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Constructive Computation in Stochastic Models with Applications pp 389–431Cite as

Transient Solution

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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.

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Authors and Affiliations

  1. Department of Industrial Engineering, Tsinghua University, Beijing, 100084, P.R. China

    Quan-Lin Li

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© 2010 Tsinghua University Press, Beijing and Springer-Verlag Berlin Heidelberg

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Li, QL. (2010). Transient Solution. In: Constructive Computation in Stochastic Models with Applications. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-11492-2_8

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