Time-bounded reachability in tree-structured QBDs by abstraction


Klink, Daniel and Remke, Anne and Haverkort, Boudewijn R. and Katoen, Joost-Pieter (2011) Time-bounded reachability in tree-structured QBDs by abstraction. Performance Evaluation, 68 (2). pp. 105-125. ISSN 0166-5316

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Abstract:This 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, result 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.
Item Type:Article
Copyright:© 2011 Elsevier
Electrical Engineering, Mathematics and Computer Science (EEMCS)
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Link to this item:http://purl.utwente.nl/publications/72833
Official URL:https://doi.org/10.1016/j.peva.2010.04.002
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