Bayesian Analysis

Bayesian Analysis of the Stationary MAP2

P. Ramírez-Cobo, R. E. Lillo, and M. P. Wiper

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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.

Article information

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

First available in Project Euclid: 24 October 2016

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Digital Object Identifier

Primary: 62F15: Bayesian inference 62M05: Markov processes: estimation 60K20: Applications of Markov renewal processes (reliability, queueing networks, etc.) [See also 90Bxx]

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

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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.

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