Estimation procedures based on control variates with known covariance matrix

ABSTRACT

This paper describes a new procedure for using control variates in multiresponse simulation when the covariance matrix of the controls is known. Assuming that the responses and the controls are jointly normal, we develop a new unbiased control-variates point estimator for the mean simulation response. We also compute the covariance matrix of this point estimator in order to construct an approximate confidence-region estimator for the mean response. If the covariances between the responses and the controls are unknown so that the optimal control coefficients must be estimated, then some of the potential efficiency improvement is lost. This loss is quantified in a new variance ratio. We summarize the results of an extensive experimental study in which we apply the proposed estimation procedure to closed queueing networks and stochastic activity networks.

REFERENCES

• 1: AntUl, J. M. and Woodhead, R. W. (1982). Critical Path Methods in Construction Practice. John Wiley, New York.
• 2: Bauer, K. W. (1987). Control variate selection for multiresponse simulation. Unpublished Ph.D. dissertation, School of Industrial Engineering, Purdue University, West Lafayette, Indiana.
• 3: Elmaghraby, S. E. (1977). Activity Networks. WileF- Interscience, New York.
• 4: Fishman, G. S. (1987). Monte Carlo, control variates, and stochastic ordering. Technical Report No. UNC/ORSA/TR--86/16, Department of Operations Research, University of North Carolina, Chapel Hill, North Carolina.
• 5: Grant, F. H. and Solberg, J. J. (1983). Variance reduction techniques in stochastic shortest route analysis: Application procedures and results. Mathematics and Gomputers in Simulation XXV, 366-375.
• 6: Lavenberg, S. S. and Welch, P. D. (1981). A perspective on the use of control variables to increase the efficiency of Monte Carlo simulation. Management Science 27, 322~335.
• 7: Lavenberg, S. S., Moeller, T. L. and Welch, P. D. (1982). Statistical results on control variables with application to queueing network simulation. Operations Research ~0, 182--202.
• 8: McKenney, J. L~ and Rosenbloom, R. S. (1969). Cases in Operations Management. John Wiley, New York.
• 9: Rubinstein, R. Y. and Marcus, R. (lg85). Efficiency of multivariate control varlates in Monte Curio simulation. Operatior~s Research 88, 661--877.
• 10: Solberg, J. J. (1080). CAN--Q user's guide. School of Industrial Engineering, Purdue University, West Lafayette, Indiana.
• 11: Sekhar Venkatraman , James R. Wilson, Using path control variates in activity network simulation, Proceedings of the 17th conference on Winter simulation, p.217-222, December 11-13, 1985, San Francisco, California, United States [doi>10.1145/21850.253156]
• 12: Venkatraman, S. and Wilson, J. R. (1986). The efficiency of control varlates in multiresponse simulation. Operations Research Letters 5, 37--42.
• 13: Wilson, J. R. and Prltsker, A. A. B. (1984). Variance reduction in queueing simulation using generalized concomitant variables. Journal of Statistical Computation and Simulation 19, 129--153.

INDEX TERMS

Primary Classification:
  G. Mathematics of Computing

Additional Classification:
  I. Computing Methodologies
  I.2 ARTIFICIAL INTELLIGENCE
      I.2.8 Problem Solving, Control Methods, and Search
          Subjects: Control theory
  I.6 SIMULATION AND MODELING

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