201. Compositional Modeling and Minimization of Time-Inhomogeneous Markov Chains
- Author
-
Joost-Pieter Katoen, Alexandru Mereacre, and Tingting Han
- Subjects
Discrete mathematics ,Markov kernel ,Markov chain ,Markov process ,EWI-12140 ,Markov model ,Time reversibility ,symbols.namesake ,METIS-250918 ,Piecewise ,symbols ,Applied mathematics ,Markov property ,Examples of Markov chains ,Mathematics ,IR-62226 - Abstract
This paper presents a compositional framework for the modeling of interactive continuous-time Markov chains with time-dependent rates, a subclass of communicating piecewise deterministic Markov processes. A poly-time algorithm is presented for computing the coarsest quotient under strong bisimulation for rate functions that are either piecewise uniform or (piecewise) polynomial. Strong as well as weak bisimulation are shown to be congruence relations for the compositional framework, thus allowing component-wise minimization. In addition, a new characterization of transient probabilities in time-inhomogeneous Markov chains with piecewise uniform rates is provided.
- Published
- 2008