Regenerative Simulation for Estimating Extreme Values

Let X ( t ) denote the regenerative process being simulated and assume that it converges in distribution to a steady state random variable. This paper considers estimating the extreme values of the regenerative process. Suppose we are interested in the largest value attained in the interval [0, t ], call it X *( t ). The paper develops a method for estimating the distribution of X *( t ). When the regenerative process is either the GI / G /1 queue or a birth-death process, theoretical results are available for the distribution of X *( t ). Our development simulated the waiting time, queue length, and virtual waiting time for an M / M /1 queue, employed the method for estimating the distribution of X *( t ), and compared the simulation results with the theoretical results.