Bayesian Analysis of the Stationary MAP2

Abstract

In this article we describe a method for carrying out Bayesian estimation for the two-state stationary Markov arrival process (${\mathit{MAP}}_2$), which has been proposed as a versatile model in a number of contexts. The approach is illustrated on both simulated and real data sets, where the performance of the ${\mathit{MAP}}_2$ is compared against that of the well-known ${\mathit{MMPP}}_2$. As an extension of the method, we estimate the queue length and virtual waiting time distributions of a stationary ${\mathit{MAP}}_2/G/1$ queueing system, a matrix generalization of the $M/G/1$ queue that allows for dependent inter-arrival times. Our procedure is illustrated with applications in Internet traffic analysis.