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IFAC 2014, 19th World Congress of the International Federation of Automatic Control, Cape Town, AFRIQUE DU SUD, 24-/08/2014 - 29/08/2014; We look at understanding the main mechanisms behind the renewal of complex systems. These systems, such as trains or airplanes, have a long operation or service duration. They should be renewed and their renewal projects are often partial for economic reasons. A renewal act is performed through integration of engineering changes. Any functional or structural change could have cascading effects on consecutive subsystems. The system architecture can be used as the main driver of renewal acts definition and planning. We position the renewal problem and define some key concepts usable for complex systems renewal. They allow to define the renewal possibilities as scenarios that should be qualified for ultimate selection. This paper explores these mechanisms and suggests a first set of propagation mechanisms. Throughout the paper, we illustrate our purposes by using examples from a train renewal project.; Nous cherchons à comprendre les principaux mécanismes de renouvellement des systèmes complexes. Ces systèmes, tels que les trains ou les avions, ont une longue durée de fonctionnement ou de service. Ils devraient être renouvelés et leurs projets de renouvellement sont souvent partiels pour des raisons économiques. Un acte de renouvellement est effectué par l'intégration de modifications techniques. Toute modification fonctionnelle ou structurelle pourrait avoir des effets en cascade sur des sous-systèmes consécutifs. L'architecture du système peut être utilisée comme principal moteur de la définition et de la planification des actes de renouvellement. Nous positionnons le problème de renouvellement et définissons des concepts clés utilisables pour le renouvellement de systèmes complexes. Ils permettent de définir les possibilités de renouvellement comme des scénarios qui devraient être qualifiés pour la sélection finale. Cet article explore ces mécanismes et suggère un premier ensemble de mécanismes de propagation. Tout au long du document, nous illustrons nos objectifs en utilisant des exemples tirés d'un projet de renouvellement de train.

A weighted embedding for the generalized pontogram fKn(t): 06t61g corresponding pointwise to a renewal process fN(s): 06s

Two limit theorems on asymptotic behaviors of some processes related to some queueing systems are investigated. In the first result (Theorem 1), sticky diffusions appear as limit processes for queues with vacations. In the second result (Theorem 2), limiting behavior of occupation times and counting processes related to open queueing networks is discussed. The core of the arguments for obtaining our results is to discuss the convergence of stochastic integrals with respect to renewal processes.

We prove that the directed random walk satisfies the strong law of large numbers if and only if the environment has a finite mean.

Let { X n , n ⩾ 1} be a sequence of identically distributed real random variables with EX 1 = μ > 0. Define S n =Σ n i=1 X i and N α (t) = inf{ n ⩾1; S n > n α t}, where t >0, α∈ [0, 1) and the infimum o f the empty set is defined to be +∞. Let P α,t be the distribution of N α (t)/t 1/(1-α) , t > 0 . In this paper, we establish the large deviation principle for { P α, t ; t > 0 } when { X n ; n⩾ 1 } is a sequence of i.i.d. random variables or, more generally, an exchangeable sequence.

Starting from recent strong and weak approximations to the partial sums of i.i.d. random vectors (cf. U. Einmahl, Ann. Probab., 15 1419–1440), some corresponding invariance principles are developed for associated renewal processes and random sums. Optimality of the approximation is proved in the case when only two moments exist. Among other applications, a Darling-Erdos type extreme value theorem for renewal processes will be derived.

Let X1, X2,… be independent random variables and define Sn≔∑i=1n Xi, n=1,2,…. Let partition of R into intervals [ka, (k+1)a), k∈Z, of any fixed length a > 0 be given. We ask for the distribution of the remainder Sn−knawhere[kna (kn+1)a) is the random interval con Sn. Necessary and sufficient conditions are given for this distribution to converge to the uniform distribution in [0, a] as n→∞.