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

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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.

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References

  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).

  2. P. Brémaud, Maximal coupling and rare perturbation analysis, in preparation (1990).

  3. P. Glynn, Likelihood ratio gradient estimation for stochastic systems, Commun. ACM 33 (1990) 76–84.

    Google Scholar 

  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.

  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. 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. P. L'Ecuyer, A unified version of the IPA, SF, and LR gradient estimation techniques, Manag. Sci. 36 (1990) 1364–1383.

    Google Scholar 

  8. M.I. Reiman and B. Simon, Open queueing systems in light traffic, Math. Oper. Res. 14 (1989) 26–59.

    Google Scholar 

  9. M.I. Reiman and A. Weiss, Sensitivity analysis for simulations via likelihood ratios, Oper. Res. 37 (1989) 830–844.

    Google Scholar 

  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. 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. 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).

  13. F. Vázquez-Abad, Stochastic recursive algorithms for optimal routing in queueing networks, Ph.D. Thesis, Applied Mathematics, Brown University (1989).

  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).

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Authors and Affiliations

  1. Laboratoire des Signaux et Systèmes, CNRS-ESE, Plateau de Moulon, 91190, Gif-sur-Yvette, France

    Pierre Brémaud

  2. INRS-Télécommunications, Université du Québec, 3 Place du Commerce, H3E 1H6, Ile-des-Soeurs, Québec, Canada

    Felisa J. Vázquez-Abad

Authors
  1. Pierre Brémaud
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  2. Felisa J. Vázquez-Abad
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Brémaud, P., Vázquez-Abad, F.J. On the pathwise computation of derivatives with respect to the rate of a point process: The phantom RPA method. Queueing Syst 10, 249–269 (1992). https://doi.org/10.1007/BF01159209

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  • DOI: https://doi.org/10.1007/BF01159209

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