Completing virtual network embedding all in one mathematical programming

This paper explores the most urgent task to initialize a virtual network in the network virtualization environment, which always called the virtual network embedding. Different to the previous works to take the embedding process as two steps: node mapping stage and then edge mapping stage, this paper contribute to solve these processes all in one discrete nonlinear combined optimization. Based on modeling the virtual network (VN) request and substrate network (SN), this paper proposed mathematical description to the embedding process which building the relationship between node mapping and edge mapping stages. After that, a virtual network embedding cost is introduced as an objective function, and then the virtual network embedding can be concluding to minimize the objective cost as a mathematical programming problem. The obtained programming results in LINGO9.0 show that the proposed method can finish a virtual network embedding by mathematical programming in one step.