1. Traffic Simulation L2 – Introduction to simulation Ing. Ondřej Přibyl, Ph.D.

2. L2: Introduction to simulationCourse: Traffic Simulation 2 Discussion What is a system? Give me some examples of a system What is a model?

3. L2: Introduction to simulationCourse: Traffic Simulation 3 System and model System Part of an environment that could be divided by a physical or logical boundary OR a collection of entities (e.g., people or machines) that act and interact together toward the accomplishment of some logical end It can be divided into subsystems, which are interconnected S inputsoutputs

4. L2: Introduction to simulationCourse: Traffic Simulation 4 Keywords 4 Model It is a simplification of the reality A (usually miniature) representation of something; an example for imitation or emulation A model can be Analytical (Queuing Theory) or by Simulation. Model Simplified, abstract tool use to observe or predict behavior of real systems

5. L2: Introduction to simulationCourse: Traffic Simulation 5 Categorization of models Physical Example: a model of an air-plane in an aerodynamic tunnel Mathematical Analytical –Example: Ohm law, differential equations Simulation – numerical –Rough power (hrubá síla) –For complex systems without analytical models

6. L2: Introduction to simulationCourse: Traffic Simulation 6 Examples: Movement 6 Consider a system when a given object move This system can be modelled by the equation S= V * t Where S is the distance run through V is the speed of the object t is the time that has been observed. This is simplification of the real world Another model can take into account the direction of movement, or the three dimension coordinate … It is therefore to study the behaviour of the system based on a specific model

7. L2: Introduction to simulationCourse: Traffic Simulation 7 Example - electromotor u i M ω System Mathematical model

8. L2: Introduction to simulationCourse: Traffic Simulation 8 Example - building 8 Real System Model of the System

9. L2: Introduction to simulationCourse: Traffic Simulation 9 Example - queuing 9

10. L2: Introduction to simulationCourse: Traffic Simulation 10 Example - transistor 10

11. L2: Introduction to simulationCourse: Traffic Simulation 11 Characteristics of a Model 11 A model is never equal to the real system, because it is always simpler than the reality The accuracy of a model is determined by its tendency to approach the real system Is that a problem? Yes, if the model ignore important parameters of the real system (over simplification) No, if the model takes into account the important parameters (ignoring some details is sometimes not problematic) No, if we simplify those features not relevant for our research - We use a mathematical model of an engine to study its power, but we do not model its heating characteristics

12. L2: Introduction to simulationCourse: Traffic Simulation 12 Discussion What is a simulation? How is it different from analytical models?

13. L2: Introduction to simulationCourse: Traffic Simulation 13 Simulation versus Analytical Modeling Simulations are often complex error-prone pieces of software Simulation often uses “rough force” Simulation only produce approximate answers Simulation can take a LONG time to execute Mathematical models are less flexible, but they are exact and efficient Simulation is not used when a suitable mathematical model exists The problem is what model represents better the real world?

14. L2: Introduction to simulationCourse: Traffic Simulation 14 SYSTEM Experiment with the Actual System Experiment with a Model of the System Analytical SolutionSimulation Too costly or disruptive Not appropriate for the design There is always the question of whether it actually reflects the system. Mathematical Model Make assumptions that take the form of mathematical or logical relationships If the model is simple enough. E.g., calculus, algebra, probability theory Highly complex systems How can we evaluate performance of a system?

15. Categorization of simulation models

16. L2: Introduction to simulationCourse: Traffic Simulation 16 Categorization of simulation models Time triggered Event triggered Macroscopic Mesoscopic Deterministic Stochastic Static Dynamic Continuous Discrete 1. Control 5. Scope 3. Randomness 2. Dynamic 4. Continuousness

17. L2: Introduction to simulationCourse: Traffic Simulation 17 Discussion What is time and event triggering of a simulation model?

18. L2: Introduction to simulationCourse: Traffic Simulation 18 Classification of Models 1. Time versus Event triggering –What is an event? Arrival of a vehicle Change of signal light Turning of a vehicle … There is a given step (for example 1sec) when the parameters are computed After an event occurs, the parameters are recomputed

19. L2: Introduction to simulationCourse: Traffic Simulation 19 Discussion What is a deterministic and what is a stochastic model?

20. L2: Introduction to simulationCourse: Traffic Simulation 20 2. Static vs. Dynamic Models: 3. Deterministic vs. Stochastic Models : Represents a system as it evolves over time (typically expressed through differential equations) Involves random variables, probabilities (e.g., most queueing and inventory systems). One run of this model is one statistical observation Time plays no role; represents a system at a particular point in time (e.g., Monte-Carlo methods) No probabilistic components (e.g., worst-case analysis of a system) Classification of Models

21. L2: Introduction to simulationCourse: Traffic Simulation 21 4. Continuous vs. Discrete Models : The state of the system changes only at discrete points in time. The state of the system changes continuously (e.g., chemical processes) # of cars in a parking lot time Bit Arrival in a Queue Discrete Model Continuous Model Classification of Models time bit

22. L2: Introduction to simulationCourse: Traffic Simulation 22 Discussion What is a difference between macro- and micro- simulation model?

23. L2: Introduction to simulationCourse: Traffic Simulation 23 Classification of Models 5. Macroscopic models   Describe behavior in large areas   Deals with aggregated variables and behavior   Not suitable for study of advanced features (affect of ITS on driver’s behavior, …)   Example:   Traffic described by its fundamental diagram (intensity, density, …)

24. L2: Introduction to simulationCourse: Traffic Simulation 24 Deterministic, Macroscopic model

25. L2: Introduction to simulationCourse: Traffic Simulation 25 Classification of Models 5. Microscopic models Describe behavior and movement of particular units (vehicles) and interactions among them Use models such as –Lane changing behavior –Car following model –Gap acceptance model The output is the behavior of all vehicles and by aggregating do we get an overall traffic state We get overview about all levels in the network

26. Conclusion

27. L2: Introduction to simulationCourse: Traffic Simulation 27  Why to use models?  Implementation on real systems is very complex and costly,  Experimentation on real systems may be dangerous (e.g. chemical systems)  If models adequately describes the reality, experimenting with them can save money and time, and reduce the development complexity  When to use simulations?  Analytic models may be very complex to evaluate, and may lead to over implication of the real system  Simulation can be a good alternative to evaluate the system behavior very close to reality Why using Models and Simulations?

28. L2: Introduction to simulationCourse: Traffic Simulation 28 Questions which can be answered by traffic simulation (examples) Is our traffic network sufficient for the travel demand in 15 years? What is going to be the effect of building a new shopping center? Which of different alternative solutions leads to the best LOS? And others

29. Thank you for your attention Questions?