Open Access
December 2017 Bayesian Analysis of the Stationary MAP2
P. Ramírez-Cobo, R. E. Lillo, M. P. Wiper
Bayesian Anal. 12(4): 1163-1194 (December 2017). DOI: 10.1214/16-BA1026


In this article we describe a method for carrying out Bayesian estimation for the two-state stationary Markov arrival process (MAP2), 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 MAP2 is compared against that of the well-known MMPP2. As an extension of the method, we estimate the queue length and virtual waiting time distributions of a stationary MAP2/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.


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P. Ramírez-Cobo. R. E. Lillo. M. P. Wiper. "Bayesian Analysis of the Stationary MAP2." Bayesian Anal. 12 (4) 1163 - 1194, December 2017.


Published: December 2017
First available in Project Euclid: 24 October 2016

zbMATH: 1384.62100
MathSciNet: MR3724982
Digital Object Identifier: 10.1214/16-BA1026

Primary: 60K20 , 62F15 , 62M05

Keywords: canonical representation , Gibbs sampler , Identifiability , Markov modulated Poisson process (MMPP) , phase-type distributions , steady-state distributions

Vol.12 • No. 4 • December 2017
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