## Bayesian Analysis

### 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.

#### Article information

Source
Bayesian Anal. Volume 12, Number 4 (2017), 1163-1194.

Dates
First available in Project Euclid: 24 October 2016

https://projecteuclid.org/euclid.ba/1477321094

Digital Object Identifier
doi:10.1214/16-BA1026

#### Citation

Ramírez-Cobo, P.; Lillo, R. E.; Wiper, M. P. Bayesian Analysis of the Stationary MAP 2. Bayesian Anal. 12 (2017), no. 4, 1163--1194. doi:10.1214/16-BA1026. https://projecteuclid.org/euclid.ba/1477321094

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