Gradient estimation for quantiles of stationary waiting times

Quantiles of customer based performance characteristics have been adopted in many areas for measuring the quality of service. Recently, sensitivity analysis of quantiles has attracted quite some attention. Sensitivity analysis of quantiles is particularly challenging as quantiles cannot be expressed as the expected value of some sample performance function, and it is therefore not evident how standard gradient estimation methods can be applied. While sensitivity analysis of quantiles of waiting times for static or fixed time horizon problems is well understood, quantile estimation for stationary waiting times remains an open question. This paper will close this gap and will provide a framework for gradient estimation for quantiles of stationary waiting times.