Bayesian Analysis of the Stationary MAP(2) Articles uri icon

publication date

  • December 2017

start page

  • 1163

end page

  • 1194

issue

  • 4

volume

  • 12

international standard serial number (ISSN)

  • 1931-6690

abstract

  • In this article we describe a method for carrying out Bayesian estimation for the two-state stationary Markov arrival process (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 MAP(2) 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 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.

keywords

  • phase-type distributions; markov modulated poisson process (MMPP); Identifiability; canonical representation; gibbs sampler; steady-state distributions