Skip to main content
SpringerLink
Log in
Book cover

Encyclopedia of Operations Research and Management Science pp 608–611Cite as

Perturbation analysis

  • Reference work entry
  • First Online:

Introduction

Perturbation analysis (PA) is a sample path technique for analyzing changes in the performance of stochastic systems due to changes in system parameters. In terms of stochastic simulation — the main setting for the application of PA — the objective is to estimate sensitivities of the performance measures of interest with respect to system parameters while obtaining estimates of performance itself, without the need for additional simulation runs. The primary application is gradient estimation during the simulation of discrete-event systems, for example, queueing and inventory systems. Besides their importance in sensitivity analysis, these gradient estimators are a critical component in gradient-based simulation optimization methods.

Let l(θ) be a performance measure of interest with parameter (possibly vector) of interest θ. We are interested in those systems where l(θ) cannot be easily obtained through analytical means and therefore must be estimated from sample paths,...

This is a preview of subscription content, log in via an institution.

Chapter
USD   29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD   532.00
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever

Tax calculation will be finalised at checkout

Purchases are for personal use only

Learn about institutional subscriptions

References

  1. Brémaud, P. and Vázquez-Abad, F.J. (1992). “On the Pathwise Computation of Derivatives with Respect to the Rate of a Point Process: The Phantom RPA Method,” Queueing Systems: Theory and Applications, 10, 249–270.

    Google Scholar 

  2. Cao, X.R. (1994). Realization Probabilities: The Dynamics of Queueing Systems, Springer Lecture Notes in Control and Optimization, 194, Springer-Verlag, New York.

    Google Scholar 

  3. Cassandras, C.G. (1993). Discrete Event Systems: Modeling and Performance Analysis, Irwin.

    Google Scholar 

  4. Cassandras, C.G. and Strickland, S.G. (1989). “On-Line Sensitivity Analysis of Markov Chains,” IEEE Trans. Automatic Control, AC-34, 76–86.

    Google Scholar 

  5. Dai, L. and Ho, Y.C. (1995). “Structural Infinitesimal Perturbation Analysis for Derivative Estimation in Discrete Event Dynamic Systems,” IEEE Trans. Automatic Control, 40, 1154–1166.

    Google Scholar 

  6. Fu, M.C. (1994). “Sample Path Derivatives for (s, S) Inventory Systems,” Operations Research, 42, 351–364.

    Google Scholar 

  7. Fu, M.C. and Hu, J.Q. (1997). Conditional Monte Carlo: Gradient Estimation and Optimization Applications, Kluwer Academic, Dordrecht.

    Google Scholar 

  8. Gaivoronski, A., Shi, L.Y., and Sreenivas, R.S. (1992). “Augmented Infinitesimal Perturbation Analysis: An Alternate Explanation,” Discrete Event Dynamic Systems: Theory and Applications, 2, 121–138.

    Google Scholar 

  9. Glasserman, P. (1991). Gradient Estimation Via Perturbation Analysis, Kluwer Academic, Dordrecht.

    Google Scholar 

  10. Gong, W.B. and Ho, Y.C. (1987). “Smoothed Perturbation Analysis of Discrete-Event Dynamic Systems,” IEEE Trans. Automatic Control, AC-32, 858–867.

    Google Scholar 

  11. Ho, Y.C. and Cao, X.R. (1991). Perturbation Analysis of Discrete Event Dynamic Systems, Kluwer Academic, Dordrecht.

    Google Scholar 

  12. Ho, Y.C., Cao, X.R., and Cassandras, C.G. (1983). “Infinitesimal and Finite Perturbation Analysis for Queueing Networks,” Automatica, 19, 439–445.

    Google Scholar 

  13. Ho, Y.C., Eyler, M.A., and Chien, T.T. (1979). “A Gradient Technique for General Buffer Storage Design in a Serial Production Line,” International Journal of Production Research, 17, 557–580.

    Google Scholar 

  14. Ho, Y.C. and Li, S. (1988). “Extensions of Infinitesimal Perturbation Analysis,” IEEE Trans. Automatic Control, AC-33, 827–838.

    Google Scholar 

  15. Shi, L.Y. (1996). “Discontinuous Perturbation Analysis of Discrete Event Dynamic Systems,” IEEE Trans. Automatic Control, 41, 1676–1681.

    Google Scholar 

  16. Suri, R. and Zazanis, M.A. (1988). “Perturbation Analysis Gives Strongly Consistent Sensitivity Estimates for the M/G/1 Queue,” Management Science, 34, 39–64.

    Google Scholar 

  17. Vakili, P. (1991). “Using a Standard Clock Technique for Efficient Simulation,” Operations Research Letters, 15, 445–452.

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. University of Maryland, College Park, USA

    Michael C. Fu

Authors
  1. Michael C. Fu
    View author publications

    You can also search for this author in PubMed Google Scholar

Editor information

Editors and Affiliations

  1. Robert H. Smith School of Business, University of Maryland, College Part, Maryland, USA

    Saul I. Gass

  2. School of Information Technology & Engineering, George Mason University, Fairfax, Virginia, USA

    Carl M. Harris

Rights and permissions

Reprints and permissions

Copyright information

© 2001 Kluwer Academic Publishers

About this entry

Cite this entry

Fu, M.C. (2001). Perturbation analysis . In: Gass, S.I., Harris, C.M. (eds) Encyclopedia of Operations Research and Management Science. Springer, New York, NY. https://doi.org/10.1007/1-4020-0611-X_748

Download citation

  • DOI: https://doi.org/10.1007/1-4020-0611-X_748

  • Published:

  • Publisher Name: Springer, New York, NY

  • Print ISBN: 978-0-7923-7827-3

  • Online ISBN: 978-1-4020-0611-1

  • eBook Packages: Springer Book Archive

Publish with us

Policies and ethics

Search

Navigation