With the advent of Network Function Virtualization (NFV), network services that traditionally run on proprietary dedicated hardware can now be realized using Virtual Network Functions (VNFs) that are hosted on general-purpose commodity hardware. This new network paradigm offers a great flexibility to Internet service providers (ISPs) for efficiently operating their networks (collecting network statistics, enforcing management policies, etc.). However, introducing NFV requires an investment to deploy VNFs at certain network nodes (called VNF-nodes), which has to account for practical constraints such as the deployment budget and the VNF-node capacity. To that end, it is important to design a joint VNF-nodes placement and capacity allocation algorithm that can maximize the total amount of network flows that are fully processed by the VNF-nodes while respecting such practical constraints. In contrast to most prior work that often neglects either the budget constraint or the capacity constraint, we explicitly consider both of them. We prove that accounting for these constraints introduces several new challenges. Specifically, we prove that the studied problem is not only NP-hard but also non-submodular. To address these challenges, we introduce a novel relaxation method such that the objective function of the relaxed placement subproblem becomes submodular. Leveraging this useful submodular property, we propose two algorithms that achieve an approximation ratio of $\frac{1}{2}(1-1/e)$ and $\frac{1}{3}(1-1/e)$ for the original non-relaxed problem, respectively. Finally, we corroborate the effectiveness of the proposed algorithms through extensive evaluations using trace-driven simulations.
翻译:随着网络功能虚拟化(NFV)的到来,传统上以专有专用硬件运行的网络服务现在可以使用通用商品硬件托管的虚拟网络功能(VNF)实现。这种新的网络模式为互联网服务供应商高效运行其网络提供了极大的灵活性(收集网络统计数据,执行管理政策等)。然而,引入NFV需要投资在某些网络节点(称为VNF-nodes)部署VNF,这需要说明部署预算和不断更新的VNF-node能力等实际制约因素。为此,必须设计一个联合VNF-nodes逻辑化配置和能力配置算法,使由VNF-nodes充分处理的网络流动总量最大化,同时尊重这些实际限制。与大多数以前常常忽视预算制约或能力制约的工作相比,我们明确考虑这两个因素。我们证明,这些制约的核算带来了一些新的挑战。具体地说,我们证明所研究的问题不仅仅是我们NP-harter-now-node 能力。为此,我们不仅需要设计一个联合的VNF-node-nf-nodeal lial lial livaldal et-al etal lavelysetrational 。为了应对这些挑战,我们提出了一种新版本1-lax-lax-lax-lax-lax-lax-lax-lax