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

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

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

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

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

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

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

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

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

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

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

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

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

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

15. 15Technische Universität München Gawron’s Model Generating the traffic network Generating the traffic network O-D Matrices O-D Matrices Describe basic movement patterns during a certain period of time (e.g. 24 hours) 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 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 Iteration for computation of the fastest route OriginDestination#Vehicles 05500 21030 73236 89037

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

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

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

19. 19Technische Universität München Modelling of Agents Replaces O-D Matrixes Replaces O-D Matrixes Activities of the single person Activities of the single person Building of activities through iterations 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)

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

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

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

23. 23Technische Universität München Parallel computing Partitioning of the network Partitioning of the network Every partition to a different processor 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)

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

25. 25Technische Universität MünchenEfficiency Linear factoring to 64 processors Linear factoring to 64 processors Best result by 4 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)

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

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

28. 28Technische Universität München Questions? Questions?