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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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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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Keywords

  • Sensitivity analysis
  • queues
  • point processes
  • perturbation analysis
  • likelihood ratios
  • routing