Skip to main content

Part of the book series: Springer Series in Operations Research ((ORFE))

Abstract

This chapter treats the problem of evaluating the sensitivity of performance measures to changes in system parameters for a class of stochastic models. The technique presented, called perturbation analysis, evaluates sensitivities from sample paths, based either on a simulation or on real data.

The chapter begins with an overview, based on a single-machine model. It proceeds to address underlying theoretical issues and then examines a variety of examples of production networks. It concludes with a discussion of issues arising in the estimation of steady-state sensitivities.

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

Access this chapter

eBook
USD 16.99
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 16.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. Asmussen, S., Applied Probability and Queues, Wiley, New York, 1987.

    Google Scholar 

  2. Baccelli, F., Massey, W.A., AND Towsley, D., Acyclic Fork-Join Queueing Networks, J. ACM 36, 615–642, 1989.

    Article  Google Scholar 

  3. Cao, X.R., Realization Probability in Closed Jackson Queueing Networks and its Application, Adv. Appl. Prob. 19, 708–738, 1987.

    Article  Google Scholar 

  4. Cao, X.R., A Sample Performance Function of Closed Jackson Queueing Networks, Operations Research 36, 128–136, 1988.

    Article  Google Scholar 

  5. Cao, X.R., AND Ho, Y.C., Estimating Sojourn Time Sensitivity in Queueing Networks Using Perturbation Analysis, JOTA 53, 353–375, 1987.

    Article  Google Scholar 

  6. Chen, H., AND Yao, D.D., Derivatives of the Expected Delay in the GI/G/1 Queue, J. Appl. Prob. 28, 899–907, 1990.

    Article  Google Scholar 

  7. Cheng, D.W. Tandem Queues with General Blocking, Ph.D. thesis, Columbia University 1990.

    Google Scholar 

  8. Cheng, D.W., AND Yao, D.D., Tandem Queues with General Blocking: A Unified Model and Stochastic Comparisons, 1991. To appear in DEDSTA.

    Google Scholar 

  9. Chung, K.L., A Course in Probability Theory, Academic Press, Orlando, Florida, 1974.

    Google Scholar 

  10. Clarke, F.H., Optimization and Nonsmooth Analysis, Wiley-Interscience, New York, 1983.

    Google Scholar 

  11. Fu, M.C., AND Hu, J.Q., Consistency of Infinitesimal Perturbation Analysis for the GI/G/m queue, European J. Oper. Res. 54, 121–139, 1991.

    Article  Google Scholar 

  12. Glasserman, P., Performance Continuity and Differentiability in Monte Carlo Optimization, Proc. Winter Sim. Conf., The Society for Computer Simulation, San Diego, California, 518–524, 1988.

    Google Scholar 

  13. Glasserman, P., Structural Conditions for Perturbation Analysis Derivative Estimation: Finite-Time Performance Indices, Oper. Res. 39, 724–738, 1991.

    Article  Google Scholar 

  14. Glasserman, P., Gradient Estimation via Perturbation Analysis, Kluwer Academic Publishers, Norwell, Massachusetts, 1991.

    Google Scholar 

  15. Glasserman, P., Regenerative Derivatives of Regenerative Sequences, Adv. Appl. Prob. 25, 116–139, 1993.

    Article  Google Scholar 

  16. Glasserman, P., Hu, J.Q., AND Strickland, S.G., Strongly Consistent Steady-State Derivative Estimates, Prob. Eng. Inf. Sci. 5, 391–413, 1991.

    Article  Google Scholar 

  17. Glynn, P. W., Construction of Process Differentiable Representations for Parametric Families of Distributions, Technical Report, University of Wisconsin Mathematics Research Center, Madison, Wisconsin, 1986.

    Google Scholar 

  18. Glynn, P.W., Likelihood Ratio Gradient Estimation: An Overview, Proc. Winter Sim. Conf., The Society for Computer Simulation, San Diego, California, 366–374, 1987.

    Google Scholar 

  19. Heidelberger, P., Cao, X.R., Zazanis, M., AND Suri, R., Convergence Properties of Infinitesimal Perturbation Analysis Estimates, Mgmt. Sci. 34, 1281–1302, 1988.

    Article  Google Scholar 

  20. Ho, Y.C., Eyler, M.A., AND Chien, T.T., A Gradient Technique for General Buffer Storage Design in a Serial Production Line, Internati. J. Prod. Res. 17, 557–580, 1979.

    Article  Google Scholar 

  21. Ho, Y.C., AND Cao, X.R., Optimization and Perturbation Analysis of Queueing Networks, JOTA 40, 559–582, 1983.

    Article  Google Scholar 

  22. Ho, Y.C., AND Cao, X.R., Perturbation Analysis of Discrete Event Dynamic Systems, Kluwer Academic Publishers, Norwell, Massachusetts, 1991.

    Book  Google Scholar 

  23. Hu, J.Q., Stong Consistency of Infinitesimal Perturbation Analysis for the G/G/1 Queue, Technical Report, Harvard University Division of Applied Sciences, Cambridge, Massachusetts, 1990.

    Google Scholar 

  24. Hu, J.Q., Convexity of Sample Path Performances and Strong Consistency of Infinitesimal Perturbation Analysis, IEEE Trans. Aut. Ctrl. 37, 258–262, 1992.

    Article  Google Scholar 

  25. Reiman, M.I. AND Weiss, A., Sensitivity analysis for simulations via likelihood ratios, Oper. Res. 37, 830–844, 1989.

    Article  Google Scholar 

  26. Ross, S.M., Stochastic Processes, John Wiley and Sons, New York, 1983.

    Google Scholar 

  27. Rockafellar, R.T., The Theory of Subgradients and its Applications to Problems of Optimization. Convex and Nonconvex Functions. Research and Education in Mathematics, No. 1, Heldermann Verlag, Berlin, 1981.

    Google Scholar 

  28. Royden, H.L., Real Analysis, Second Edition, Macmillan, New York, 1968.

    Google Scholar 

  29. Rubinstein, R., Sensitivity Analysis and Performance Extrapolation for Computer Simulation Models, Oper. Res. 37, 72–81, 1989.

    Article  Google Scholar 

  30. Shanthikumar, J.G., AND Yao, D.D. Second-Order Stochastic Properties of Queueing Systems, Proc. IEEE 77, 162–170, 1989.

    Article  Google Scholar 

  31. Suri, R., Implementation of Sensitivity Calculations on a Monte-Carlo Experiment, JOTA 40, 625–630, 1983.

    Article  Google Scholar 

  32. Suri, R., Infinitesimal Perturbation Analysis for General Discrete Event Systems, J. ACM 34, 686–717, 1987.

    Article  Google Scholar 

  33. Suri, R., AND Zazanis, M., Perturbation Analysis Gives Strongly Consistent Estimates for the M/G/1 Queue, Mgmt. Sci. 34, 39–64, 1988.

    Article  Google Scholar 

  34. Wardi, Y., AND Hu, J.Q., Strong Consistency of Infinitesimal Perturbation Analysis for Tandem Queueing Networks, DEDSTA 1, 37–60, 1991.

    Google Scholar 

  35. Zazanis, M., Weak Convergence of Sample Path Derivatives for the Waiting Time in a Single-Server Queue, Proc. 25th Allerton Conf., 297–304, 1987.

    Google Scholar 

  36. Zazanis, M., AND Suri, R., Perturbation Analysis of the GI/G/1 Queue, Working Paper, Northwestern University, 1986.

    Google Scholar 

Download references

Authors

Editor information

Editors and Affiliations

Rights and permissions

Reprints and permissions

Copyright information

© 1994 Springer-Verlag New York Inc

About this chapter

Cite this chapter

Glasserman, P. (1994). Perturbation Analysis of Production Networks. In: Yao, D.D. (eds) Stochastic Modeling and Analysis of Manufacturing Systems. Springer Series in Operations Research. Springer, New York, NY. https://doi.org/10.1007/978-1-4612-2670-3_6

Download citation

  • DOI: https://doi.org/10.1007/978-1-4612-2670-3_6

  • Publisher Name: Springer, New York, NY

  • Print ISBN: 978-1-4612-7628-9

  • Online ISBN: 978-1-4612-2670-3

  • eBook Packages: Springer Book Archive

Publish with us

Policies and ethics