### Abstract

In this paper algorithms for model checking CSL (continuous stochastic logic) against infinite-state continuous-time Markov chains of so-called quasi birth-death type are developed. In doing so we extend the applicability of CSL model checking beyond the recently proposed case for finite-state continuous-time Markov chains, to an important class of infinite-state Markov chains. We present syntax and semantics for CSL and develop efficient model checking algorithms for the steady-state operator and the time-bounded next and until operator. For the former, we rely on the so-called matrix-geometric solution of the steady-state probabilities of the infinite-state Markov chain. For the time-bounded until operator we develop a new algorithm for the transient analysis of infinite-state Markov chains, thereby exploiting the quasi birth-death structure. A case study shows the feasibility of our approach.

Original language | Undefined |
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Place of Publication | Enschede |

Publisher | Centre for Telematics and Information Technology (CTIT) |

Number of pages | 16 |

Publication status | Published - Dec 2004 |

### Publication series

Name | CTIT technical report series |
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Publisher | University of Twente, Centre for Telematics and Information Technology (CTIT) |

No. | TR-CTIT-04-49 |

### Keywords

- IR-56984
- EWI-5757

## Cite this

Remke, A. K. I., Haverkort, B. R. H. M., & Cloth, L. (2004).

*Model Checking Infinite-State Markov Chains*. (CTIT technical report series; No. TR-CTIT-04-49). Enschede: Centre for Telematics and Information Technology (CTIT).