Travel Time Prediction Using Higher Traffic Flow Models...
Transcript of Travel Time Prediction Using Higher Traffic Flow Models...
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
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
Figure: Test bed18-10-2018 Travel time prediction using Higher order traffic flow models 11
Results – Sample 1
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Time indices, minutes
Speed Prediction Actual Predicted
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Traveltime prediction Actual Predicted
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Results – Sample 2
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1 2 3 4 5 6 7 8 9 1011121314151617181920212223242526272829303132333435363738394041424344454647484950515253
Tra
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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
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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
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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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