Markov Chains of GI/G/1 Type

Quan-Lin Li ()
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Quan-Lin Li: Tsinghua University, Department of Industrial Engineering

Chapter 3 in Constructive Computation in Stochastic Models with Applications, 2010, pp 131-175 from Springer

Abstract: Abstract In this chapter, we simplify the R-, U- and G-measures and the RG-factorizations for Markov chains of GI/G/1 type. Also, we derive a new RG-factorization for the repeated blocks and the four basic inequalities for the boundary blocks, which are useful in spectral analysis of Markov chains of GI/G/1 type. We analyze the dual Markov chain of any irreducible blockstructured Markov chain, and specifically discuss the dual chain of a Markov chain of GI/G/1 type. Furthermore, we simplify the A- and B-measures for Markov chains of GI/G/1 type, and also express the A- and B-measures by means of the R- and G-measures, respectively. Based on the A- and B-measures, we provide spectral analysis for the R- and G-measures, and provide conditions for the state classification of Markov chains of GI/G1 type.

Keywords: stochastic model; block-structured Markov chain; Markov chain of GI/G/1 type; RG-factorization; dual Markov chain; spectral analysis; state classification (search for similar items in EconPapers)
Date: 2010
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Persistent link: https://EconPapers.repec.org/RePEc:spr:sprchp:978-3-642-11492-2_3

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DOI: 10.1007/978-3-642-11492-2_3

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