×

Bounds and approximations for the transient behavior of continuous-time Markov chains. (English) Zbl 1134.60366

Summary: Discretization is a simple, yet powerful tool in obtaining time-dependent probability distribution of continuous-time Markov chains. One of the most commonly used approaches is uniformization. A recent addition to such approaches is an external uniformization technique. In this paper, we briefly review these different approaches, propose some new approaches, and discuss their performances based on theoretical bounds and empirical computational results. A simple method to get lower and upper bounds for first passage time distribution is also proposed.

MSC:

60J27 Continuous-time Markov processes on discrete state spaces
PDF BibTeX XML Cite
Full Text: DOI

References:

[1] Keilson, Markov chain models–rarity and exponentiality (1979) · Zbl 0411.60068
[2] DOI: 10.1016/0377-2217(77)90049-2 · Zbl 0371.60110
[3] Van, Probability in the Engineering and Informational Sciences 2 pp 471– (1988)
[4] Cinlar, Introduction to stochastic processes (1975) · Zbl 0341.60019
[5] Ross, Stochastic processes (1983)
[6] Stoyan, Comparison methods for queues and other stochastic models (1983) · Zbl 0536.60085
[7] DOI: 10.1016/0304-4149(87)90002-0 · Zbl 0628.60095
[8] Ross, Probability in the Engineering and Informational Sciences 1 pp 251– (1987)
[9] DOI: 10.1109/TR.1986.4335507
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.