Variance reduction methods

ABSTRACT

A computer simulation model is unusual in that the random error is under the total control of the experimenter. Variance reduction methods aim to take advantage of this to improve experimental accuracy. The fundamental ideas behind the most important of these methods will be described and illustrated with simple examples.

REFERENCES

• 1: Paul Bratley , Bennett L Fox , Linus E Schrage, A guide to simulation (2nd ed.), Springer-Verlag New York, Inc., New York, NY, 1986
• 2: Russell C.H. Cheng, Random samples with known sample statistics: With application to variance reduction, Proceedings of the 15th conference on Winter Simulation, p.395-402, December 12-14, 1983, Arlington, Virginia, United States
• 3: Cheng, R.C.H. (1984). Generation of inverse Gaussian variates with given sample mean and dispersion. Applied Statistics, 33, 309-316.
• 4: Cheng, R.C.H. and Feast, G.M. (1980). Control variables with known mean and variance. Journal of the Operational Research Society, 31, 51-56.
• 5: Fieller, E.C. and Hartley, H.O. (1954). Sampling with control variables, Biometrika, 41, 494-501.
• 6: George S. Fishman, Principles of Discrete Event Simulation, John Wiley & Sons, Inc., New York, NY, 1978
• 7: George S. Fishman , Baosheng D. Huang, Antithetic variates revisited, Communications of the ACM, v.26 n.11, p.964-971, Nov. 1983 [doi>10.1145/182.358462]
• 8: Hammersley, J.M. and Handscomb, D.C. (1964). Monte Carlo Methods. Methuen & Co. Ltd., London.
• 9: Kleijnen, J.P.C. (1974). Statistical Techniques in ~imu lat ion, Part I. Marcel Dekker, New Yo~ck.
• 10: Lavenberg, S.S. and Welch, P.D. (1981) . A perspective on the use of control variables to increase the efficiency of Monte Carlo simulations. Management Science, 27, 322-335.
• 11: Averill M. Law , W. David Kelton, Simulation Modeling and Analysis, McGraw-Hill Higher Education, 1997
• 12: Byron J.T. Morgan, Elements of simulation, Chapman & Hall, Ltd., London, UK, 1984
• 13: Nelson, B.L. and Schmeiser, B.TT. (1985) . Decomposition of some well-known varlance reduction techniques. Research Memorandum 84-6, School o~- Industrial Engineering, Purdue Univers:_ty, West Lafayette, Indiana.
• 14: Ross, S.M. (19801 . Introduction to Probability Models, 2nd ed, Academic Press, New York.
• 15: Schruben, L.W. and Margolin, B.H. (1978). Pseudorandom number assignment in statistically designed simulation and distribution s~npling experiments. Journal of the American Statistical Association, 73, 504-520.
• 16: James R. Wilson, Variance reduction techniques, Proceedings of the 14th conference on Winter Simulation, December 06-08, 1982, San Diego, California
• 17: Wilson, J.R. (1984). Variance reduction techniques fo~ digital simulation. American Journal of Mathematical and Management Sciences, 4, 277-312.
• 18: Wilson, J.R. and Pritsker, A.A.B. (1984) . Varlance reduction in queueing simulation using general~zed concoL%itant variables. Journal of Stavistical Computation and Simulation, 19~ 129-153.

INDEX TERMS

Primary Classification:
  A. General Literature

Additional Classification:
  I. Computing Methodologies
  I.6 SIMULATION AND MODELING
      I.6.8 Types of Simulation
          Subjects: Monte Carlo

General Terms:
Design, Experimentation, Performance, Reliability, Theory