IDEAS home Printed from https://ideas.repec.org/a/inm/ormnsc/v40y1994i11p1562-1578.html
   My bibliography  Save this article

Stochastic Optimization by Simulation: Convergence Proofs for the GI/G/1 Queue in Steady-State

Author

Listed:
  • Pierre L'Ecuyer

    (Département d'I.R.o., Université de Montréal, C.P. 6128, Montréal, Quebec, Canada, H3C 3J7)

  • Peter W. Glynn

    (Operations Research Department, Stanford University, Stanford, California 94305)

Abstract

Approaches like finite differences with common random numbers, infinitesimal perturbation analysis, and the likelihood ratio method have drawn a great deal of attention recently as ways of estimating the gradient of a performance measure with respect to continuous parameters in a dynamic stochastic system. In this paper, we study the use of such estimators in stochastic approximation algorithms, to perform so-called "single-run optimizations" of steady-state systems. Under mild conditions, for an objective function that involves the mean system time in a GI/G/1 queue, we prove that many variant of these algorithms converge to the minimizer. In most cases, however, the simulation length must be increased from iteration to iteration, otherwise the algorithm may converge to the wrong value. One exception is a particular implementation of infinitesimal perturbation analysis, for which the single-run optimization converges to the optimum even with a fixed (and small) number of ends of service per iteration. As a by-product of our convergence proofs, we obtain some properties of the derivative estimators that could be of independent interest. Our analysis exploits the regenerative structure of the system, but our derivative estimation and optimization algorithms do not always take advantage of that regenerative structure. In a companion paper, we report numerical experiments with an M/M/1 queue, which illustrate the basis convergence properties and possible pitfalls of the various techniques.

Suggested Citation

  • Pierre L'Ecuyer & Peter W. Glynn, 1994. "Stochastic Optimization by Simulation: Convergence Proofs for the GI/G/1 Queue in Steady-State," Management Science, INFORMS, vol. 40(11), pages 1562-1578, November.
    • Handle: RePEc:inm:ormnsc:v:40:y:1994:i:11:p:1562-1578
    DOI: 10.1287/mnsc.40.11.1562
    as

    Download full text from publisher

    File URL: http://dx.doi.org/10.1287/mnsc.40.11.1562
    Download Restriction: no
    File URL: https://libkey.io/10.1287/mnsc.40.11.1562?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. Gürkan, G., 1997. "Simulation Optimization of Buffer Allocations in Production Lines with Unreliable Machines," Discussion Paper 1997-97, Tilburg University, Center for Economic Research.
    2. 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.
    3. A. B. Dieker & S. Ghosh & M. S. Squillante, 2017. "Optimal Resource Capacity Management for Stochastic Networks," Operations Research, INFORMS, vol. 65(1), pages 221-241, February.
    4. Sumit Kunnumkal & Huseyin Topaloglu, 2009. "A stochastic approximation method for the single-leg revenue management problem with discrete demand distributions," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 70(3), pages 477-504, December.
    5. Sumit Kunnumkal & Huseyin Topaloglu, 2011. "A stochastic approximation algorithm to compute bid prices for joint capacity allocation and overbooking over an airline network," Naval Research Logistics (NRL), John Wiley & Sons, vol. 58(4), pages 323-343, June.
    6. Paul Glasserman & Sridhar Tayur, 1996. "A simple approximation for a multistage capacitated production‐inventory system," Naval Research Logistics (NRL), John Wiley & Sons, vol. 43(1), pages 41-58, February.
    7. 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.
    8. 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.
    9. A. B. Dieker & S. Ghosh & M. S. Squillante, 2017. "Optimal Resource Capacity Management for Stochastic Networks," Operations Research, INFORMS, vol. 65(1), pages 221-241, February.
    10. Tito Homem-de-Mello, 2001. "Estimation of Derivatives of Nonsmooth Performance Measures in Regenerative Systems," Mathematics of Operations Research, INFORMS, vol. 26(4), pages 741-768, November.
    11. Leyuan Shi & Sigurdur O´lafsson, 2000. "Nested Partitions Method for Stochastic Optimization," Methodology and Computing in Applied Probability, Springer, vol. 2(3), pages 271-291, September.
    12. Sumit Kunnumkal & Huseyin Topaloglu, 2008. "Using Stochastic Approximation Methods to Compute Optimal Base-Stock Levels in Inventory Control Problems," Operations Research, INFORMS, vol. 56(3), pages 646-664, June.
    13. Huseyin Topaloglu, 2008. "A Stochastic Approximation Method to Compute Bid Prices in Network Revenue Management Problems," INFORMS Journal on Computing, INFORMS, vol. 20(4), pages 596-610, November.

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:inm:ormnsc:v:40:y:1994:i:11:p:1562-1578. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    We have no bibliographic references for this item. You can help adding them by using this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Chris Asher (email available below). General contact details of provider: https://edirc.repec.org/data/inforea.html .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.