Download Analytical and Stochastic Modelling Techniques and by Marco Gribaudo, Daniele Manini, Anne Remke PDF

By Marco Gribaudo, Daniele Manini, Anne Remke

This e-book constitutes the refereed complaints of the twenty second overseas convention on Analytical and Stochastic Modelling concepts and purposes, ASMTA 2015, held in Albena, Bulgaria, in could 2015. The 15 complete papers offered during this publication have been conscientiously reviewed and chosen from quite a few submissions. The papers talk about the newest advancements in analytical, numerical and simulation algorithms for stochastic platforms, together with Markov techniques, queueing networks, stochastic Petri nets, technique algebras, online game concept, etc.

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Extra resources for Analytical and Stochastic Modelling Techniques and Applications: 22nd International Conference, ASMTA 2015, Albena, Bulgaria, May 26-29, 2015. Proceedings

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The same argument as in the proof of Theorem 2 shows that, model checking of PCTL formulas on CMCs can be done by first closing the system of in-equations, this is done by replacing the strict inequalities (<, >) with non-strict inequalities (≤, ≥), and then model checking on the closed model. Acknowledgement. The authors thank Hongfei Fu for discussions on the topic of this paper. 42 S. -P. Katoen References 1. : Principles of Model Checking (Representation and Mind Series). The MIT Press (2008) 2.

Interval Markov chains are generalizations of discrete time Markov chains where the transition probabilities are intervals, instead of constant values. We focus on the case where the intervals are open. At first sight, open intervals present technical challenges, as optimal (min, max) value for reachability may not exist. We show that, as far as model checking (and reachability) is concerned, open intervals does not cause any problem, and with minor modification existing algorithms can be used for model checking interval Markov chains against PCTL formulas.

The ith state of the path π is denoted by πi = si . Let Ωs be the set of paths starting from state s. The cylinder (open) set Cyl(ρ) is the set of all paths with ρ as prefix. Let B be the smallest Borel σ-algebra 32 S. -P. Katoen defined on the cylinder sets. Let ρ be a finite sequence of states s0 s1 . . sn such that δ(si , si+1 ) > 0 for all 0 ≤ i < n. The unique measure μ is thus induced from δ as, μ(Cyl(ρ)) = δ(s0 , s1 )·δ(s1 , s2 ) . . ·δ(sn−1 , sn ). Definition 3. An Interval Markov chain (IMC) is a tuple M (S, L, δ), where S is a (finite) set of states and L is a labeling function L : S → 2AP , where AP is the set of atomic propositions.

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