A wavelet-based spectral procedure for steady-state simulation analysis

European Journal of Operational Research

Volumn 174, Issue 3, 2006, Pages 1769-1801

  Lada, Emily K ^a   Wilson, James R ^b  

^a SAS INSTITUTE INC   (United States)

^b North Carolina State University   (United States)

Author keywords

Simulation; Spectral method; Steady state analysis; Time series; Wavelet analysis

Indexed keywords

APPROXIMATION THEORY; COMPUTATION THEORY; COMPUTER SIMULATION; ESTIMATION; GAUSSIAN NOISE (ELECTRONIC); PARAMETER ESTIMATION; THRESHOLD ELEMENTS;

SPECTRAL METHOD; STEADY-STATE ANALYSIS; TIME SERIES; WAVELET ANALYSIS;

WAVELET TRANSFORMS;

EID: 33746852113     PISSN: 03772217     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.ejor.2005.04.025     Document Type: Article

References (50)

1. Brillinger D.R. Time Series: Data Analysis and Theory. expanded ed. (1981), Holden-Day, San Francisco
2. Bruce A., and Gao H.-Y. Applied Wavelet Analysis with S-PLUS (1996), Springer, New York
3. Chatfield C. The Analysis of Time Series: An Introduction. third ed. (1984), Chapman and Hall, London
4. Chen E.J., and Kelton W.D. Determining simulation run length with the runs test. Simulation Modelling Practice and Theory 11 3-4 (2003) 237-250
5. Chien C., Goldsman D., and Melamed B. Large-sample results for batch means. Management Science 43 9 (1997) 1288-1295
6. Chow Y.S., and Robbins H. On the asymptotic theory of fixed-width sequential confidence intervals for the mean. The Annals of Mathematical Statistics 36 (1965) 457-462
7. Donoho D.L. De-noising by soft-thresholding. IEEE Transactions on Information Theory 41 3 (1995) 613-627
8. Donoho D.L., and Johnstone I.M. Ideal spatial adaptation by wavelet shrinkage. Biometrika 81 3 (1994) 425-455
9. Donoho D.L., and Johnstone I.M. Adapting to unknown smoothness via wavelet shrinkage. Journal of the American Statistical Association 90 432 (1995) 1200-1224
10. Fishman G.S. Grouping observations in digital simulation. Management Science 24 5 (1978) 510-521
11. Fishman, G.S., 1998. LABATCH.2 for analyzing sample path data. Technical report, Department of Operations Research, University of North Carolina, Chapel Hill, NC. Available on-line via www.unc.edu/depts/or/downloads/tech_reports/fishman/uncor97-04.ps [accessed April 12, 2005].
12. Fishman G.S., and Kiviat P.J. The analysis of simulation-generated time series. Management Science 13 7 (1967) 525-557
13. Fishman G.S., and Yarberry L.S. An implementation of the batch means method. INFORMS Journal on Computing 9 3 (1997) 296-310
14. Gao H.-Y. Choice of thresholds for wavelet shrinkage estimate of the spectrum. Journal of Time Series Analysis 18 3 (1997) 231-251
15. Gradshteyn, I.S., Ryzhik, I.M., 2000. Table of Integrals, Series, and Products, sixth ed. Edited by Alan Jeffrey and translated from the Russian by Scripta Technica, Inc. Academic Press, San Diego.
16. Heidelberger P., and Welch P.D. A spectral method for confidence interval generation and run length control in simulations. Communications of the ACM 24 4 (1981) 233-245
17. Heidelberger P., and Welch P.D. Adaptive spectral methods for simulation output analysis. IBM Journal of Research and Development 25 6 (1981) 860-876
18. Heidelberger P., and Welch P.D. Simulation run length control in the presence of an initial transient. Operations Research 31 6 (1983) 1109-1144
19. Irizarry M.A., Kuhl M.E., Lada E.K., Subramanian S., and Wilson J.R. Analyzing transformation-based simulation metamodels. IIE Transactions 35 11 (2003) 271-283
20. Lada, E.K., 2003. A wavelet-based procedure for steady-state simulation output analysis. Ph.D. dissertation, Graduate Program in Operations Research, North Carolina State University, Raleigh, NC. Available on-line via [accessed April 12, 2005].
21. Lada, E.K., Wilson, J.R., 2003. Online companion to "A wavelet-based spectral procedure for steady-state simulation analysis." Technical report, Department of Industrial Engineering, North Carolina State University, Raleigh, NC. Available on-line via [accessed April 12, 2005].
22. Lada, E.K., Wilson, J.R., Steiger, N.M., 2003. A wavelet-based spectral method for steady-state simulation analysis. In: Chick, S., Sánchez, P.J., Ferrin, D., Morrice, D.J. (Eds.), Proceedings of the 2003 Winter Simulation Conference, Institute of Electrical and Electronics Engineers, Piscataway, NJ, pp. 422-430. Available on-line via [accessed April 12, 2005].
23. Lada, E.K., Wilson, J.R., 2004. WASSP software and user's manual. Department of Industrial Engineering, North Carolina State University, Raleigh, North Carolina. Available on-line as a self-extracting archive via [accessed April 12, 2005].
24. Lada, E.K., Steiger, N.M., Wilson, J.R., Joines, J.A., 2004a. Performance evaluation of a wavelet-based spectral method for steady-state simulation analysis. In: Ingalls, R.G., Rossetti, M.D., Smith, J.S., Peters, B.A. (Eds.), Proceedings of the 2004 Winter Simulation Conference, Institute of Electrical and Electronics Engineers, Piscataway, NJ, pp. 694-702. Available on-line via [accessed April 12, 2005].
25. Lada, E.K., Wilson, J.R., Steiger, N.M., Joines, J.A., 2004b. Performance of a wavelet-based spectral procedure for steady-state simulation analysis. INFORMS Journal on Computing, in review. Available on-line via [accessed April 12, 2005].
26. Law A.M., and Carson J.S. A sequential procedure for determining the length of a steady-state simulation. Operations Research 27 5 (1979) 1011-1025
27. Law A.M., and Kelton W.D. Simulation Modeling and Analysis. third ed. (2000), McGraw-Hill, Boston
28. 2(R). Transactions of the American Mathematical Society 315 1 (1989) 69-87
29. Moulin P. Wavelet thresholding techniques for power spectrum estimation. IEEE Transactions on Signal Processing 42 11 (1994) 3126-3136
30. Nádas A. An extension of a theorem of Chow and Robbins on sequential confidence intervals for the mean. The Annals of Mathematical Statistics 40 2 (1969) 667-671
31. Percival D.B., and Walden A.T. Wavelet Methods for Time Series Analysis (2000), Cambridge University Press, Cambridge
32. Royston J.P. An extension of Shapiro and Wilk's W test for normality to large samples. Applied Statistics 31 2 (1982) 115-124
33. Royston P. A toolkit for testing for non-normality in complete and censored samples. The Statistician 42 1 (1993) 37-43
34. Royston P. Remark AS R94: A remark on algorithm AS 181: The W-test for normality. Applied Statistics 44 4 (1995) 547-551
35. Satterthwaite F.E. Synthesis of variance. Psychometrika 6 5 (1941) 309-316
36. Shapiro S.S., and Wilk M.B. An analysis of variance test for normality (complete samples). Biometrika 52 3-4 (1965) 591-611
37. Steiger N.M., and Wilson J.R. An improved batch means procedure for simulation output analysis. Management Science 48 12 (2002) 1569-1586
38. Steiger, N.M., Lada, E.K., Wilson, J.R., Alexopoulos, C., Goldsman, D., Zouaoui, F., 2002. ASAP2: An improved batch means procedure for simulation output analysis. In: Yücesan, E., Chen, C.-H., Snowdon, J.L., Charnes, J.M. (Eds.), Proceedings of the 2002 Winter Simulation Conference, Institute of Electrical and Electronics Engineers, Piscataway, NJ, pp. 336-344. Available on-line via [accessed October 2, 2004].
39. Steiger N.M., Lada E.K., Wilson J.R., Joines J.A., Alexopoulos C., and Goldsman D. ASAP3: A batch means procedure for steady-state simulation analysis. ACM Transactions on Modeling and Computer Simulation 15 1 (2005) 39-73
40. Stuart A., and Ord J.K. Kendall's Advanced Theory of Statistics. Distribution Theory. sixth ed. 1 (1994), Edward Arnold, London
41. Vidakovic B. Statistical Modeling by Wavelets (1999), Wiley, New York
42. von Neumann J. Distribution of the ratio of the mean square successive difference to the variance. The Annals of Mathematical Statistics 12 (1941) 367-395
43. Wahba G. Automatic smoothing of the log periodogram. Journal of the American Statistical Association 75 369 (1980) 122-132
44. Wahba G., and Wold S. Periodic splines for spectral density estimation: The use of cross validation for determining the degree of smoothing. Communications in Statistics 4 2 (1975) 125-141
45. Walden A.T., Percival D.B., and McCoy E.J. Spectrum estimation by wavelet thresholding of multitaper estimators. IEEE Transactions on Signal Processing 46 12 (1998) 3153-3165
46. Welch B.L. On linear combinations of several variances. Journal of the American Statistical Association 51 273 (1956) 132-148
47. Wilcox H.J., and Myers D.L. An Introduction to Lebesgue Integration and Fourier Series (1978), R.E. Krieger Publishing Co., Huntington, NY
48. Wilson J.R., and Pritsker A.A.B. A survey of research on the simulation startup problem. Simulation 31 2 (1978) 55-58
49. Wilson J.R., and Pritsker A.A.B. Evaluation of startup policies in simulation experiments. Simulation 31 3 (1978) 79-89
50. Young L.C. On randomness in ordered sequences. The Annals of Mathematical Statistics 12 (1941) 293-300