1 Ole Steuernagel and Maria Schilstra University of Hertfordshire Hatfield.

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Presentation transcript:

1 Ole Steuernagel and Maria Schilstra University of Hertfordshire Hatfield

1

Cellular Automaton ModellingCellular Automaton Modelling Typical behaviourTypical behaviour Some semi-analytical resultsSome semi-analytical results Deriving the master equationDeriving the master equation 1

Heavy Traffic

Heavy traffic – solutions?

No other distinguishing features: same size, same acceleration, same behaviour… Traffic flow modelled by point particles 10 units V max 5 units V max No other distinguishing features: same size, same acceleration, same behaviour…

Cellular Automaton – Evolution Rules p

Heavy Traffic – Modelling with Cellular automata A la Nagel and Schreckenberg

Heavy Traffic – Modelling with Cellular automata A la Nagel and Schreckenberg

Traffic – Modelling = (remaining free road) (drive-off probability)

Acceleration Matrix A

Randomization Matrix R

Slow-down Matrix S

Joint Transformation Matrix T T contractive

Steady state of Joint Transformation J  simulation master equation

Steady state of Joint Transformation   simulation master equation

Slow-down due to other vehicles Follower Leader

Follower Leader Slow-down due to other vehicles

Slow Down Matrix S(P) Follower Leader

Slow Down Matrix S(P)

S(P) nonlinear in P

Steady state of Joint Transformation J  modified master equation simulation master equation

Steady state of Joint Transformation   modified master equation simulation master equation

Fundamental Diagrams J  p=0.1 p=0.5 p=0.9

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

OUTLOOK ON NOISE Maria Schilstra’S recent simulations…