Delay times in an M/M/1 queue: Estimating the sampling distributions for the steady-state mean and MSER truncation point

MSER is a method for determining the length of the warm-up period needed to mitigate systematic error in the estimate of the steady-state mean of an output resulting from the arbitrary initialization of a simulation. While a considerable corpus of empirical and theoretical research supports the effectiveness of MSER on a range of test problems, it has been suggested recently that MSER may fail to delete a significant amount of highly biased data for some simulation models (Law, 2015). One example given in support of this suggestion addresses the delay time in an M/M/1 queue for different initial conditions. We expand this example, applying replication/deletion to develop point estimates, confidence bounds, and approximations to the sampling distributions for both MSER-truncated mean and the MSER truncation point. We illustrate that the suggestion is not supported by this example.