Abstract
The computing power of modern workstations has made it possible to simulate many queueing systems interactively. Recent development in simulation software has mainly concentrated on interactive facilities. Unfortunately the precision of estimates has widely been overlooked in interactive simulation. In this paper we propose a method for controlling the precision of estimated means during an interactive simulation run. Since in a typical situation of interactive simulation the user is simultaneously interested in several means, we consider both the simultaneous precision and individual precisions of the estimated means. The method is based on the existing methods for estimating standard errors and on the Bonferroni inequality. The Bonferroni inequality is used to obtain a lower bound for the simultaneous precision.
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References
Y. Chow and H. Robbins, On the asymptotic theory of fixed-width sequential confidence intervals for the mean, Ann. Math. Statist. 36(1965)457–462.
D.R. Cox and D.V. Hinkley,Theoretical Statistics (Chapman and Hall, London, 1974).
H. Damerdji, On strong consistency of the variance estimator,Proc. Winter Simulation Conf. (1987) pp. 305–308.
P. Heidelberger and P.D. Welch, A spectral method for confidence interval generation and run length control in simulations, Commun. ACM 24(1981)233–245.
J.P.C. Kleijnen,Statistical Tools for Simulation Practitioners (Marcel Dekker, New York, 1987).
S.S. Lavenberg and C.H. Sauer, Sequential stopping rules for the regenerative method of simulation, IBM J. Res. Develop. 21(1977)545–558.
A.M. Law, Statistical analysis of simulation output data, Oper. Res. 31(1983)983–1029.
A.M. Law and W.D. Kelton, Confidence intervals for steady-state simulations, II: a survey of sequential procedure, Manag. Sci. 28(1982)550–562.
A.M. Law and W.D. Kelton,Simulation, Modeling and Analysis, 2nd ed. (McGraw-Hill, New York, 1991).
A.M. Law, W.D. Kelton and L.W. Koening, Relative width sequential confidence intervals for the mean, Commun. Statist. — Simul. Comp. B10(1981)29–39.
A. Nadas, An extension of a theorem of Chow and Robbins on sequential confidence intervals for the mean, Ann. Math. Statist. 40(1969)667–671.
K. Pawlikowski, Steady-state simulation of queueing processes: a survey of problems and solutions, ACM Comp. Surv. 22(1990)123–170.
K.E.E. Raatikainen, Simultaneous sequential confidence intervals of fixed widths for several means using Bonferroni inequality, Tech. Report, Dept. of Comp. Sci., University of Helsinki (1992).
K.E.E. Raatikainen, A sequential procedure for simultaneous estimation of several means, ACM TOMACS 3(1993)108–133.
L. Schruben, Using simulation to solve problems: a tutorial on the analysis of simulation output,Proc. Winter Simulation Conf. (1987) pp. 40–42.
P.D. Welch, Statistical analysis of simulation results, in:Computer Performance Modeling Handbook, ed. S.S. Lavenberg (Academic Press, New York, 1983).
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Raatikainen, K.E.E. Controlling the precision of estimated means in interactive simulation. Ann Oper Res 53, 485–505 (1994). https://doi.org/10.1007/BF02136840
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DOI: https://doi.org/10.1007/BF02136840