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Stochastic Optimization by Simulation: Numerical Experiments with the M/M/1 Queue in Steady-State


  • Pierre L'Ecuyer

    (Départment d'I.R.O., Universitedé Montréal, C.P. 6128, Montréal, H3C 3J7, Canada)

  • Nataly Giroux

    (Bell Northern Research, Dept. 6J33, Fitzgerald Building, P.O. Box 3511, Ottawa, K1Y 4H7, Canada)

  • Peter W. Glynn

    (Operations Research Department, Stanford University, Stanford, CA 94305, USA)


This paper gives numerical illustrations of the behavior of stochastic approximation, combined with different derivative estimation techniques, to optimize a steady-state system. It is a companion paper to L'Ecuyer and Glynn (1993), which gives convergence proofs for most of the variants experimented here. The numerical experiments are made with a simple M/M/1 queue, which while simple, serves to illustrate the basic convergence properties and Possible pitfalls of the various techniques.

Suggested Citation

  • Pierre L'Ecuyer & Nataly Giroux & Peter W. Glynn, 1994. "Stochastic Optimization by Simulation: Numerical Experiments with the M/M/1 Queue in Steady-State," Management Science, INFORMS, vol. 40(10), pages 1245-1261, October.
  • Handle: RePEc:inm:ormnsc:v:40:y:1994:i:10:p:1245-1261

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    Cited by:

    1. Sridhar Bashyam & Michael C. Fu, 1998. "Optimization of (s, S) Inventory Systems with Random Lead Times and a Service Level Constraint," Management Science, INFORMS, vol. 44(12-Part-2), pages 243-256, December.
    2. Gürkan, G. & Ozge, A.Y. & Robinson, S.M., 1997. "Sample-path solutions for simulation optimization problems and stochastic variational inequalities," Discussion Paper 1997-78, Tilburg University, Center for Economic Research.
    3. Gürkan, G., 1997. "Simulation Optimization of Buffer Allocations in Production Lines with Unreliable Machines," Discussion Paper 1997-97, Tilburg University, Center for Economic Research.
    4. Kao, Chiang & Chen, Shih-Pin, 2006. "A stochastic quasi-Newton method for simulation response optimization," European Journal of Operational Research, Elsevier, vol. 173(1), pages 30-46, August.
    5. Chen, Shih-Pin, 2007. "Solving fuzzy queueing decision problems via a parametric mixed integer nonlinear programming method," European Journal of Operational Research, Elsevier, vol. 177(1), pages 445-457, February.
    6. Gürkan, G. & Ozge, A.Y., 1996. "Sample-Path Optimization of Buffer Allocations in a Tandem Queue - Part I : Theoretical Issues," Discussion Paper 1996-98, Tilburg University, Center for Economic Research.
    7. Rubinstein, Reuven Y., 1997. "Optimization of computer simulation models with rare events," European Journal of Operational Research, Elsevier, vol. 99(1), pages 89-112, May.
    8. (Yale) Gong, Yeming & Yücesan, Enver, 2012. "Stochastic optimization for transshipment problems with positive replenishment lead times," International Journal of Production Economics, Elsevier, vol. 135(1), pages 61-72.


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