Traffic Simulation with Queues

1. Traffic Simulation with Queues Ferienakademie, Sarntal Neven Popov Technische Universität München 09.2008

2. Outline • Motivation • Introduction • Traffic simulation • Two models • Nagel-Schreckenberg model • Cellular automaton • Essential steps • Disadvategous • Queue model • Queue data structure • Model of Simao and Powell • Gawron’s model • Extensions • Parallel computing • Results • Comparison between the two models Technische Universität München

3. Motivation • How to avoid traffic jams? • Cities with light traffic? • In the USA with the name “Transims” for parallel computing • Basis for the OSLIM-Traffic predictions in Nordrhein-Westfalen Technische Universität München

4. Outline • Motivation • Introduction • Traffic simulation • Two models • Nagel-Schreckenberg model • Cellular automaton • Essential steps • Disadvategous • Queue model • Queue data structure • Model of Simao and Powell • Gawron’s model • Extensions • Parallel computing • Results • Comparison between the two models Technische Universität München

5. Introduction – Traffic Simulation • Microscopic model – through description of the decisions of the single cars • Decisions and conditions of the system Source: http://ebus.informatik.uni-leipzig.de Technische Universität München

6. Introduction – Two models • Nagel-Schreckenberg model • Interactions between the vehicles • Four essential steps • Queue model • No interactions between the vehicles • Faster movement of the vehicles Technische Universität München

7. Outline • Motivation • Introduction • Traffic simulation • Two models • Nagel-Schreckenberg model • Cellular automaton • Essential steps • Disadvategous • Queue model • Queue data structure • Model of Simao and Powell • Gawron’s model • Extensions • Parallel computing • Results • Comparison between the two models Technische Universität München

8. Cellular automaton • Cellular automaton • Neighborhood conditions • The condition depends on the previous time step Moore Neighborhood Von-Neumann Neighborhood Source: http://www.wikipedia.org Source: http://www.wikipedia.org Technische Universität München

9. Cellular automaton • Game of Life Source: http://www.wikipedia.org Technische Universität München

10. Nagel-Schreckenberg Model - Four Essential Steps Source: http://ebus.informatik.uni-leipzig.de • Four important steps 1) Acceleration (if vn, < vmax set vn = vn + 1) 2) Slowing down (if sites to n+1-th vehicle (j) <= vn so set vn = j-1) 3) Randomization (if vn > 0 so set vn = vn – 1 with probability p) 4) Car motion (move the cars with vn cells forward) • Configuration at time step t • Acceleration with vmax = 2 • Slowing down • Randomization with probability p • Car motion (time step t+1) Technische Universität München

11. Reason for applying Queue model • Cellular automata too complex • Too many cells to represent • The behavior of the driver too complex That’s why : • Transition to Queue model • Simplifying the Cellular automation • More realistic by building of traffic jams Technische Universität München

12. Outline • Motivation • Introduction • Traffic simulation • Two models • Nagel-Schreckenberg model • Cellular automaton • Essential steps • Disadvategous • Queue model • Queue data structure • Model of Simao and Powell • Gawron’s model • Extensions • Parallel computing • Results • Comparison between the two models Technische Universität München

13. Queue • Important data structure • Access only to the border elements Source: http://www.wikipedia.org Example FIFO-Queue (First In, First Out) Technische Universität München

14. Queue model • Model of Simao and Powell • Traffic network • Nodes (Places) • Edges (Streets) • Edges • In sub edges • FIFO-Queues • Leaving depends on the capacity Technische Universität München

15. Gawron’s Model • Generating the traffic network • O-D Matrices • Describe basic movement patterns during a certain period of time (e.g. 24 hours) • N Vehicles leave origin o in order to get to the destination d during time t Origin node -> Destination node = #Vehicles • Iteration for computation of the fastest route Technische Universität München

16. Gawron’s Model • Computation of the departure time • Through laminar traffic • Through a preferred speed • Edges have limited space • Leaving only if there is a next free edge • Building of traffic jams Technische Universität München

17. Dependency between Velocity and Density • Laminar Traffic • Capacity dominating • Congestion area Source: http://www.wikipedia.org Technische Universität München

18. Extensions • However, • O-D Matrices not realistic enough • O-D Matrices not flexible • It can be achieved even more efficiency • Applying of: • Agents • Event-Driven Queue Based Simulations Technische Universität München

19. Modelling of Agents • Replaces O-D Matrixes • Activities of the single person • Building of activities through iterations • Plan 1 • - Home till 9 am • - Drive to work (car) • - Work 8h, begin • approx 9.30 am • Drive to sports (car) • Sports 19 pm to • 22 pm (optional) • - Drive home (car) • Plan 2 • - Home till 8 am • - Drive to work (pt) • - Work 8h, begin • approx 8.30 am • Drive to sports (pt) • Sports 18 pm to • 21 pm (optional) • - Drive home (pt) Technische Universität München

20. Event-Driven Queue Based Simulations • Substitution of the constant time-step through direct treatment of actions • Most computational time where traffic flow is maximal • Results : • Simulation performance is being boosted • Advantageous for the parallel computing • Fast simulation of huge traffic networks Technische Universität München

21. Elements of the Event-Driven Queue Based Simulations Activity plan Entry/arrival time Set timer Road segment Clock Agent Register Wake up Technische Universität München

22. Results from the Event-Driven Queue Based Simulations • Independent from the size of the traffic network • Boosting up with factor of ten in comparison to simple Queue model • There is no case where the other models are faster Technische Universität München

23. Parallel computing • Partitioning of the network • Every partition to a different processor Source: D. Charypar und K.W. Axhausen und K. Nagel, An event-driven parallel queue-based microsimulation for large scale traffic scenarios, VSP Working Paper, 07-03. (2007) Technische Universität München

24. Results • Test cases : Berlin and Brandenburg • 11,6k nodes and 27,7k edges • 7,05M simulated persons for 24 hours • 249M used edges for 24 hours • Used computer system • Shared memory parallel computer with 256GB RAM • 64 dual-core Intel Itanium 2 processors with 1,65 GHz • Results • Boosting up with factor of 53 • Time for simulation : 87s Technische Universität München

25. Efficiency • Linear factoring to 64 processors • Best result by 4 processors Source: D. Charypar und K.W. Axhausen und K. Nagel, An event-driven parallel queue-based microsimulation for large scale traffic scenarios, VSP Working Paper, 07-03. (2007) Technische Universität München

26. Outline • Motivation • Introduction • Traffic simulation • Two models • Nagel-Schreckenberg model • Cellular automaton • Essential steps • Disadvategous • Queue model • Queue data structure • Model of Simao and Powell • Gawron’s model • Extensions • Parallel computing • Results • Comparison between the two models Technische Universität München

27. Comparison between the two models • The Queue model (in general) • Higher efficiency • More realism by building of congestions • Nagel-Schreckenberg model • A better observation of the interactions between the vehicles • More complex than the Queue model Technische Universität München

28. Questions? Technische Universität München