CSL model checking algorithms for QBDs

Remke, Anne; Haverkort, Boudewijn R.; Cloth, Lucia

doi:10.1016/j.tcs.2007.05.007

Cited by 23 publications

(33 citation statements)

References 36 publications

(46 reference statements)

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“…Recently, direct techniques based on uniformization or variants thereof [15], have been proposed for reachability properties for general infinite-state CTMCs [32] and for highly structured infinite-state CTMCs, such as normal QBDs [24] and Jackson queueing networks [23]. However, they all lead to an exponential blow-up when applied to tree-structured QBDs.…”

Section: Introduction Probabilistic Model Checking Is a Verificatimentioning

confidence: 99%

Time-Bounded Reachability in Tree-Structured QBDs by Abstraction

Klink

Remke

Haverkort

et al. 2009

2009 Sixth International Conference on the Quantitative Evaluation of Systems

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Abstract-This paper studies quantitative model checking of infinite tree-like (continuous-time) Markov chains. These treestructured 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 processeswhich 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 gridlike schemes, in contrast to chain-and tree-like ones, yield extremely precise approximations for rather coarse abstractions.

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Section: Introduction Probabilistic Model Checking Is a Verificatimentioning

confidence: 99%

Time-Bounded Reachability in Tree-Structured QBDs by Abstraction

Klink

Remke

Haverkort

et al. 2009

2009 Sixth International Conference on the Quantitative Evaluation of Systems

Self Cite

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“…Symmetry reduction [20], bisimulation minimization [16], and advances in quotienting algorithms for simulation pre-orders [28] show encouraging experimental results. Tailored abstraction techniques for regular infinite-state CTMCs have been reported [22], as well as bounding techniques that approximate CTMCs by ones having a special structure allowing closed-form solutions [21]. Predicate abstraction techniques have been extended to (among others) CTMCs [14].…”

Section: Introductionmentioning

confidence: 99%

Abstraction for Stochastic Systems by Erlang’s Method of Stages

Katoen

Klink

Leucker³

et al. 2008

CONCUR 2008 - Concurrency Theory

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Abstract. This paper proposes a novel abstraction technique based on Erlang's method of stages for continuous-time Markov chains (CTMCs). As abstract models Erlang-k interval processes are proposed where state residence times are governed by Poisson processes and transition probabilities are specified by intervals. We provide a three-valued semantics of CSL (Continuous Stochastic Logic) for Erlang-k interval processes, and show that both affirmative and negative verification results are preserved by our abstraction. The feasibility of our technique is demonstrated by a quantitative analysis of an enzyme-catalyzed substrate conversion, a well-known case study from biochemistry.

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“…* This work is supported by the NWO-DFG bilateral project VOSS and by the DFG as part of the Transregional Collaborative Research Center SFB/TR 14 AVACS We consider the model checking problem for CSL over infinite CTMCs. For highly structured infinite CTMCs, this has been already studied in [22,21]. We consider arbitrary infinite CTMCs, including rates unbounded CTMCs.…”

Section: Introductionmentioning

confidence: 99%