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Dimensionnement robuste des réseaux de télécommunications face à l'incertitude de la demande

Abstract : One of the main problems in telecommunications is the robust network design under demand uncertainty. Having the network's architecture and a given budget for the capacity allocation problem, the aims is to identify a feasible capacity that minimizes the worst case of non-satisfying demand. Firstly, the demand's uncertainty is formulated as a convex hull defined by a finite number of scenarios. We prove that the problem can be rewritten as the minimization of a convex function over a polyhedral. So, an optimal solution is calculated using three cutting-plane methods: Kelley, Elzinga-Moore and Bundle. Then the uncertainty is formulated as a polyhedral described by a unite number of linear inequalities, which leads to a problem considerably more difficult. In consequence, we search only for upper and lower bounds. Some innovating ideas are presented and Falk & Soland Branch & Bound algorithm is used in order to calculate the maximum of an additive convex function; moreover, we define a variant of this algorithm, adapted to our particular problem. After having defined the network's design, the next step is to calculate the optimal routing in the network. The congestion is minimized using as objective function the Kleinrock delay function. The resulting problem is convex but non-linear and the dual function is the sum of a polyhedral function and of a smooth function. To solve this problem, a hybrid algorithm is implemented, based on Lagrangian relaxation.
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Submitted on : Wednesday, February 25, 2009 - 11:06:57 AM
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Georgios Petrou. Dimensionnement robuste des réseaux de télécommunications face à l'incertitude de la demande. Mathématiques [math]. Université Panthéon-Sorbonne - Paris I, 2008. Français. ⟨tel-00364079⟩

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