Deploying Virtual Network Functions With Non-Uniform Models in Tree-Structured Networks

Network Function Virtualization (NFV) has promoted 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 on servers is challenging because the traffic rate of flows must be fully processed by their requested VNFs when they reach destinations, and the deployed positions of VNFs are restricted by the server capacity. In addition, each network function offers non-uniform VNF models (types) with different configurations of processing volumes and costs. This paper focuses on minimizing the total cost of deploying VNFs for providing a specific network function to all flows in tree-structured networks. First, we prove the NP-hardness of non-uniform VNF deployment in a tree topology and propose a dynamic programming based solution with a pseudo-polynomial time complexity. Then we narrow it down to three simplified cases by focusing on either uniform VNFs or the linear line topology. Specifically, three algorithms are introduced: an improved dynamic programming based algorithm for deploying uniform VNFs in a tree topology, a performance-guaranteed algorithm for deploying non-uniform VNFs in a linear line topology, and an optimal greedy algorithm for deploying uniform VNFs in a linear line topology. Additionally, we generalize our approach to a case of deploying a service chain, which consists of multiple network functions applied to flows in a specific order. We propose two solutions: one is optimal but time-consuming while another is heuristic but efficient. Extensive simulations are conducted to evaluate our algorithms.