Virtual Network Function Deployment in Tree-Structured Networks

Network Function Virtualization (NFV) evolves the implementation of network functions from expensive hardwares to software middleboxes. These software middleboxes, also called Virtual Network Functions (VNFs), are executed on switch-connected servers. Efficiently deploying such VNFs is challenging, because VNFs must fully process all flows with their traffic rates before they reach their destinations while VNF locations are restricted by the constraint of vertex capacity. In addition, each network function offers heterogeneous VNF types with different configurations of processing volumes and costs. This paper focuses on minimizing the total cost of deploying VNF instances for providing a specific network function to all flows in tree-structured networks. First we prove the NP-hardness of heterogeneous VNF deployment in a tree topology and propose a dynamic programming based solution with a pseudo-polynomial time complexity. Then we narrow down to three simplified cases by focusing on homogeneous VNFs or the linear line topology. Specifically, three algorithms are introduced: an improved dynamic programming based algorithm for deploying homogeneous VNFs in a tree topology, a performance-guaranteed algorithm for deploying heterogeneous VNFs in a linear line topology, and an optimal greedy algorithm for deploying homogeneous VNFs in a linear line topology. Extensive simulations are conducted to evaluate the performance of our algorithms.