Selecting the best system in transient simulations with variances known

ABSTRACT

Selection of the best system among k different systems is investigated. This selection is based upon the results of finite-horizon simulations. Since the distribution of the output of a transient simulation is typically unknown, it follows that this problem is that of selection of the best population (best according to some measure) among k different populations, where observations within each population are independent, and identically distributed according to some general (unknown) distribution. In this work in progress, it is assumed that the population variances are known. A natural single-stage sampling procedure is presented. Under Bechbofer's indifference zone approach, this procedure is asymptotically valid.

REFERENCES

• 1: Bechhofer, R. E. 1954. A single-sample multiple decision procedure for ranking means of normal populations with known variances. The Annals of Mathema~ical Statistics, 25, 16-39.
• 2: Beehhofer, R. E., Dunnett, C. W., and M. Sobel. 1954. A two-sample multiple-decision procedure for ranking means of normal populations with a common unknown variance. Biometrika, 41, 170- 176.
• 3: Bechhofer, R. E., T. J. Santner, and D. M. Goldsman. 1995. Design and Analysis of Experiments for Statistical Selection, Screening, and Multiple Comparisons. Wiley, New York.
• 4: Damerdji, H., P. W. Glynn, M. K. Nakayama, and J. R. Wilson. 1996. Selection of the best system in a finite-horizon simulation context. Working paper.
• 5: Dudewiez, E. J., and S. R. Dalai. 1975. Allocation of observations in ranking and selection with unequal variances. Sankhy~, B37', 28-78.
• 6: Jean Dickinson Gibbons , Ingram Olkin , Milton Sobel, Selecting and ordering populations: a new statistical methodology, Society for Industrial and Applied Mathematics, Philadelphia, PA, 1999
• 7: Gupta, S. S., and G. C. McDonald. 1980. Nonpammetric procedures in multiple decisions (ranking and selection procedures). Colloquia Mathematica Societatis Jdnos Bolyai, 32,361-389.
• 8: Gupta, S. S., and S. Panchapakesan. 1979. Multiple Decision Procednres: Theory and Methodology of Selecting and 1~anking Populations. Wiley, New York.
• 9: Mukhopadhyay, N., and T. K. S. Solanky. 1994. Multistage Selection and Ranking Procedures. Marcel Dekker, New York.
• 10: Petrov, V. V. 1975. Sums of Independenll Random Variables. Springer-Verlag, New York.
• 11: Rinott, Y. 1978. On two-stage selection procedures and related probability-inequalities. Communication in Statistics: Theory and Method,a, A7(8), 799-811.
• 12: D. W. Sullivan , J. R. Wilson, Restricted subset selection procedures for simulation, Operations Research, v.37 n.1, p.52-71, Jan.-Feb. 1989 [doi>10.1287/opre.37.1.52]