1 / 27

Ole Steuernagel and Maria Schilstra University of Hertfordshire Hatfield

Velocity class master equations for single-lane traffic models. Ole Steuernagel and Maria Schilstra University of Hertfordshire Hatfield. 1. Velocity class master equations for single-lane traffic models. 1. Cellular Automaton Modelling Typical behaviour Some semi-analytical results

jasmined
Download Presentation

Ole Steuernagel and Maria Schilstra University of Hertfordshire Hatfield

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript

  1. Velocity class master equations for single-lane traffic models Ole Steuernagel and Maria Schilstra University of Hertfordshire Hatfield 1

  2. Velocity class master equations for single-lane traffic models 1

  3. Cellular Automaton Modelling • Typical behaviour • Some semi-analytical results • Deriving the master equation 1

  4. Heavy Traffic

  5. Heavy traffic – solutions?

  6. 10 units Vmax 5 units Vmax 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…

  7. p Cellular Automaton – Evolution Rules

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

  11. Acceleration Matrix A

  12. Randomization Matrix R

  13. Slow-down Matrix S

  14. Joint Transformation Matrix T T contractive

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

  16. simulation master equation Steady state of Joint Transformation u r

  17. Leader Follower Slow-down due to other vehicles

  18. Leader Follower Slow-down due to other vehicles

  19. Leader Slow Down Matrix S(P) Follower Leader

  20. Slow Down Matrix S(P)

  21. S(P) nonlinear in P Slow Down Matrix S(P)

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

  23. modified master equation Steady state of Joint Transformation u simulation master equation r

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

  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 NOISEMaria Schilstra’S recent simulations…

  27. Thank you for your for your attention!

More Related