Estimating derivatives of conditional expected system times in the GI/GI/1 queue

The authors use smoothed perturbation analysis (SPA) to develop an estimator of the derivative of the conditional expected system time in the GI/GI/1 queue with respect to a parameter of the service time distribution. The authors then prove that their estimator is strongly consistent. For a more general class of estimation problems, the authors also extend the SPA methodology for estimating derivatives of “tail probabilities”, to encompass service distributions with finite support. The authors include a simulation result to demonstrate the performance of their estimator