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2016 Clearing analysis on phases: Exact limiting probabilities for skip-free, unidirectional, quasi-birth-death processes
Sherwin Doroudi, Brian Fralix, Mor Harchol-Balter
Stoch. Syst. 6(2): 420-458 (2016). DOI: 10.1214/15-SSY183

Abstract

A variety of problems in computing, service, and manufacturing systems can be modeled via infinite repeating Markov chains with an infinite number of levels and a finite number of phases. Many such chains are quasi-birth-death processes with transitions that are skip-free in level, in that one can only transition between consecutive levels, and unidirectional in phase, in that one can only transition from lower-numbered phases to higher-numbered phases. We present a procedure, which we call Clearing Analysis on Phases (CAP), for determining the limiting probabilities of such Markov chains exactly. The CAP method yields the limiting probability of each state in the repeating portion of the chain as a linear combination of scalar bases raised to a power corresponding to the level of the state. The weights in these linear combinations can be determined by solving a finite system of linear equations.

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Sherwin Doroudi. Brian Fralix. Mor Harchol-Balter. "Clearing analysis on phases: Exact limiting probabilities for skip-free, unidirectional, quasi-birth-death processes." Stoch. Syst. 6 (2) 420 - 458, 2016. https://doi.org/10.1214/15-SSY183

Information

Received: 1 April 2015; Published: 2016
First available in Project Euclid: 22 March 2017

zbMATH: 1359.60096
MathSciNet: MR3633540
Digital Object Identifier: 10.1214/15-SSY183

Subjects:
Primary: 60J22, 60J27

JOURNAL ARTICLE
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Vol.6 • No. 2 • 2016
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