Output analysis of a single model
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This document analyzes output from various types of simulations, including terminating and nonterminating simulations, focusing on performance estimation measures. It describes point and interval estimation techniques, as well as ways to minimize initialization bias through intelligent initialization and deletion methods. The document also discusses considerations for determining the run length in steady state simulations and computing sample sizes.
Output analysis of a single model
- 1. Output Analysis of a Single Model Adapted from J. Banks
- 2. Purpose Analysis of data generated by a simulation. To predict and compare performance of a model
- 3. Simulation exhibits randomness, thus it is necessary to estimate the: Performance measure of the model, . And by the models precision of the point estimator or std. Error (variance).
- 4. Types of simulation w/ respect to output analysis: Terminating/transient simulation Nonterminating/steady state simulation
- 5. Terminating/transient simulation One that runs for some duration T E , where E is a specified event (or set of events) which will stop the simulation. Such a model “opens” at time 0 under specified conditions and “closes” at T E.
- 6. Nonterminating/Steady state simulation Simulation whose objective is to study the long run, or steady state, behavior of nonterminating systems. The system “opens” at time 0 under defined initial conditions by the analyst, and runs for some analyst-specified period of T E .
- 7. Measures of Performance and their estimation: Point estimation of the performance values from the model. Two types: A. Within replication. B. Among replication. Interval estimation.
- 8. For Terminating Simulations: Compute for confidence intervals with fixed replications using same formulas except that n = R. Compute for confidence intervals with specified precision using half length criterion.
- 9. For Steady State Simulations: Choose the run length with the following considerations: A.) Bias in the point estimator due to artificial or arbitrary initial condition. B.) Bias can be severe if run length is too short, but decreases as run length is increased. C.) Precision of the estimator is measured based on an estimate of point-estimator variability. D.) Budget constraints on computer resources.
- 10. Initialization Bias can be minimized by: Intelligent initialization - initialized based on expected long run state A.) Use existing data of a system as basis (if system exists) B.) Use results from a simplified model (if system does not exists) Deletion - r educe impact of initial conditions by dividing a run into two phases. Let the first phase be from t = 0 to t = t o , followed the 2nd phase which is from t o to T E ., Thus the simulation will stop at time t = t o + T E .
- 11. Deletion can be done is the following ways: Ensemble averages. Plotting the mean and confidence limits. The intervals can used to judge whether or not the plot is precise enough to judge that bias has diminished. Preferred method. Using Cumulative averages. Useful in situations where single replication is only possible.
- 12. Computing for the sample size in steady state simulation: 1. Solve for R, based on initial sample of R o . 2. Compute for R/R o . 3. Apply it to first phase, (R/R o )( t o ), and (R/R o )( t o +T E ), for the second phase.