 Minimal LST representations of MAP(n)s: Moment fittings and queueing approximationsSunkyo Kim Naval Research Logistics (NRL), 2016, vol. 63, issue 7, 549-561 Abstract: A Markovian arrival process of order n, MAP(n), is typically described by two n × n transition rate matrices in terms of 2 n 2 − n rate parameters. While it is straightforward and intuitive, the Markovian representation is redundant since the minimal number of parameters is n2 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. © 2016 Wiley Periodicals, Inc. Naval Research Logistics 63: 549–561, 2016 Date: 2016 Downloads: (external link) Related works: Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text Persistent link: https://EconPapers.repec.org/RePEc:wly:navres:v:63:y:2016:i:7:p:549-561 Access Statistics for this article More articles in Naval Research Logistics (NRL) from John Wiley & Sons |
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