Abstract
Interactive Markov Chains (IMCs) are compositional behaviour models extending both Continuous Time Markov Chain (CTMC) and Labelled Transition System (LTS). They are used as semantic models in different engineering contexts ranging from ultramodern satellite designs to industrial system-on-chip manufacturing. Different approximation algorithms have been proposed for model checking of IMCs, with time bounded reachability probabilities playing a pivotal role. This paper addresses the accuracy and efficiency of approximating time bounded reachability probabilities in IMCs, improving over the state-of-the-art in both efficiency of computation and tightness of approximation. Moreover, a stable numerical approach, which provides an effective framework for implementation of the theory, is proposed. Experimental evidence demonstrates the efficiency of the new approach.
Highlights
Why interactive Markov chains (IMCs)? Over the last decade, a formal approach to quantitative performance and dependability evaluation of concurrent systems has gained maturity
We compute minimum and maximum time bounded reachability with respect to the set of goal states G using both the first- and the second-order approximations on different intervals of time. The former has been implemented in the IMCA tool [18], and our implementation is derived from that
This paper has presented an improvement of time bounded reachability computations in IMC, based on previous work [29], which has established a digitisation approach for IMC, together with a stable error bound
Summary
Why IMCs? Over the last decade, a formal approach to quantitative performance and dependability evaluation of concurrent systems has gained maturity. Opposed to classical concurrency theory models, CTMCs neither support compositional modelling [23] nor do they allow nondeterminism in the model. IMCs conservatively extend classical concurrency theory with exponentially distributed delays, and this induces several further benefits [8]. It enables compositional modelling with intermittent weak bisimulation minimisation [21] and allows to augment existing untimed process algebra specifications with random timing [7]. The IMC formalism is not restricted to exponential delays but allows to encode arbitrary phase-type distributions such as hyper- and hypoexponentials [28]. Since IMCs smoothly extend classical LTSs, the model has received attention in academic as well as in industrial settings [6, 13, 12, 16]
Sign-in/Register to view highlights & summary Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
