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Tree structured QBD Markov chains and tree-like QBD processes. Stochastic Models

By B. Van Houdt and C. Blondia

Abstract

Abstract. In this paper we show that an arbitrary tree structured QBD Markov chain can be embedded in a tree-like QBD process with a special structure. Moreover, we present an algebraic proof that applying the natural fixed point iteration (FPI) to the nonlinear matrix equation V = B + ∑ d s=1 Us(I − V) −1 Ds that solves the tree-like QBD process, is equivalent to the more complicated iterative algorithm presented by Yeung and Alfa [1].

Year: 2003
OAI identifier: oai:CiteSeerX.psu:10.1.1.413.2924
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