vehicle and left adjacent leader vehicle Relative speed between subject vehicle and leader vehicle Relative speed between leader vehicle and right adjacent leader vehicle Relative speed between leader vehicle and left adjacent leader vehicle Lateral gap between leader vehicle and opposing vehicle
0.486 3.116 1.741 0.082 0.659 0.230 0.195 0.264 0.093 1.545 1.714 0.019 0.432 0.871 0.196 0.079 0.407 0.317
1.455 0.702 0.487 0.165 0.191 0.119 0.071 0.087 0.142 1.438 0.432 0.395 0.172 0.181 0.099 0.066 0.081 0.120
0.111 19.680 12.760 2.251 11.870 3.725 7.577 9.208 3.428 1.155 15.740 2.002 6.317 23.140 3.869 2.412 25.420 6.992
0.73 0.00 0.00 0.00 0.00 0.04 0.00 0.00 0.00 0.28 0.00 0.01 0.01 0.00 0.04 0.02 0.00 0.00
Note: a means the reference category is current path, where the number of observations for current path is 126, prediction success for current path is 84.1%, number of observations for right shift is 101, prediction success for right shift is 83.2%, number of observations for left shift is 40, and prediction success for left shift is 60.1%.
6.
Summary and conclusion
The present study aims to analyse and model the lateral placement and movement of vehicles on urban undivided roads in mixed traffic conditions. For this purpose, traffic data collected from an urban undivided road in Bangalore city, India, was used. The lateral placement and separation of different types of vehicles were extracted and investigated to study the effect of speed of ongoing and opposing vehicles on lateral placement and separation of vehicles. Multiple linear regression model was developed for predicting the lateral placement of subject vehicle and it was found that lateral placement of a subject vehicle was influenced by types and speeds of subject and opposing vehicles. The various factors which motivate the lateral shift of vehicles were analysed. Also, the selection of path of vehicles during lateral shifts were also analysed and modelled using multinomial logistic regression. The key conclusions arising from this study are as follows. It was found that the majority of the vehicles (70.9%) preferred to travel in the middle of the road, with a lateral placement of 3e7 m. Two-wheelers, cars and auto-rickshaws adjust their lateral placement when opposed by vehicles. Heavy vehicles are not much influenced by opposing vehicles due to their larger sizes and thus, lateral placements do not vary significantly when opposed than when unopposed. Lateral separation of vehicles decreases with increase in subject vehicle size and increases with increase in the speed of opposing vehicle. The probability of a subject vehicle choosing either left or right lateral shift increases with decrease in subject vehicle size and increases with leader vehicle size. The increase in lateral gap between leader vehicle in current path and opposing vehicle increases the probability of
a subject vehicle shifting to the right and decreases the probability of shifting to the left. This study finds interesting applications in development of traffic simulation models to carry out various traffic control and management measures. MLR model developed for lateral placement can be used in traffic simulation model (vehicle placement logic) to assign the lateral position of vehicles in the starting point of simulation road stretch. The path choice model developed for lateral shifts can be used in microscopic traffic simulation to model the lateral movements of vehicles. The factors such as road width, road type, driver characteristics, weather conditions, time of day, etc., can be considered in the models for better results. The model for lateral placement and movement can be further improved by developing class-wise model. In the study of lateral movement, only lateral shift was taken into consideration for analysis and modelling due to limited field of view of study section. In the future, the execution of lateral movements (i.e., overtaking behaviour of vehicles) can also be studied and modelled. The findings of the study can be generalized by collecting and analysing large amount of data.
Conflict of interest The authors do not have any conflict of interest with other entities or researchers.
Acknowledgements The authors are thankful to Additional Commissioner, Bangalore Traffic Police, India, for permitting us to record the traffic data necessary for present study. Authors also thank
Please cite this article as: Kotagi, P.B et al., Modeling lateral placement and movement of vehicles on urban undivided roads in mixed traffic: A case study of India, Journal of Traffic and Transportation Engineering (English Edition), https://doi.org/10.1016/ j.jtte.2018.06.008
14
J. Traffic Transp. Eng. (Engl. Ed.) xxxx; xxx (xxx): xxx
the editor and the reviewers for their valuable comments and suggestions which helped us in refining and improving this paper.
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Punith B. Kotagi is an assistant professor at Department of Civil Engineering in The National Institute of Engineering Mysuru, Mysuru, India. He completed his PhD from National Institute of Technology Karnataka, Surathkal, India, and master of technology in highway technology from Resource Centre for Asphalt and Soil Training Academy (RASTA), Bangalore, India. His research area includes development of traffic simulation model and its application in various traffic operations and management measures under mixed traffic conditions.
Pooja Raj completed her master of technology (research) from the Department of Civil Engineering in National Institute of Technology Karnataka, Surathkal, India, in 2016. Presently, she is pursuing her PhD in the same organization. Her research interests include traffic flow modelling and simulation, pedestrian studies, PCU and capacity estimation under mixed traffic conditions.
Dr. Gowri Asaithambi is currently working as an assistant professor in the Department of Civil and Environmental Engineering at Indian Institute of Technology (IIT) Tirupati, India. Prior to joining the IIT Tirupati, she was an assistant professor at the Department of Civil Engineering in National Institute of Technology (NIT) Karnataka, Surathkal, India. She received her PhD from Indian Institute of Technology (IIT) Madras, India, in 2011. Her main research interests are traffic flow modelling and simulation, traffic operations and management, capacity of traffic facilities, pedestrian safety, and intelligent transportation systems.
Please cite this article as: Kotagi, P.B et al., Modeling lateral placement and movement of vehicles on urban undivided roads in mixed traffic: A case study of India, Journal of Traffic and Transportation Engineering (English Edition), https://doi.org/10.1016/ j.jtte.2018.06.008