We propose to apply the perfect simulation to perform statistical model checking of large Markov chains. Perfect simulation is an extension of Monte Carlo Markov Chain (MCMC) methods, it allows us to obtain exact steadystate samples of the underlying chain thus it avoids the burn-in time problem to detect the steady-state. The statistical model checking by MCMC methods has been already proposed in the last years. However the steady-state formulas can not be checked by this approach because of the problem of detecting steady-state. Thus we propose to do statistical model checking by combining perfect simulation and statistical hypothesis testing in order to verify steady state formulas. We apply our proposed method to verify the saturation and availability properties at long run for a multistage interconnection queueing network illustrating its efficiency when considering very large models.
Model checking of probabilistic models can be done either by numerical analysis or by simulation and statistical methods. In this paper, we compare the efficiency and the scalability of different model checking approaches when they are applied to the verification of steady-state properties of large models. We provide an experimental comparison study between the statistical model checking using perfect sampling implemented in Ψ 2 [15] and proposed in [11, 10] and the numerical method implemented in PRISM [6], for the verification of CSL [2] steady-state properties. We show that the proposed statistical approach lets us to consider very large models.
In this paper, we show the difference between management and leadership through a case study, by presenting a management situation in a company and by studying the facts in this situation, the events in this situation, the analysis of these facts and events, and the learned lessons from this case study. We analyze in this case study the managerial situation especially for a manager X in our case study, who had some flaws in his style of management leaking of leadership. We learn some general and specific lessons in relation to our studied managerial situation. Our analysis proposes multiple improvements of this managerial situation especially for the manager X by combining his management skills with his leadership skills. We show through this case study the main differences between the management and the leadership. Also, we illustrate in this paper the interest to combine leadership skills with management skills for the manager X in our studied managerial situation and to adapt the management styles for the manager X according to the managerial situation.
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