Validation and Verification of Simulation Models

1. Validation and Verification of Simulation Models

2. Outline • Introduction • Definitions of validation and verification • Techniques for verification of simulation models • Techniques for validation of simulation models • Statistical Methods for Comparing real-world observations with simulation output data • Inspection Approach • Confidence-Interval Approach • Summary

3. Introduction • One of the most difficult problems facing the simulation analyst is determining whether a simulation model is an accurate representation of the actual system being studied ( i.e., whether the model is valid). • If the simulation model is not valid, then any conclusions derived from it is of virtually no value. • Validation and verification are two of the most important steps in any simulation project.

4. What are Validation and Verification? • Validation is the process of determining whether the conceptual model is an accurate representation of the actual system being analyzed. Validation deals with building the right model. • Verification is the process of determining whether a simulation computer program works as intended (i.e., debugging the computer program). Verification deals with building the model right. Validation Conceptual Model Real -World System Verification Validation Simulation Program

5. Techniques for Verification of Simulation Models • Use good programming practice: • Write and debug the computer program in modules or subprograms. • In general, it is always better to start with a “moderately detailed” model, and later embellish, if needed. • Use “structured walk-through”: • Have more than one person to read the computer program. • Use a “trace”: • The analyst may use a trace to print out some intermediate results and compare them with hand calculations to see if the program is operating as intended.

6. Techniques for Verification of Simulation Models • Check simulation output for reasonableness: • Run the simulation model for a variety of input scenarios and check to see if the output is reasonable. • In some instances, certain measures of performance can be computed exactly and used for comparison. • Animate: • Using animation, the users see dynamic displays (moving pictures) of the simulated system. • Since the users are familiar with the real system, they can detect programming and conceptual errors.

7. Techniques for Verification of Simulation Models • Compare final simulation output with analytical results: • May verify the simulation response by running a simplified version of the simulation program with a known analytical result. If the results of the simulation do not deviate significantly from the known mean response, the true distributions can then be used. • For example, for a queuing simulation model, queuing theory can be used to estimate steady state responses (e.g., mean time in queue, average utilization). These formulas, however, assume exponential interarrival and service times with n servers (M/M/n).

8. Techniques for Validation of Simulation Models • A three-step approach for developing a valid and credible model: 1. Develop a model with high face validity: • The objective of this step is to develop a model that, on the surface, seems reasonable to people who are familiar with the system under study. • This step can be achieved through discussions with system experts, observing the system, or the use of intuition. • It is important for the modeler to interact with the client on a regular basis throughout the process. • It is important for the modeler to perform a structured walk-through of the conceptual model before key people to ensure the correctness of model’s assumptions .

9. Techniques for Validation of Simulation Models 2. Test the assumptions of the model empirically: • In this step, the assumptions made in the initial stages of model development are tested quantitatively. For example, if a theoretical distribution has been fitted to some observed data, graphical methods and goodness of fit tests are used to test the adequacy of the fit. • Sensitivity analysis can be used to determine if the output of the model significantly changes when an input distribution or when the value of an input variable is changed. If the output is sensitive to some aspect of the model, that aspect of the model must be modeled very carefully.

10. Techniques for Validation of Simulation Models 3. Determine how representative the simulation output data are: • The most definitive test of a model’s validity is determining how closely the simulation output resembles the output from the real system. • The Turing test can be used to compare the simulation output with the output from the real system. The output data from the simulation can be presented to people knowledgeable about the system in the same exact format as the system data. If the experts can differentiate between the simulation and the system outputs, their explanation of how they did that should improve the model. • Statistical methods are available for comparing the output from the simulation model with those from the real-world system .

11. Statistical Methods for Comparing Real-World Observation With Simulation Output Data • Suppose are observations from a real-world system and are output data from the simulation model. • Both, the real-world system outputs and simulation outputs are almost always non-stationary (the distribution of the successive observations change over time) and autocorrelated(the observations are correlated with each other). • Therefore, because classical statistical tests ( the t-test, chi-square test, K-S test, etc.) assume I.I.D data, they can not directly be used to compare the two data sets to determine model validity.

12. Statistical Methods for Comparing Real-World Observation With Simulation Output Data • 2 approaches for comparing the outputs from the real-world system with the simulation outputs are: • Inspection Approach • Confidence-Interval Approach

13. Inspection Approach • Run the simulation model with historical system input data (e.g., actual observed interarrival and service times) instead of sampling from the input probability distributions, and compare the system and model output data. • The system and the model experience exactly the same observations from the input random variables. • This approach results in model and system outputs being positively correlated.

14. Inspection Approach Historical system input data Historical system input data Simulation model Actual system System output data Model output data

15. Inspection Approach • If X is the output from the real-world system and Y is the corresponding output from the model, we are interested in estimating . • We make n experiments (using historical data) and compute Xj - Yj (for j = 1, 2, …, n) as an estimate of . Note that Xj and Yj use exactly the same interarrival times and service times). • Xj and Yjcan then be plottedsuch that the horizontal axis denotes time and the vertical axis denotes the real and simulated outputs. The user can then eyeball timepaths to see if the model accurately represents the real-world system.

16. Inspection Approach • Due to positive correlation between X and Y, Var (X-Y) is much smaller than if X and Y were independent which makes Xj - Yj a much better estimate of : Reason: -- In general, Var (X-Y) = Var (X) + Var (Y) - 2Cov(X, Y) -- If X and Y are independent, Cov (X, Y)=0 and Var (X-Y) = Var (X) + Var (Y) -- But, if X and Y are positively correlated, Cov(X, Y) > 0 leading to a smaller value for Var (X-Y).

17. Inspection Approach • Inspection approach (also called trace driven method)may provide valuable insight into the adequacy of the simulation model for some simulation studies. • In fact, this may be the only feasible approach because of severe limitations on the amount of data available on the operation of some real-world systems (e.g., military situation). • Care must, however, be taken in interpreting the result of this approach.

18. Confidence-Interval Approach • A more reliable approach for comparing a simulation model with the real-world system. • Requires a large amount of data. • Suppose we collect m independent sets of data from the system and n independent sets of data from the model (m and n can be equal). • Let Xj be the average of observations in the jth set of system data with mean and let Yj be the output from the jth replication of the simulation model with . • The objective is to build a confidence- interval for

19. Confidence-Interval Approach • In the case of correlated outputs where Xj is correlated with Yj (e.g., using trace driven simulation), let m = n and pair Xj ‘s and Yj’s. Let Zj =Xj -Yjfor j=1, 2 …, n. Zj’sare IID random variables with E(Zj) = . • Let and • Then, the approximate 100(1- ) percent C.I. is • If the confidence interval does not include a zero, then the observed difference between and is statistically different at level .

20. Summary • Validation and verification are two of the most important steps in any simulation study. • Validation is not something to be attempted after the simulation model has already been developed, and only if there is time and money still remaining. Instead, model development should be done throughout the entire simulation study.