Markovian trees: properties and algorithms

Nigel Bean (), Nectarios Kontoleon and Peter Taylor

Annals of Operations Research, 2008, vol. 160, issue 1, 50 pages

Abstract: In this paper we introduce a structure called the Markovian tree (MT). We define the MT and explore its alternative representation as a continuous-time Markovian Multitype Branching Process. We then develop two algorithms, the Depth and Order algorithms to determine the probability of eventual extinction of the MT process. We show that both of these algorithms have very natural physically intuitive interpretations and are analogues of the Neuts and U algorithms in Matrix-analytic Methods. Furthermore, we show that a special case of the Depth algorithm sheds new light on the interpretation of the sample paths of the Neuts algorithm. Copyright Springer Science+Business Media, LLC 2008

Keywords: Branching processes; Matrix analytic methods (search for similar items in EconPapers)
Date: 2008
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Citations: View citations in EconPapers (3)

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DOI: 10.1007/s10479-007-0295-9

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