1. 1 Ole Steuernagel and Maria Schilstra University of Hertfordshire Hatfield

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

4. Heavy Traffic

5. Heavy traffic – solutions?

6. 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…

7. Cellular Automaton – Evolution Rules p

8. Heavy Traffic – Modelling with Cellular automata A la Nagel and Schreckenberg http://www.traffic.uni-duisburg.de/model/index.html

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

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

11. Acceleration Matrix A

12. Randomization Matrix R

13. Slow-down Matrix S

14. Joint Transformation Matrix T T contractive

15. Steady state of Joint Transformation J  simulation master equation

16. Steady state of Joint Transformation   simulation master equation

17. Slow-down due to other vehicles Follower Leader

18. Follower Leader Slow-down due to other vehicles

19. Slow Down Matrix S(P) Follower Leader

20. Slow Down Matrix S(P)

21. S(P) nonlinear in P

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

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

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

25. 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

26. OUTLOOK ON NOISE Maria Schilstra’S recent simulations…