Bayesian Analysis of a Queueing System with a Long-Tailed Arrival Process Articles uri icon

publication date

  • April 2008

start page

  • 697

end page

  • 712

issue

  • 4

volume

  • 37

international standard serial number (ISSN)

  • 0361-0918

electronic international standard serial number (EISSN)

  • 1532-4141

abstract

  • Internet traffic data is characterized by some unusual statistical properties, in particular, the presence of heavy-tailed variables. A typical model for heavy-tailed distributions is the Pareto distribution although this is not adequate in many cases. In this article, we consider a mixture of two-parameter Pareto distributions as a model for heavy-tailed data and use a Bayesian approach based on the birth-death Markov chain Monte Carlo algorithm to fit this model. We estimate some measures of interest related to the queueing system k-Par/M/1 where k-Par denotes a mixture of k Pareto distributions. Heavy-tailed variables are difficult to model in such queueing systems because of the lack of a simple expression for the Laplace Transform (LT). We use a procedure based on recent LT approximating results for the Pareto/M/1 system. We illustrate our approach with both simulated and real data.