Application of smoothed perturbation analysis to a discrete-time stationary queue

We investigate the sensitivity analysis for a discrete-time queueing system using perturbation analysis. In discrete-time queues, not only the sample performance function but also the sampled event lifetimes are essentially discontinuous in some system parameter, and therefore the well-known infinitesimal perturbation analysis (IPA) technique fails to apply to even a simple single-server queue. We here apply an idea similar to the smoothed perturbation analysis for probabilistic routing problem (or equivalently, negative customer rare perturbation analysis), and under the stationarity and ergodicity assumptions, we obtain the strongly consistent estimator. Some simulation experiments demonstrate the validity of our estimator.