Work

Time-Bounded Reachability in Tree-Structured QBDs by Abstraction

Year: 2009

Type: conference-paper

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, 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.

Source: International Conference on the Quantitative Evaluation of Systems (QEST)

DOI: 10.1109/qest.2009.9

Authors: Daniel Klink, Anne Remke, Boudewijn R. Haverkort, Joost-Pieter Katoen

Institutions: RWTH Aachen University, University of Twente

Language: English

Topic: Formal Methods in Verification

Subfield: Computational Theory and Mathematics

Field: Computer Science

Domain: Physical Sciences

Open Access status: green

Funders: Deutsche Forschungsgemeinschaft, Nederlandse Organisatie voor Wetenschappelijk Onderzoek

OpenAlex ID: W2121884216