Sequential Analysis of Quantiles and Probability Distributions by Replicated Simulations

Abstract

Discrete event simulation is well known to be a powerful approach to investigate behaviour of complex dynamic stochastic systems, especially when the system is analytically not tractable. The estimation of mean values has traditionally been the main goal of simulation output analysis, even though it provides limited information about the analysed system's performance. Because of its complexity, quantile analysis is not as frequently applied, despite its ability to provide much deeper insights into the system of interest. A set of quantiles can be used to approximate a cumulative distribution function, providing fuller information about a given performance characteristic of the simulated system. This thesis employs the distributed computing power of multiple computers by proposing new methods for sequential and automated analysis of quantile-based performance measures of such dynamic systems. These new methods estimate steady state quantiles based on replicating simulations on clusters of workstations as simulation engines. A general contribution to the problem of the length of the initial transient is made by considering steady state in terms of the underlying probability distribution. Our research focuses on sequential and automated methods to guarantee a satisfactory level of confidence of the final results. The correctness of the proposed methods has been exhaustively studied by means of sequential coverage analysis. Quantile estimates are used to investigate underlying probability distributions. We demonstrate that synchronous replications greatly assist this kind of analysis.