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Klink, D. and Remke, A.K.I. and Haverkort, B.R.H.M. and Katoen, J.P.
(2009)
Time-Bounded Reachability in Tree-Structured QBDs by Abstraction.
In: Sixth International Conference on the Quantitative Evaluation of Systems, (QEST '09), 13-16 Sept 2009, Budapest, Hungary.
pp. 133-142.
IEEE Computer Society.
ISBN 978-0-7695-3808-2
Full text available as:
Official URL: http://dx.doi.org/10.1109/QEST.2009.9  AbstractThis paper studies quantitative model checking of infinite tree-like (continuous-time) Markov chains. These tree-structured quasi-birth death processes are equivalent to probabilistic pushdown automata and recursive Markov chains and are widely used in the field of performance evaluation. We determine time-bounded reachability probabilities in these processes ---which with direct methods, i.e., uniformization, results in an exponential blow-up--- by applying abstraction. We contrast abstraction based on Markov decision processes (MDPs) and interval-based abstraction; study various schemes to partition the state space, and empirically show their influence on the accuracy of the obtained reachability probabilities. Results show that grid-like schemes, in contrast to chain- and tree-like ones, yield extremely precise approximations for rather coarse abstractions.
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