A note on bias and mean squared error in steady-state quantile estimation

We show that, under reasonable assumptions, the performance of the jackknife, classical and batch means estimators for the estimation of quantiles of the steady-state distribution exhibit similar properties as in the case of the estimation of a nonlinear function of a steady-state mean. We present some experimental results from the simulation of the waiting time in queue for an M/M/1 system to confirm our theoretical results.