Queueing Systems

, Volume 10, Issue 3, pp 249–269 | Cite as

On the pathwise computation of derivatives with respect to the rate of a point process: The phantom RPA method

  • Pierre Brémaud
  • Felisa J. Vázquez-Abad
Articles

Abstract

The Rare Perturbation Analysis (RPA) method is presented using two approaches: a direct one and an indirect one via a pathwise interpretation of the Likelihood Ratio Method (LRM). These two approaches give a new point of view for the Smoothed Perturbation Analysis (SPA) discussed in Gong [4] and extend the validity of the formulas therein, in particular to the estimation of derivatives of quantities that can be computed over a busy cycle. A heuristic comparison with LRM is given and simulation results are presented to compare the performance of LRM, RPA, and a finite difference RPA in a simple system.

Keywords

Sensitivity analysis queues point processes perturbation analysis likelihood ratios routing 

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. [1]
    F. Baccelli and P. Brémaud, Virtual customers in sensitivity and light traffic analysis via Campbell's formula for point processes, submitted to AAP (1990).Google Scholar
  2. [2]
    P. Brémaud, Maximal coupling and rare perturbation analysis, in preparation (1990).Google Scholar
  3. [3]
    P. Glynn, Likelihood ratio gradient estimation for stochastic systems, Commun. ACM 33 (1990) 76–84.Google Scholar
  4. [4]
    W.B. Gong, Smoothed perurbation analysis algorithm for aG/G/1 routing problem, in:Proc. 1988 Winter Simulation Conf., eds. M. Abrams, P. Haigh and J. Comfort (1988) pp. 525–531.Google Scholar
  5. [5]
    W.B. Gong and Y.C. Ho, Smoothed perturbation analysis of discrete event dynamical systems, IEEE Trans. Auto. Control AC-10 (1987) 858–866.Google Scholar
  6. [6]
    Y.C. Ho and X.R. Cao, Perturbation analysis and optimization of queueing networks, J. Optim. Theory Appl. 40 (1983) 559–582.Google Scholar
  7. [7]
    P. L'Ecuyer, A unified version of the IPA, SF, and LR gradient estimation techniques, Manag. Sci. 36 (1990) 1364–1383.Google Scholar
  8. [8]
    M.I. Reiman and B. Simon, Open queueing systems in light traffic, Math. Oper. Res. 14 (1989) 26–59.Google Scholar
  9. [9]
    M.I. Reiman and A. Weiss, Sensitivity analysis for simulations via likelihood ratios, Oper. Res. 37 (1989) 830–844.Google Scholar
  10. [10]
    B. Simon, A new estimator of sensitivity measures for simulation based on light traffic theory, ORSA J. Comput. 1 (1989) 172–180.Google Scholar
  11. [11]
    R. Suri, Perturbation analysis: the state of the art and research issues explained via theG/G/1 queue, Proc. IEEE 77 (1989) 114–137.Google Scholar
  12. [12]
    R. Suri and X.R. Cao, The phantom customer and the marked customer methods for optimization of closed queueing networks with blocking and general service times,AGM-Sigmetrics Conf., Minneapolis (1983).Google Scholar
  13. [13]
    F. Vázquez-Abad, Stochastic recursive algorithms for optimal routing in queueing networks, Ph.D. Thesis, Applied Mathematics, Brown University (1989).Google Scholar
  14. [14]
    F. Vázquez-Abad and H. Kushner, A surrogate estimation approach for adaptive routing in communication networks, Brown University Report LCDS/CCS No. 90-2 (May 24, 1990).Google Scholar

Copyright information

© J.C. Baltzer A.G. Scientific Publishing Company 1992

Authors and Affiliations

  • Pierre Brémaud
    • 1
  • Felisa J. Vázquez-Abad
    • 2
  1. 1.Laboratoire des Signaux et SystèmesCNRS-ESEGif-sur-YvetteFrance
  2. 2.INRS-TélécommunicationsUniversité du QuébecIle-des-SoeursCanada

Personalised recommendations