On approximating higher order MAPs with MAPs of order two

Authors:
Jeffrey E. Diamond;Attahiru Sule Alfa
Affiliations:
TR Labs, 10-75 Scurfield, Winnipeg, MB, Canada R3Y 1P6 E-mail: diamond@win.trlabs.ca;Department of Industrial and Manufacturing Systems Engineering, University of Windsor, Windsor, Ontario, Canada N9B 3P4 E-mail: alfa@uwindsor.ca
Venue:
Queueing Systems: Theory and Applications
Year:
1999

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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.