Automating the Analysis of Simulation Output Data

1. Automating the Analysis of Simulation Output Data Katy Hoad, Stewart Robinson, Ruth Davies SSIG Meeting, 24th October 2007 http://www.wbs.ac.uk/go/autosimoa

2. The Problem • Prevalence of simulation software: ‘easy-to-develop’ models and use by non-experts. • Simulation software generally have very limited facilities for directing/advising user how to run the model to get accurate estimates of performance. • With a lack of the necessary skills and support, it is highly likely that simulation users are using their models poorly.

3. 3 Main Decisions: • How long a warm-up is needed? • How long a run length is needed? • How many replications should be run?

4. Continuing theoretical developments BUT little put into practical use. • Why? • Limited testing of methods • Requirement for detailed statistical knowledge • Methods generally not implemented in simulation software (AutoMod/AutoStat is an exception) A solution? Provide an automated output ‘Analyser’.

5. Simulation model Output data Analyser Warm-up analysis Obtain more output data Use replications or long-run? Replications analysis Run-length analysis Recommendation possible? Recommend- ation An Automated Output Analyser • Analyser advises user on: • Warm-up length • Run-length • Number of replications

6. The AutoSimOA Project A 3 year, EPSRC funded project in collaboration with SIMUL8 Corporation. • Main Objective: • To propose a procedure for automated output analysis of warm-up, replications and run-length • Only looking at analysis of a single scenario

7. The AutoSimOA Project • WORK CARRIED OUT TO DATE: • Creation of a representative and sufficient set of models / data output for testing chosen simulation output analysis methods. • Development of an automated algorithm for estimating the number of replications to run. • Selection and testing of warm-up methods from the literature.

8. Part 1.Creation of models and data sets

9. AIMS: • Provide a representative and sufficient set of models / data output for use in discrete event simulation research. • Use models / data sets to test the chosen simulation output analysis methods in the AutoSimOA Project.

10. Auto Correlation Non-terminating In/out of control Terminating Group B Normality Cycling/Seasonality Steady state Transient

11. Output data characteristics • Model characteristics • Deterministic or random • Significant pre-determined model changes (by time) • Dynamic internal changes i.e. ‘feed-back’ • Empty-to-empty pattern • Initial transient (warm-up) • Out of control trend ρ≥1 • Cycle • Auto-correlation • Statistical distribution

12. Modelling Warm-up Period: Shapes of Initial Bias Functions • Mean Shift: • Linear: • Quadratic: • Exponential: • Oscillating (decreasing):

13. Artificial Data: Construct data which resembles real model output with known values for some specific attribute. Example: Known steady state mean and variance. Example data: AR(1) with N(0,1) errors & linear initial bias. Real Models: Collect range of models created in “real circumstances”. Examples: • Swimming Pool complex: average number in system • Production Line Manufacturing Plant: through-put / hour • Fast Food Store: average queuing time

14. Part 2.WORK IN PROGRESSAutomating estimation of warm-up length

15. The Initial Bias Problem • Model may not start in a “typical” state. • This may cause initial bias in the output. • Many methods proposed for dealing with initial bias: e.g. Initial steady state conditions; run model for ‘long’ time… • This project uses: Deletion of the initial transient data by specifying a warm-up period.

16. Question is: How do you estimate the length of the warm-up period required?

17. 5 main types of methods: • Graphical Methods. • Heuristic Approaches. • Statistical Methods. • Initialisation Bias Tests. • Hybrid Methods.

18. Literature search – 42 methods Summary of methods and literature references on project web site: http://www.wbs.ac.uk/go/autosimoa Currently testing methods

19. Part 3.Automating analysis of number of replications

20. = summary statistic from rep1 N replications = summary statistic from repN Response measure of interest Output data from model Introduction • Initial Setup: • Any warm-up problems already dealt with. • Run length (m) decided upon. • Modeller decided to use multiple replications to obtain better estimate of mean performance. • Multiple replications performed by changing the random number streams used by the model and re-running the simulation.

21. QUESTION IS… How many replications are needed? • Limiting factors: computing time and expense. If performing N replications achieves a sufficient estimate of mean performance: > N replications: Unnecessary use of computer time and money. < N replications: Inaccurate results → incorrect decisions.

23. Confidence Interval Method • User decides size of error they can tolerate. • Run increasing numbers of replications, • Construct Confidence Intervals around sequential cumulative mean of output variable until desired precision achieved. Advantages: Relies upon statistical inference to determine number of replications required. Allows the user to tailor accuracy of output results to their particular requirement or purpose for that model and result. Disadvantage:Many simulation users do not have the skills to apply such an approach.

24. AUTOMATE Confidence Interval Method: Algorithm interacts with simulation model sequentially.

25. We define the precision, dn, as the ½ width of the Confidence Interval expressed as a percentage of the cumulative mean: Where n is the current number of replications carried out, is the student t value for n-1 df and a significance of 1-α, is the cumulative mean, snis the estimate of the standard deviation, calculated using results Xi (i = 1 to n) of the n current replications. ALGORITHM DEFINITIONS

26. Stopping Criteria • Simplest method: Stop when dn 1st found to be ≤ desired precision, drequired , and recommend that number of replications, Nsol, to the user. • Problem: Data series could prematurely converge, by chance, to incorrect estimate of the mean, with precision drequired , then diverge again. • ‘Look-ahead’ procedure: When dn 1st found to be ≤ drequired, algorithm performs set number of extra replications, to check that precision remains ≤ drequired.

27. Replication Algorithm 95% confidence limits Precision ≤ 5% Cumulative mean, f(kLimit) Nsol + f(kLimit) Nsol

28. Precision ≤ 5% Precision > 5% Precision ≤ 5% f(kLimit) Nsol2 + f(kLimit) Nsol2 Nsol1

29. TESTING METHODOLOGY • 24 artificial data sets created: Left skewed, symmetric, right skewed; Varying values of relative standard deviation (stdev/mean). • Advantage: true mean and variance known. • Artificial data set: 100 sequences of 2000 data values. • 8 real models selected. • Different lengths of ‘look ahead’ period looked at: kLimit values = 0 (i.e. no ‘look ahead’ period), 5, 10, 25. • drequiredvalue kept constant at 5%.

30. 5 performance measures • Coverage of the true mean • Bias • Absolute Bias • Average Nsol value • Comparison of 4. with Theoretical Nsol value • For real models: ‘true’ mean & variance values - estimated from whole sets of output data (3000 to 11000 data points).

31. Results • Nsol values for individual algorithm runs are very variable. • Average Nsol values for 100 runs per model close to the theoretical values of Nsol. • Normality assumption appears robust. • Using a ‘look ahead’ period improves performance of the algorithm.

33. Impact of different look ahead periods on performance of algorithm

34. Examples of changes in Nsol & improvement in estimate of true mean

35. Replication Work Discussion • kLimit default value set to 5. • Initial number of replications set to 3. • Multiple response variables - Algorithm run with each response - use maximum estimated value for Nsol. • Different scenarios - advisable to repeat algorithm every few scenarios to check that precision has not degraded significantly. • Inclusion into SIMUL8 package: Full explanations of algorithm and results.

36. Summary Of Replications Work • Selection and automation of Confidence Interval Method for estimating the number of replications to be run in a simulation. • Algorithm created with ‘look ahead’ period -efficient and performs well on wide selection of artificial and real model output. • ‘Black box’ - fully automated and does not require user intervention.

37. PROJECT OVERVIEW • Created set of artificial and “real” model data including warm-up bias functions. • Created replication algorithm. Currently: • Testing warm-up methods.

38. Thank you for listening. ACKNOWLEDGMENTSThis work is part of the Automating Simulation Output Analysis (AutoSimOA) project that is funded by the UK (EPSRC) Engineering and Physical Sciences Research Council (EP/D033640/1). The work is being carried out in collaboration with SIMUL8 Corporation, who are also providing sponsorship for the project. Stewart Robinson, Katy Hoad, Ruth Davies SSIG Meeting, 24th October 2007 http://www.wbs.ac.uk/go/autosimoa