Generating correlated matrix exponential random variables

Abstract

In this paper, we focus on inter-arrival time autocorrelation and its impact on model performance. We present a technique to generate matrix exponential random variables that match first-order statistics (moments) and second-order statistics (autocorrelation) from an empirical distribution. We briefly explain the matrix exponential distribution and show that we can represent any empirical distribution arbitrarily closely as matrix exponential. We then show how we can incorporate an autocorrelation structure into our matrix exponential random variables using the autoregressive to anything technique. We present examples showing how we match first and second-order statistics from empirical distributions and finally we show that our autocorrelation matrix exponential random variables produce more accurate performance metrics from simulation models than traditional techniques.