In this paper, the extremal behavior of the waiting time and queue size in some queueing systems is considered, based on the regenerative property of these systems. The basic properties of the extremal index of a stationary sequence are discussed, which further relate to the maximum waiting time and queue size processes. Simulation results are presented with the aim to construct estimate and to evaluate the sensitivity of the extremal index to the level of the exceedance of the process of a threshold. We discuss the additional conditions placed on the normalizing sequences to compare extremal indexes of two different stationary sequences of random variables. This analysis is then applied to compare the waiting time extremal indexes in two M/G/1 systems with the ordered service times having Pareto distribution.