### Abstract

Semi-Markov decision processes (SMDPs) are continuous-time Markov decision processes where the residence-time on states is governed by generic distributions on the positive real line. In this paper we consider the problem of comparing two SMDPs with respect to their time-dependent behaviour. We propose a hemimetric between processes, which we call simulation distance, measuring the least acceleration factor by which a process needs to speed up its actions in order to behave at least as fast as another process. We show that this distance can be computed in time O(n2(f(l)+k)+mn7), where n is the number of states, m the number of actions, k the number of atomic propositions, and f(l) the complexity of comparing the residence-time between states. The theoretical relevance and applicability of this distance is further argued by showing that (i) it is suitable for compositional reasoning with respect to CSP-like parallel composition and (ii) has a logical characterisation in terms of a simple Markovian logic.

Original language | English |
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Title of host publication | Quantitative Evaluation of Systems - 15th International Conference, QEST 2018, Proceedings |

Editors | Annabelle McIver, Andras Horvath |

Place of Publication | Cham |

Publisher | Springer-Verlag |

Pages | 339-355 |

Number of pages | 17 |

ISBN (Print) | 9783319991535 |

DOIs | |

Publication status | Published - 4 Sep 2018 |

Event | 15th International Conference on Quantitative Evaluation of Systems, QEST 2018 - Beijing, China Duration: 4 Sep 2018 → 7 Sep 2018 |

### Publication series

Name | Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) |
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Volume | 11024 LNCS |

ISSN (Print) | 0302-9743 |

ISSN (Electronic) | 1611-3349 |

### Conference

Conference | 15th International Conference on Quantitative Evaluation of Systems, QEST 2018 |
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Country | China |

City | Beijing |

Period | 4/09/18 → 7/09/18 |

### Keywords

- semi-Markov decision processes
- Markovian logic

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## Cite this

*Quantitative Evaluation of Systems - 15th International Conference, QEST 2018, Proceedings*(pp. 339-355). (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 11024 LNCS). Cham: Springer-Verlag. https://doi.org/10.1007/978-3-319-99154-2_21