Discrete_and_Continuous_Simulation.ppt
- 1. Discrete and Continuous Simulation Marcio Carvalho Luis Luna PAD 824 – Advanced Topics in System Dynamics Fall 2002
- 2. PAD 824 – Advanced Topics in System Dynamics Fall 2002 What is it all about? Numerical simulation approach Level of Aggregation Policies versus Decisions Aggregate versus Individuals Aggregate Dynamics versus Problem solving Difficulty of the formulation Nature of the system/problem Nature of the question Nature of preferred lenses
- 3. PAD 824 – Advanced Topics in System Dynamics Fall 2002 Basic concepts 1. Static or dynamic models 2. Stochastic, deterministic or chaotic models 3. Discrete or continuous change/models 4. Aggregates or Individuals
- 4. PAD 824 – Advanced Topics in System Dynamics Fall 2002 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. PAD 824 – Advanced Topics in System Dynamics Fall 2002 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. PAD 824 – Advanced Topics in System Dynamics Fall 2002 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. PAD 824 – Advanced Topics in System Dynamics Fall 2002 3. Discrete or Continuous models Continuous model: Bank account Principal Interest Average Interest Rate Noise Simulated Principal Sim Interest Estimated Interest Rate Noise Seed Observed Interest Rate Continuous and Stochastic Continuous and Deterministic
- 8. PAD 824 – Advanced Topics in System Dynamics Fall 2002 3. Discrete and Continuous models Discrete model: Bank Account Simulated Principal 1 0 Sim Interest 1 0 Average Principal 0 Averaging time 0 <Time> <TIME STEP> Observed Interest Rate 0 <Average Interest Rate> Simulated Principal 1 Sim Interest 1 Average Principal Averaging time <Time> <TIME STEP> Observed Interest Rate <Average Interest Rate> <Noise> Discrete and Stochastic Discrete and Deterministic
- 9. PAD 824 – Advanced Topics in System Dynamics Fall 2002 4. Aggregate and Individual models Aggregate model: we look for a more distant position. Modeler is more distant. Policy model. This view tends to be more deterministic. Individual model: modeler is taking a closer look of the individual decisions. This view tends to be more stochastic.
- 10. PAD 824 – Advanced Topics in System Dynamics Fall 2002 The “Soup” of models Waiting in line Waiting in line 1B Busy clerk Waiting in line (Stella version) Mortgages (ARENA model)
- 11. PAD 824 – Advanced Topics in System Dynamics Fall 2002 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.
- 12. PAD 824 – Advanced Topics in System Dynamics Fall 2002 Alternative views of Discreteness Culberston’s feedback view TOTE model (Miller, Galanter and Pribram, 1960) ) )( ' ( ) ' ( 2 1 1 t t t t t Y Y d d Y g g a Y Test Operate (Congruity) (Incongruity)
- 13. PAD 824 – Advanced Topics in System Dynamics Fall 2002 Peoples thoughts “The system contains a mixture of discrete events, discrete and different magnitudes, and continuous processes. Such mixed processes have generally been difficult to represent in continuous simulation models, and the common recourse has been a very high level of aggregation which has exposed the model to serious inaccuracy” (Coyle, 1982)
- 14. PAD 824 – Advanced Topics in System Dynamics Fall 2002 Peoples thoughts “Only from a more distant perspective in which events and decisions are deliberately blurred into patterns of behavior and policy structure will the notion that ‘behavior is a consequence of feedback structure’ arise and be perceived to yield powerful insights.” (Richardson, 1991)
- 15. PAD 824 – Advanced Topics in System Dynamics Fall 2002 So, is it all about these? Numerical simulation approach Level of Aggregation Policies versus Decisions Aggregate versus Individuals Problem solving versus Aggregate Dynamics Difficulty of the formulation Nature of the system/problem Nature of the question Nature of preferred lenses