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  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
- Sensitivity analysis
- point processes
- perturbation analysis
- likelihood ratios