Halim Damerdji
ABSTRACT
Suppose that we have k different stochastic systems, where /spl mu/i denotes the steady-state mean of system i. We assume that the system labeled k is a control and want to compare the performance of the other sys tems, labeled 1,2,...,k - 1, relative to this control. This problem is known in the statistical literature as multiple comparisons with a control (MCC). Independent steady-state simulations will be performed to compare the systems to the control. Two-stage procedures, based on the method of batch means, are presented to construct simultaneous lower one sided confidence intervals for/spl mu/i - /spl mu/k (i = 1, 2, . . ., k), each having prespecified (absolute or relative) half width 6. Under the assumption that the stochastic processes representing the evolution of the systems satisfy a functional central limit theorem, it can be shown that asymptotically (as /spl delta/ /spl rarr/ 0 with the size of the batches proportional to 1//spl delta//sup 2/), the joint probability that the confidence intervals simultaneously contain the /spl mu/i - /spl mu/k (i = 1, 2,..., k - 1) is at least 1 - /spl alpha/, where /spl alpha/ is prespecified by the user.
- Billingsley, P. 1968. Convergence of Probability Measures. New York: John Wiley.Google Scholar
- Damerdji, H. and M. K. Nakayama. 1996. Two-Stage Procedures for Multiple Comparisons with the Best in Steady-State Simulations. In preparation. Google ScholarDigital Library
- Dudewicz, E. J. and S. R. Dalal. 1983. Multiple comparisons with a control when variances are unknown and unequal. American Journal of Mathematics and Management Sciences 4:275-295.Google Scholar
- Dudewicz, E. J. and J. S. Ramberg. 1972. Multiple comparison with a control: Unknown variances. Ann. Tech. Conf. Amer. Soc. Quality Control 26:483-488.Google Scholar
- Dudewicz, E. J., J. S. Ramberg, and H. j. Chen. 1972. New tables for multiple comparisons with a control (unknown variances). Biometrische Zeitschrift 17:437-445.Google Scholar
- Ethier, S. N. and T. G. Kurtz. 1986. Markov Processes: Characterization and Convergence. John Wiley, New York.Google ScholarCross Ref
- Glynn, P. W. 1990. Diffusion approximations. Chapter 4 of Handbooks in Operations Research and Management Science, Vol. 2, Stochastic Models, ed. D. Heyman and M. Sobel. Elsevier Science Publishers B. V. (North-Holland).Google Scholar
- Glynn, P. W. and W. Whitt. 1987. Sufficient conditions for functional-limit-theorem versions of L = )~W. Queueing Systems: Theory and Applications 1:279-287. Google ScholarDigital Library
- Goldsman, D. and B. L. Nelson. 1994. Ranking, selection and multiple comparisons in computer simulation. In Proceedings of the 1994 Winter Simulation Conference, ed. J. D. Tew, S. Manivannan, D. A. Sadowski, and A. F. Seila, 192-199. Piscataway, New Jersey: Institute of Electrical and Electronics Engineers. Google ScholarDigital Library
- Hochberg, Y. and A. C. Tamhane. 1987. Multiple Comparison Procedures. John Wiley, New York. Google ScholarDigital Library
- Nakayama, M. K. 1994. Two-stage stopping procedures based on standardized time series. Management Science 40:1189-1206. Google ScholarDigital Library
- Newman, C. M. and A. L. Wright. 1981. An invariance principle for certain dependent sequences. Annals of Probability 9:671-675.Google ScholarCross Ref
- Rinott, Y. 1978. On two-stage selection procedures and related probability-inequalities. Communications in Statistics--Theory and Methods A7:799- 811.Google ScholarCross Ref
- Tamhane, Y. 1977. Multiple comparisons in model i: One-way ANOVA with unequal variances. Communications in Statistics--Theory and Methods A6:15-32.Google ScholarCross Ref
- Whitt, W. 1989a. Planning queueing siraulations. Management Science 35:1341-1366. Google ScholarDigital Library
- Whitt, W. 1989b. Simulation run length planning. in Proceedings of the 1989 Winter Simulation Conference, ed. E. A. MacNair, K. J. Musselman, and P. Heidelberger, 106-112. Piscataway, New Jersey" institute of Electrical and Electronics Engineers. Google ScholarDigital Library
- Wilcox, R. R. 1984. A table for Rinott's selection procedure. Journal of Quality Technology 16:97- 100.Google ScholarCross Ref
- Two-stage procedures for multiple comparisons with a control in steady-state simulations
Recommendations
Selecting the best system in steady-state simulations using batch means
WSC '95: Proceedings of the 27th conference on Winter simulationSuppose that we want to compare k different systems, where /spl mu//sub i/ denotes the steady state mean performance of system i. Our goal is to use simulation to pick the "best" system (i.e., the one with the largest or smallest steady state mean). To ...
Comments