HEADWAY DISTRIBUTION

1. Headway Distribution On Urban
Roads Under Heterogeneous
Traffic Conditions
Reg: 189282J
Yahampath Y.A.P.M

2. Introduction
Headway in Traffic Engineering measured in temporal and spatial forms;
Headway
Time Headway
Time space between two consecutive
vehicles
Measured by:
Time elapse between the arrival of the
front bumper of the leading vehicle
and the front bumper of the following
vehicle to a designated test point
Space Headway
Time space between two
consecutive vehicles
Measured by:
Physical distance between front
bumper of the leading vehicle and
the front bumper of the following
vehicle.

3. • Headway
Microscopic
level
Macroscopic
level
• Density
• Flow

4. Importance Of Modeling Headway Data
• Congestion prediction
• Reflect Level of Service
• Capacity analysis of a transportation system – maximize
capacity
• Safety studies – Accident analysis
• Car following and Lane changing behaviour modelling
• Microscopic simulations
• Automated highway systems control
(Arasan and koshy,2003), (Ye F,Zhang Y, 2009)

5. Headway distribution varies with,
• Vehicle flow
Identify suitable distribution for various flow ranges
• Vehicle density
Identify suitable distribution for various density ranges
• Type of vehicle
Identify suitable distribution for different vehicle types
• Vehicle combination of headway
Identify suitable distribution for different vehicle combinations

6. Research Gaps
Majority of researches are based on
• Homogeneous traffic conditions
• Low and medium flow conditions only
• Lane based vehicle flow

7. Objectives
• To identify most efficient distributions for headway
distribution for heterogeneous flow traffic conditions under
different flow rate ranges in Sri Lankan context.
• To develop Set of Probability Density Functions (PDF) for
headway distribution typical for the road segments under
heterogeneous traffic conditions to providing information
about headway distribution under different flow rate ranges
in Sri Lankan context.

8. Heterogeneous Traffic conditions
• Various physical dimensions
• Various axle configurations
• Weight
• Power to weight ratio
• Breaking power
• Acceleration

9. Heterogeneity cont…..
• Traffic streams that consist of vehicles with a wide range of static and
dynamic characteristics with no spatial segregation as opposed to
homogeneous traffic streams where the majority of vehicles in the
traffic stream are similar.
• Hertogeneous traffic mixes exist when the percentage of the
dominant vehicle mode is less than 80% of the traffic mix,
Arasan & Krishnamurthy(2008)

10. Factors Influence the Headway Distribution
• Traffic volume
• Proportion of heavy vehicles
• Lateral position of vehicle on the road
• Road structure
• Time of the day ( peak and off peak )
• Interruption to flow ( Eg: Intersections, )

11. Why we use PDF’s to describe traffic variables?
• Traffic characteristics are statistical rather than deterministic.
• Therefore, traffic variables such as volume , speed , delay
and headways can be described by probability distributions.

12. Constraints
• In this study headway will be considered only when vehicle
exactly follows the leading vehicle or there is an overlap between
leader and follower, In terms of space.
• And also, headway values bigger than threshold value, 5 secs
also not considered since they are apart for any interaction to
happen.

13. Difficulties to be faced during headway data
collection
Bike riders and three wheelers have high maneuverability,
so they creep through gap between bigger vehicles and
retard the free movement of bigger vehicles.
 They do not follow any lane discipline or lane markings.
These circumstances make the traffic flow complex .

14. Data collection

15. Factors considered selecting suitable location for
data collection
Free from any side hindrance such as parking lot, gradient, bus stop,
intersection
 Approximately Straight and flat
 Availability of enough shoulder
 Weather condition
 Good visibility
 Homogeneous section ( in geometric and functional terms) for at least 1km
up and down stream.
 Relatively Good pavement surface condition
(Riccardo & Massimiliano, 2012), (Maurya, Das, Dey, & Nama, 2016)

16. Assumptions & Considerations for Data Analysis
• Uni-directional traffic.
• Headways are analyzed separately along lanes.
• Size of the sample.
• Time sub-interval suitable for observation.
[E.g: 15 min intervals such that sample size is large enough for all flow
ranges. And also assumes that steady traffic flow condition prevailed]
(Riccardo & Massimiliano, 2012)
• Appropriate PCU factors.
• Suitable number of volume ranges for classification of sub interval
based on traffic volume.
(Maurya, Das, Dey, & Nama, 2016)

17. Identified Locations For Data Collection
• Baseline road section
• A004 road (High level road) section
• B84 road (120 bus route) section

18. Nature of Identified Road Sections
Road
section
Directional
split
Center median
separated or not
No of lanes per
direction (Nos)
Avg width of a lane
(m)
Baseline road
section 50/50 Separated 4
High level road
section (near
Pannipitiya)
50/50 Not separated 2
B84 road (120 bus
route) section
50/50 Separated 2

19. Vehicle Classification ( Axel based)
Malaysia Highway capacity manual(2011)
ATC scheme F classification system (USA)
Vehicle class Description
1 Motor cycles
2 Three Wheelers
3 Cars, small vans, Utilities
4 Large vans, small lorries, or trucks with two
axels
5 Buses (two axel)
6 Large lorries or trucks with 3 axels
7 Large lorries or trucks with 4 or more axels

20. Data collection Techniques
Automatic
• Loop detector based recording
 Pneumatic tube
(Riccardo & Massimiliano, 2012)
• Video graphic data collection - Drone Placed exactly above the lane
(Roy & Saha, 2018)
• Automatic sensors
 The Infra-Red Traffic Logger
[Badhrudeen, Ramesh, & Vanajakshi, 2016)
 TURTL –radar based method
• Probe vehicle
[Pueboobpahan,Park,Kim, and Choo(2012)]
Manual
• Recording of vehicle in times with reference to arbitrary reference line using Stop
watch
[Ako & Yusuf, (2016)]

21. Extraction of Data from Video Recordings and
Determination of Headways
Image processing using software to detect headways
• Every vehicle, timestamp of it's front bumper leaving the frame, it's
type and the time headway of it and the vehicle in front of it can
extracted from ATC using a software.
• And also, this software allows to classify vehicles based on the wheel
base length pre-defined by user.

22. Calculation of Vehicular Flow
Rates

23. Identification of Time Sub Intervals
• Sub time interval should be defined to calculate flow rates.
• Sub time intervals should be defined in a manner that sample size
(No of headways) is large enough for all flow ranges. Otherwise
during low flow ranges sample size may not be enough for analyze.
• And also it is assumed that steady vehicle flow condition is prevailed
during the each sub time interval.
• For each selected road section, vehicular flow rates (veh/hr) should
be calculated for each pre-defined sub time intervals (eg : 15 min sub
time intervals) separately.

24. Classification of Sub-Time Intervals Having
Similar Flow Rates
• After calculation of flow rates for each pre-defined time sub
interval for each selected road section, time sub intervals
having similar flow rates are identified.

25. Defining Traffic flow Ranges
• Several traffic flow ranges are defined based on the reported flow
rate values calculated for each sub time intervals for each road
section.
• Proposed traffic flow ranges,
Low traffic flow condition - Less than 400 vph
Medium traffic flow condition – Between 400 vph and 1200 vph
More than 1200 vph

26. HEADWAY DATA ANALYSIS
 To analyze variation of headway under different traffic flow
conditions.
 To analyze headway data based on different leader-follower
pairs.

27. To Analyze Variation Of Headway
Under Different Traffic Flow
Conditions.

28. Developing time Headway Samples for each Flow
Range
• Time headway samples are created by joining sub sets contains the
headway data belonging to subsequent sub time intervals included in
particular flow rate range.
Developing Frequency Distribution for each flow
Range
• Frequency distributions should be developed separately for each
identified flow range for each road section to demonstrate headway
distribution within that flow range.

29. Developing Cumulative Frequency Distribution for
each flow Range
• Cumulative Frequency distributions should be developed based on
frequency distributions separately for each identified flow range for
each road section to compare with selected empirical distribution
functions to model headway within that flow range.

30. To Analyze Headway Data Based
On Different Leader-follower Pairs

31. • In order to analyses headway data based on different leader-follower pairs
all possible combination pairs of vehicle types were identified.
Possible different leader- follower pairs
Develop Time Headway Samples for each Leader
Follower Pairs
Vehicle class Description
MC Motor cycles
TW Three Wheelers
CAR Cars, small vans, SUV
COM Utilities, pickup, single cab, double cab
HV Bus, truck, mini bus, canter, tipper
Leader-Follower
Follow
MC TW CAR COM HV
Lead
MC MC-MC MC-TW MC-CAR MC-COM MC-HV
TW TW-MC TW-TW TW-CAR TW-COM TW-HV
CAR CAR-MC CAR-TW CAR-CAR CAR-COM CAR-HV
COM COM-MC COM-TW COM-CAR COM-COM COM-HV
HV HV-MC HV-TW HV-CAR HV-COM HV-HV

32. Develop Time Headway Samples for each Leader
Follower Pairs
• Headway data will be classified based on vehicle pairs.
• Develop frequency distributions for headway data sets classified
based on leader follower pairs.
• Develop Cumulative frequency distributions based on frequency
distributions developed for headway data sets classified based on
leader follower pairs to compare with selected empirical distribution
function to model headway based on leader follower pairs.

33. Headway Distribution
Modelling

34. Descriptive Statics of Headway Data
The fundamental statistical properties of headway data such as
• Mean
• Median
• Standard deviation
• Co -efficient of variation
Will be examined at different flow levels to be calculated and tabulated.

35. Based on calculated statistical parameters for different
distributions nature headway of the traffic flow can be
predicted. Such as,
• If Mean < Median ,
Concentration of short headways; in a way that most drivers chose headways
less than mean.
 This attributes high risk ability of driver population.
(Roy & Saha, 2018)
• Mean and Standard deviation degreases with increase of traffic flow.
 Change in headway from random to constant state.
(Abtahi SM,2011)

36. Selection of Suitable Empirical Distribution Model
• Standard static models are used to study time headway.
• Based on literature reviews and past studies several distribution
models were selected.

37. Selection of Best Fitting Distribution
• Then best fitting distribution to the headway data was identified
using log-likelihood values.
• Similar to probability, likelihood measures the support that the data
offer to a specific model.

38. Selection of Best Fitting Distribution Cont….
• Then best fitting distribution to the headway data can be identified
using “Goodness of fit” by,
• K-S test
• Chi-square test
Advantages of K-S test over chi-square;
• Can use with a continuous distribution
• No minimum frequency per test interval

39. Kolmogorov – Smirnov (K-S) Test
The Kolmogorov–Smirnov statistic quantifies a distance between
the empirical distribution function of the sample and the cumulative
distribution function of the reference distribution.
D value
• Difference between the,
Cumulative frequency of measured frequency and cumulative
frequency of expected frequency.
• D is computed at the desired significance level for the selected
distributions.
• Distribution which gives least D value is considered as the best fit
model.

40. Develop Hypothesis
Null Hypothesis
• The compatibility hypothesis of headway distribution with fitted
model is accepted - if (p-value> α)
Alternative Hypothesis
• The compatibility hypothesis of headway distribution with fitted
model is rejected - if (p-value< α)

41. Software used for Data analysis
IBM SPSS Software is used to,
• A set of probability density functions for each volume range with
reference to each section/lane.
• Probability density functions are fitted to the frequency distribution
by using software.
• goodness of fit by the k-s test can be evaluated using .

42. References
• Roy, R., & Saha, P. (2018). Headway distribution models of two-lane roads under mixed traffic conditions: A case study
from India. European Transport Research Review, 10(1), 3. https://doi.org/10.1007/s12544-017-0276-2
• Maurya, A. K., Das, S., Dey, S., & Nama, S. (2016). Study on Speed and Time-headway Distributions on Two-lane
Bidirectional Road in Heterogeneous Traffic Condition. Transportation Research Procedia, 17, 428–437.
https://doi.org/10.1016/j.trpro.2016.11.084
• Moridpour, S. (2014). Evaluating the Time Headway Distributions in Congested Highways. Journal of Traffic and Logistics
Engineering, 2(3). https://doi.org/10.12720/jtle.2.3.224-229
• Ako, T., & Yusuf, I. T. (2016). Time Headway and Vehicle Speed Studies of a Road Section in Ilorin, Nigeria. 12.
• Riccardo, R., & Massimiliano, G. (2012). An Empirical Analysis of Vehicle Time Headways on Rural Two-lane Two-way
Roads. Procedia - Social and Behavioral Sciences, 54, 865–874. https://doi.org/10.1016/j.sbspro.2012.09.802
• Touhbi, S., Babram, M. A., Nguyen-Huu, T., Marilleau, N., Hbid, M. L., Cambier, C., & Stinckwich, S. (2018). Time Headway
analysis on urban roads of the city of Marrakesh. Procedia Computer Science, 130, 111–118.
https://doi.org/10.1016/j.procs.2018.04.019
• Badhrudeen, M., Ramesh, V., & Vanajakshi, L. (2016). Headway Analysis Using Automated Sensor Data under Indian Traffic
Conditions. Transportation Research Procedia, 17, 331–339. https://doi.org/10.1016/j.trpro.2016.11.103
• Radhakrishnan, S., & Ramadurai, G. (2015). Discharge Headway Model for Heterogeneous Traffic Conditions.
Transportation Research Procedia, 10, 145–154. https://doi.org/10.1016/j.trpro.2015.09.064

43. THANK YOU