Hostname: page-component-76fb5796d-9pm4c Total loading time: 0 Render date: 2024-04-28T17:32:57.484Z Has data issue: false hasContentIssue false
  • English
  • Français

USING EXCURSIONS TO ANALYZE SIMULATION OUTPUT

Published online by Cambridge University Press:  18 March 2010

James M. Calvin
James M. Calvin
Affiliation:
Department of Computer Science, New Jersey Institute of Technology, Newark, NJ 07102 E-mail: calvin@njit.edu
Get access Rights & Permissions [Opens in a new window]

Abstract

We consider the steady-state simulation output analysis problem for a process that satisfies a functional central limit theorem. We construct an estimator for the time-average variance constant that is based on excursions of a process above the minimum. The resulting estimator does not require a fixed run length, and the memory requirement can be dynamically bounded. Standardized time series methods based on excursions are also described.

Type
Research Article
Information
Probability in the Engineering and Informational Sciences , Volume 24 , Issue 2 , April 2010 , pp. 201 - 218
Copyright
Copyright © Cambridge University Press 2010

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

1.Billingsley, P. (1968). Convergence of probability measures. New York: Wiley.Google Scholar
2.Calvin, J. (1995). Average performance of passive algorithms for global optimization. Journal of Mathematical Analysis and Applications 191: 608–617.CrossRefGoogle Scholar
3.Calvin, J.M. (2004) Simulation output analysis based on excursions. In Ingalls, R.G., Rosetti, M.D., Smith, J.S. & Peters, B.A., (eds.) Proceedings of the 2004 winter simulation conference. (Piscataway, NJ), Institute of Electrical and Electronics Engineers, pp. 681–684.Google Scholar
4.Chien, C., Goldsman, D. & Melamed, B. (1997). Large-sample results for batch means. Management Science 43: 1288–1295.CrossRefGoogle Scholar
5.Chung, K.L. (1976). Excursions in Brownian motion. Arkiv för Matematik 14: 155–177.CrossRefGoogle Scholar
6.Futschik, A. & Pflug, G. (1997). Optimal allocation of simulation experiments in discrete stochastic optimization and approximative algorithms. European Journal of Operational Research 101: 245–260.CrossRefGoogle Scholar
7.Glynn, P.W. & Iglehart, D.L. (1990). Simulation output analysis using standardized time series. Mathematics of Operations Research 14: 1–16.CrossRefGoogle Scholar
8.Goldsman, D. & Schmeiser, B.W. (1997). Computational efficiency of batching methods. In Andradóttir, S., Healy, K.J., Withers, D.H. & Nelson, B.L., (eds.) Proceedings of the 1997 winter simulation conference. Piscataway, NJ: Institute of Electrical and Electronics Engineers, pp. 202–207.Google Scholar
9.Karatzas, I. & Shreve, S.E. (2000). Brownian motion and stochastic calculus, 2nd ed.New York: Springer-Verlag.Google Scholar
10.Kim, S.-H. & Nelson, B.L. (2006). On the asymptotic validity of fully sequential selection procedures for steady-state simulation. Operations Research 54: 475–488.CrossRefGoogle Scholar
11.Meketon, M.S. & Schmeiser, B.W. (1984). Overlapping batch means: Something for nothing? In Sheppard, S., Pooch, U. & Pegden, D. (eds.) Proceedings of the 1984 winter simulation conference. Piscataway, NJ: Institute of Electrical and Electronics Engineers, pp. 227–230.Google Scholar
12.Revuz, D. & Yor, M. (1994). Continuous martingales and brownian motion. Berlin: Springer-Verlag.Google Scholar
13.Rogers, L.C.G. & Williams, D. (1994). Diffusions, Markov processes and martingales: Vol. 1: Foundations. Cambridge: Cambridge University Press.Google Scholar
14.Schruben, L.W. (1983). Confidence interval estimation using standardized time series. Operations Research, Volume 31, pp. 1090–1108.CrossRefGoogle Scholar
15.Vervaat, W. (1979). A relation between Brownian bridge and Brownian excursion. Annals of Probability, Volume 7, pp. 141–149.CrossRefGoogle Scholar
16.Yeh, Y. & Schmeiser, B.W. (2000). Simulation output analysis via dynamic batch means. In Joines, J.A., Barton, R.R., Kang, K. & Fishwick, P.A., (eds.) Proceedings of the 2000 winter simulation conference. Piscataway, NJ: Institute of Electrical and Electronics Engineers, pp. 637–645.Google Scholar