Minimal LST Representations of MAP(n)s: Moment Fittings and Queueing Approximations

作者：Kim Sunkyo^*

来源：Naval Research Logistics, 2016, 63(7): 549-561.

DOI：10.1002/nav.21719

• Markovian arrival processes
• Markov modulated Poisson process
• characteristic polynomial equations
• LaplaceStieltjes transform
• minimal representation
• moment fittings
• queueing networks

A Markovian arrival process of order n, MAP(n), is typically described by two nxn transition rate matrices in terms of 2n(2) - n rate parameters. While it is straightforward and intuitive, the Markovian representation is redundant since the minimal number of parameters is n(2) for non-redundant MAP(n). It is well known that the redundancy complicates exact moment fittings. In this article, we present a minimal and unique Laplace-Stieltjes transform (LST) representations for MAP(n) s. Even though the LST coefficients vector itself is not a minimal representation, we show that the joint LST of stationary intervals can be represented with the minimum number of parameters. We also propose another minimal representation for MAP(3) s based on coefficients of the characteristic polynomial equations of the two transition rate matrices. An exact moment fitting procedure is presented for MAP(3) s based on two proposed minimal representations. We also discuss how MAP(3)/G/1 departure process can be approximated as a MAP(3). A simple tandem queueing network example is presented to show that the MAP(3) performs better than the MAP(2) in queueing approximations especially under moderate traffic intensities.

• 出版日期2016-10