On approximating higher order Markovian arrival processes (MAPs) with MAPs of order two

On approximating higher order Markovian arrival processes (MAPs) with MAPs of order two

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Article ID: iaor20012923
Country: Netherlands
Volume: 34
Issue: 1/4
Start Page Number: 269
End Page Number: 288
Publication Date: Jan 2000
Journal: Queueing Systems
Authors: ,
Abstract:

We show that the autocorrelation sequence of interarrival times for a Markovian arrival process (MAP) of order two is geometric. We determine the set of feasible values for the autocorrelation decay parameter and the first two or three moments of the interarrival time distribution. A method is derived for matching these parameters to a MAP of order two and some numerical examples are included to illustrate approximating higher dimensional MAPs by two dimensional ones. The numerical examples have helped us pose important questions regarding the significance of correlation in a MAP of order two when it is used as input to a queueing model.

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