Transient Solution

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

Chapter 8 in Constructive Computation in Stochastic Models with Applications, 2010, pp 389-431 from Springer

Abstract: Abstract In this chapter, we apply the RG-factorizations to provide a unified algorithmic framework for dealing with transient solution in stochastic models. The transient solution includes the transient probability, the first passage time, the sojourn time and time-inhomogeneous Markov chains. Based on the first passage time, we extends the PH distribution and the MAP to the GPH distribution and the GMAP from finite phases to infinite phases, respectively, and also study the time-inhomogeneous PH (PH(t)) distribution and the time-inhomogeneous MAP (MAP(t)). Finally, we analyze some queueing examples such as GMAP/GPH/1 and MAP(t)/PH(t)/1.

Keywords: stochastic models; RG-factorization; time-inhomogeneous Markov chain; transient solution; the first passage time; the sojourn time GPH distribution GMAP; time-inhomogeneous PH distribution; timeinhomogeneous MAP (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_8

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DOI: 10.1007/978-3-642-11492-2_8

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