Virtual network embedding under uncertainty: Exact and heuristic approaches

Given a physical substrate network and a collection of requests of virtual networks, the Virtual Network Embedding problem (VNE) calls for the embedding onto the physical substrate of a selection of virtual networks in such a way that the profit is maximized. The embedding corresponds to a virtual-to-physical mapping of nodes and links, subject to capacity constraints. Since, in practical scenarios, node and link demands are typically much smaller than the peak values specified in the virtual network requests, in this work we propose and investigate a robust optimization approach. This allows us to find solutions with a much larger profit which, at the same time, are guaranteed to be feasible with a high probability. To this end, we propose a robust Mixed-Integer Linear Programming (MILP) formulation for VNE, based on the well-known model of Γ-robustness. To solve larger scale instances, for which the exact approach is computationally too demanding, we also propose a MILP-based two-phase heuristic which relies on Γ-robustness.