In real life, individuals play an important role in the social networking system. When epidemic breaks out individual’s recovery rate depends heavily on network which he or she lives. For this reason, paper a nonlinear coupling dynamic model hyper was built. The upper layer is under hypernetwork vision, and lower physical contact layer. Thus, evolutionary mechanism between transmission establis...

Parametric Markov chains have been introduced as a model for families of stochastic systems that rely on the same graph structure, but differ in the concrete transition probabilities. The latter are specified by polynomial constraints for the parameters. Among the tasks typically addressed in the analysis of parametric Markov chains are (1) the computation of closed-form solutions for reachabil...

Classified Markov chains have been extensively applied to model and analyze various stochastic systems in many engineering and scientific domains. Traditionally, the analysis of these systems has been conducted using computer simulations and, more recently, also probabilistic model-checking. However, these methods either cannot guarantee accurate analysis or are not scalable due to the unaccept...

A parallel composition is defined for Markov reward chains with stochastic discontinuity, and with fast and silent transitions. In this setting, compositionality with respect to the relevant aggregation preorders is established. For Markov reward chains with fast transitions the preorders are τ -lumping and τ -reduction. Discontinuous Markov reward chains are ‘limits’ of Markov reward chains wi...

Deadlocks constitute a major issue in the design and operation of discrete event systems. In automated manufacturing systems, deadlocks assume even greater importance in view of the automated operation. In this paper, we show that Markov chains with absorbing states provide a natural model of manufacturing systems with deadlocks. With illustrative examples, we show that performance indices such...

The computation of counterexamples for probabilistic model checking has been an area of active research over the past years. In spite of the achieved theoretical results in this field, there is no freely available tool that allows for the computation and representation of probabilistic counterexamples. We present an open source tool called DiPro that can be used with the PRISM and MRMC probabil...

I. The construction problem for continuous time Markov chains Reference: Part II of David Freedman, Markov Chains, Holden-Day, 1971. Suppose that S is a countable set, Ω = the set of all right continuous step functions ω : [0,∞) → S with finitely many jumps in any finite time interval, Xt(ω) = ω(t), and {P , x ∈ S} are probability measures on Ω that satisfy (i) P (X0 = x) = 1 for all x ∈ S, and...

The most commonly used models for analysing local dependencies in DNA sequences are (high-order) Markov chains. Incorporating knowledge relative to the possible grouping of the nucleotides enables to define dedicated sub-classes of Markov chains. The problem of formulating lumpability hypotheses for a Markov chain is therefore addressed. In the classical approach to lumpability, this problem ca...