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Travel Time Prediction Using Higher Traffic Flow Models
B. DhivyabharathiPhD. Research ScholarDepartment of Civil EngineeringIndian Institute of Technology MadrasChennai – 600036, IndiaE-mail: [email protected]
Dr. Lelitha Devi,Associate Professor,Department of Civil Engineering,Indian Institute of Technology Madras,Chennai – 600036, India.E-mail: [email protected]
Mathematics Applied in Transport and Traffic Systems 2018
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Outline of the presentation
Introduction
Background
Methodology
Data Collection
Results
Conclusions
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Introduction
• Travel time is an important system performance measure.
• Availability of travel time information• Control traffic and reduce congestion.
• Identification of shortest path between a pair of origin and destination.
• Essential for various Intelligent Transportation Systems (ITS) applications such as Advanced Traveler Information Systems (ATIS), Advanced Public Transportation System (APTS) and Advanced Traffic Management Systems (ATMS).
• Dynamic route guidance, incident detection, freeway ramp metering control etc.
• Travel time - a spatial parameter- Prediction is challenging.
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Background
• Various techniques - reported in literature.• Data driven approach
• Traffic flow theory based approach
• Data driven – extracts system characteristics from the huge amount of data – data intensive.
• Traffic flow theory based approach – concepts of physics – relates traffic flow variables – complete picture of the system- aggregate level- minimal data.
• Developing countries- Minimal data collection infrastructure.
• Travel time prediction using traffic flow theory based approach –Suitable.
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Back ground
• Traffic flow models – Modified/Rewritten/discretized/state space – travel time prediction/estimation.
• Macroscopic traffic models – First order models- Higher order models.• Models: LWR, Payne, Zhang, Aw-Rascle.
• First order • LWR- simplest – explored to an extent.
• Higher order models• Payne- Negative speeds – Characteristics speed higher than vehicle speed.
• Aw-Rascle– Answers the limitations of Payne’s model -not yet explored.
• Adopted – Aw-Rascle’s traffic flow model– Travel time prediction.
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Aw Rascle Model
Where,
v is speed,
Ꝭ is traffic density,
p is the traffic pressure and
t is the independent variables represent time.
x is the independent variables represent space.
(Conservation equation)
(Velocity dynamics equation)
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Modelling
• Purely hyperbolic and conservative form of Aw-Rascle Model i.e. under no diffusion and no relaxation conditions (Aw & Rascle, 2000).
• Taking the velocity dynamics equation and modified for travel time prediction.
• Assumption• Equations are independent to each other
(1)
(2)
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Modelling
• Adopting the pressure function suggested by Zhang et al., (2016)
• Assuming Greenshield speed-density function for V(k), eqn. (3) becomes
• Subs (4) in (2), the modified form of Aw-Rascle’s velocity dynamics equation is
(3)
(4)
(5)
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Modelling
• Discretization: Finite difference method• Forward Time Backward Space scheme
• Discretizing the eqn. (5) and rewriting as (6)
Where,
t is the time index
i is the space index
(6)
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Implementation
• Assumptions• First sections(Entry) speed and density values – initial conditions.
• Overtaking of vehicles are permitted
• Stability Condition of the numerical scheme: (vehicle travelling at Vf cannot travel more than one time step)
• Adopting the discretized form of conservation eqn. suggested by Kumar et al., (2011).
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Implementation
A
B
C
• Study stretch : Rajiv Gandhi Salai (IT Corridor), Chennai, India.• Section 1: Location A to Location B
• Section 2 : Location B to Location C
• Total Length: 1.72 km
• Six lane highway road
• Only direction of traffic considered
• Road stretch similar to the field test bed was created in VISSIM using a satellite image
• Five hours simulation – implementation
• Density and speed values for both section 1 and 2 - Collected
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Results – Sample 1
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Sp
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, km
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Time indices, minutes
Speed Prediction Actual Predicted
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Time indices, minute
Traveltime prediction Actual Predicted
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Results – Sample 2
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Sp
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Speed Prediction Actual Predicted
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1 2 3 4 5 6 7 8 9 1011121314151617181920212223242526272829303132333435363738394041424344454647484950515253
Tra
vel
tim
e, s
eco
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Time indices, minutes
Traveltime prediction Actual Predicted
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Results – Sample 3
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1 3 5 7 9 11 13 15 17 19 21 23 25 27 29 31 33 35 37 39 41 43 45 47 49 51 53 55 57
Sp
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ph
Time indices, minutes
Speed Prediction Actual Predicted
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1 3 5 7 9 11 13 15 17 19 21 23 25 27 29 31 33 35 37 39 41 43 45 47 49 51 53
Tra
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Time indices, minutes
Traveltime prediction Actual Predicted
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Conclusions
• Explored the possibility of travel time prediction using higher order traffic flow model equations.
• MAPE-15% to 21% - Satisfactory
• Model is very sensitive towards the input – variations in output -higher errors in certain places
• Initial implementation - need refinements – better predictions
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Future scope
• Exponential speed density relationship.
• State space representation integrated with filtering algorithm for real time prediction.
• Possibility of using another source of data in the correction step.
• Finite Volume discretization
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Thank you.
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