1. Modeling and Simulation Dr. X

2. Topics What is Continuous Simulation Why is it useful? Continuous simulation design

3. Basic concepts 1.Static or dynamic models 2.Stochastic, deterministic or chaotic models 3.Discrete or continuous change/models

4. 1. Static or Dynamic models Dynamic: State variables change over time (System Dynamics, Discrete Event, Agent- Based, Econometrics?) Static: Snapshot at a single point in time (Monte Carlo simulation, optimization models, etc.)

5. 2. Deterministic, Stochastic or Chaotic Deterministic model is one whose behavior is entire predictable. The system is perfectly understood, then it is possible to predict precisely what will happen. Stochastic model is one whose behavior cannot be entirely predicted. Chaotic model is a deterministic model with a behavior that cannot be entirely predicted

6. 3. Discrete or Continuous models Discrete model: the state variables change only at a countable number of points in time. These points in time are the ones at which the event occurs/change in state. Continuous: the state variables change in a continuous way, and not abruptly from one state to another (infinite number of states).

7. Continuous Simulation Continuous time flow It can only really be accomplished with an analog computer. Why? We approximate a continuous simulation – Make time steps really small – Continuous time flow ~ continuous step increments

8. Why continuous simulation? Systems that change a lot during time Physical systems Chemical reactions

9. Continuous Simulation Examples

10. Time handling 2 approaches: Time-slicing: move forward in our models in equal time intervals. Next-event technique: the model is only examined and updated when it is known that a state (or behavior) changes. Time moves from event to event.

11. How do we implement continuous simulation?? Unit time simulation Studying physical phenomena Linear or differential equations

12. A savings account

13. Model of a savings account

14. Savings account equations Principal(t) = Principal(t - dt) + (interest) * dt INIT Principal = 100 interest_Rate =.05 INFLOWS: interest = Principal * Interest_Rate

15. 3. Discrete or Continuous models Continuous model: Bank account Continuous and Stochastic Continuous and Deterministic

16. 3. Discrete and Continuous models Discrete model: Bank Account Discrete and StochasticDiscrete and Deterministic

17. References Continuous Simulation – the flow view http://www.systems- thinking.org/simulation/contsim.htm http://www.systems- thinking.org/simulation/contsim.htm Discrete vs. Continuous Simulation: When Does It Matter? http://www.systemdynamics.org/conferences /2009/proceed/papers/P1199.pdf http://www.systemdynamics.org/conferences /2009/proceed/papers/P1199.pdf