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Published byBernice Richardson Modified over 9 years ago
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1 Ole Steuernagel and Maria Schilstra University of Hertfordshire Hatfield
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Cellular Automaton ModellingCellular Automaton Modelling Typical behaviourTypical behaviour Some semi-analytical resultsSome semi-analytical results Deriving the master equationDeriving the master equation 1
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Heavy Traffic
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Heavy traffic – solutions?
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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…
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Cellular Automaton – Evolution Rules p
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Heavy Traffic – Modelling with Cellular automata A la Nagel and Schreckenberg http://www.traffic.uni-duisburg.de/model/index.html
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Heavy Traffic – Modelling with Cellular automata A la Nagel and Schreckenberg
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Traffic – Modelling = (remaining free road) (drive-off probability)
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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 J simulation master equation
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Steady state of Joint Transformation simulation master equation
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Slow-down due to other vehicles Follower Leader
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Follower Leader 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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S(P) nonlinear in P
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Steady state of Joint Transformation J modified master equation simulation master equation
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Steady state of Joint Transformation modified master equation simulation master equation
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Fundamental Diagrams J p=0.1 p=0.5 p=0.9
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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 NOISE Maria Schilstra’S recent simulations…
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