Compositional Modeling and Minimization of Time-Inhomogeneous Markov Chains

Authors:
Tingting Han;Joost-Pieter Katoen;Alexandru Mereacre
Affiliations:
Software Modeling and Verification Group, RWTH Aachen University, Germany and Formal Methods and Tools Group, University of Twente, The Netherlands;Software Modeling and Verification Group, RWTH Aachen University, Germany and Formal Methods and Tools Group, University of Twente, The Netherlands;Software Modeling and Verification Group, RWTH Aachen University, Germany and Dept. of Information and Communication Technology, University of Trento, Italy
Venue:
HSCC '08 Proceedings of the 11th international workshop on Hybrid Systems: Computation and Control
Year:
2008

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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.