New PDF release: Analytical and Stochastic Modelling Techniques and

By Marco Gribaudo, Daniele Manini, Anne Remke

ISBN-10: 3319185780

ISBN-13: 9783319185781

ISBN-10: 3319185799

ISBN-13: 9783319185798

This publication constitutes the refereed lawsuits of the twenty second foreign convention on Analytical and Stochastic Modelling thoughts and purposes, ASMTA 2015, held in Albena, Bulgaria, in could 2015. The 15 complete papers awarded during this ebook have been conscientiously reviewed and chosen from quite a few submissions. The papers speak about the newest advancements in analytical, numerical and simulation algorithms for stochastic platforms, together with Markov strategies, queueing networks, stochastic Petri nets, method algebras, video game conception, etc.

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Example text

From the original ones; ii) the queues of the two aggregated stations are empty with high probability. The second experiment considers as initial condition n9 (0) = 40. In this situation, both the aggregated stations receive customers directly. Figure 4 illustrates the results obtained by using the second initial condition. In this case the population within station 9 stays almost unchanged and reaches a stable condition soon. On the other hand, even if the number of customers at station 5 is small the station requires 100 time units to stabilize completely.

This can be done in polynomial time by solving linear constraints. Finally, a state s |= f if f ∈ L(s) and the model checking problem can be solved in polynomial time. Model checking in UMC semantics uses the existential theory of reals [10]. An IMC M, s |=u f in UMC semantics iff for all DTMC M ∈ [M]u , M, s |= f , or equivalently, M, s |=u f iff there exists a M ∈ [M]u such that M, s |= ∼f . Basically, we use parameters to encode the transition probabilities which are constrained by the intervals and construct a formula Γ in existential theory of reals such that Γ is satisfiable iff there exists a M ∈ [M]u such that M, s |= ∼f [4].

It follows event of reaching the goal states T , and E = R ∩ B and E = R from the construction that E ⊆ E . Define Ai {w | ∃u ∈ E : w0 . . wi = ∗ u0 . . ui and η(wi , wi+1 ) = 0, ηˆ(wi , i, wi+1 ) > 0}. Let A = i Ai . It is easy to see that, E ∩ A¯ = E. We will first show that the event A has a very small probability measure in S : ηˆ (A) = μ ˆ(A) = P rM η ˆ P rM (Ai ) i=0 ∗ If w ∈ Ai then δ(wi , wi+1 )↑ > 0 and η(s, t) = 0. Thus, ηˆ ηˆ (Ai ) ≤ 2−i κρ or P rM (A) ≤ κρ P rM Model Checking of Open Interval Markov Chains 37 Thus, μ ˆ(A) ≤ κρ (4) We will now show that the probability of E can be made infinitesimally close to ¯(E)| ≤ ε.

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Analytical and Stochastic Modelling Techniques and Applications: 22nd International Conference, ASMTA 2015, Albena, Bulgaria, May 26-29, 2015. Proceedings by Marco Gribaudo, Daniele Manini, Anne Remke


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