Parametric expression for MSER with geometrically decaying bias

The MSER algorithm for determining the warm-up period in steady-state simulations was introduced in 1990. Over the past two decades, empirical evaluations by different research teams have demonstrated the effectiveness of the procedure. These extensive empirical results illustrate the relative advantage of MSER over other approaches under alternative bias scenarios. In this paper, we develop parametric expressions to explore how MSER should behave in the case of simulation output with geometrically decaying bias and white noise. We derive a closed-form expression for the expected optimal truncation point for this scenario. This permits computation of the threshold bias-to-noise ratio for bias detection in terms of the rate of decay of the initial bias and the strength of autocorrelation in the output sequence.