Convergence properties of ordinal comparison in the simulation of discrete event dynamic systems

Recent research has demonstrated that ordinal comparison converges fast despite possible presence of large estimation noise in the design of discrete event dynamic systems. In this paper, we address a fundamental problem of characterizing the convergence of ordinal comparison. To achieve the goal, an indicator process is formulated and its properties are examined. For several performance measures frequently used in simulation, rate of convergence for the indicator process is proven to be exponential for regenerative simulations. Therefore, the fast convergence of ordinal comparison is supported and explained in a rigorous framework. Many performance measures of averaging type have asymptotic normal distributions. The results of this paper show that ordinal comparison converges monotonically in the case of averaging normal random variables. Such monotonicity is useful in simulation planning.