Ole Steuernagel

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Velocity class master equations for single-lane
traffic models
Ole Steuernagel and Maria Schilstra University
of Hertfordshire Hatfield
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Velocity class master equations for single-lane
traffic models
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• Cellular Automaton Modelling
• Typical behaviour
• Some semi-analytical results
• Deriving the master equation

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Heavy Traffic
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Heavy traffic solutions?
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Traffic flow modelled by point particles
No other distinguishing features same size,
same acceleration, same behaviour
No other distinguishing features same size,
same acceleration, same behaviour
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Cellular Automaton Evolution Rules
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Heavy Traffic Modelling with Cellular
automata A la Nagel and Schreckenberg
http//www.traffic.uni-duisburg.de/model/index.htm
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Heavy Traffic Modelling with Cellular
automata A la Nagel and Schreckenberg
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Traffic Modelling
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Acceleration Matrix A
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Randomization Matrix R
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Slow-down Matrix S
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Joint Transformation Matrix T
T contractive
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Steady state of Joint Transformation
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Steady state of Joint Transformation
u
r
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Slow-down due to other vehicles
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Slow-down due to other vehicles
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Slow Down Matrix S(P)
Follower
Leader
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Slow Down Matrix S(P)
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Slow Down Matrix S(P)
S(P) nonlinear in P
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Steady state of Joint Transformation
J
simulation
master equation
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Steady state of Joint Transformation
u
simulation
master equation
r
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Fundamental Diagrams
J
r
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• OUTLOOK
• Insert real world numbers
• Study effects of
• length
• acceleration
• lane bias
• noise
• structure formation
• Related fields?
• network traffic

• OUTLOOK
• Insert real world numbers
• Study effects of
• length
• acceleration
• lane bias
• noise
• structure formation
• Related fields?
• network traffic

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OUTLOOK ON NOISEMaria SchilstraS recent
simulations
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Thank you for your for your attention!