Capacity allocation in multilevel virtual networks under uncertainty

This paper concerns the capacity allocation problem in multilevel virtual networks. The utility and cost functions are used to determine network performance in the economic terms. The considered problem is formulated as an optimization issue. This allocation problem (referred to as master problem) is decomposed into series of constrained concave maximization subproblems. The hierarchical procedure, which enables finding the optimal solution of master problem, is presented. Proposed method consists in solving all subproblems and exchanging information concerning obtained results. The analytical solution for a special case is given. Moreover, the uncertainties appearing during virtualization process are also taken into consideration. It is stressed that not whole of the virtual links' capacity is available for further virtualization. In the paper, it is assumed that such an uncertainty may be modeled with uncertain variables (a special case of fuzzy variables) formalism. Two approaches (for determinization knowledge about decision-making and for determinization knowledge about plant) are considered. Simple numerical experiment completes the paper.