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Parallélisation d'une Combinaison des Méthodes de Monte-Carlo et Quasi-Monte-Carlo et Application aux Réseaux de Files d'Attente

Bruno Tuffin, Louis-Marie Le Ny (2010)

RAIRO - Operations Research

We propose a parallel algorithm which uses both Monte-Carlo and quasi-Monte-Carlo methods. A detailed analysis of this algorithm, followed by examples, shows that the estimator's efficiency is a linear function of the processor number. As a concrete application example, we evaluate performance measures of a multi-class queueing network in steady state.

Path functionals over Wasserstein spaces

Alessio Brancolini, Giuseppe Buttazzo, Filippo Santambrogio (2006)

Journal of the European Mathematical Society

Given a metric space X we consider a general class of functionals which measure the cost of a path in X joining two given points x 0 and x 1 , providing abstract existence results for optimal paths. The results are then applied to the case when X is aWasserstein space of probabilities on a given set Ω and the cost of a path depends on the value of classical functionals over measures. Conditions for linking arbitrary extremal measures μ 0 and μ 1 by means of finite cost paths are given.

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