Middleboxes have gained popularity due to the significant value-added services these network elements provide to traffic flows, in terms of enhanced performance and security. Policy-aware traffic flows usually need to traverse multiple middleboxes in a predefined order to satisfy their associated policy, also known as Service Function Chaining. Typically, Middleboxes run on specialized hardware, which make them highly inflexible to handle the unpredictable and fluctuating-nature of traffic, and contribute to significant capital and operational expenditures (Cap-ex and Op-ex) to provision, accommodate, and maintain them. Network Function Virtualization is a promising technology with the potential to tackle the aforementioned limitations of hardware middleboxes. Yet, NFV is still in its infancy, and there exists several technical challenges that need to be addressed, among which, the Virtual Network Function assignment problem tops the list. The VNF assignment problem stems from the newly gained flexibility in instantiating VNFs (on-demand) anywhere in the network. Subsequently, network providers must decide on the optimal placement of VNF instances which maximizes the number of admitted policy-aware traffic flows across their network. Existing work consists of Integer Linear Program (ILP) models, which are fairly unscalable, or heuristic-based approaches with no guarantee on the quality of the obtained solutions. This work proposes a novel Logic-Based Benders Decomposition (LBBD) based approach to solve the VNF assignment problem. It consists of decomposing the problem into two subproblems: a master and a subproblem; and at every iteration constructive Benders cuts are introduced to the master to tighten its search space. We compared the LBBD approach against the ILP and a heuristic method, and we show that our approach achieves the optimal solution (as opposed to heuristic-based methods) 700 times faster than the ILP.

中文翻译：

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VNF 分配问题的一种基于切割和求解的方法

由于这些网络元素在增强的性能和安全性方面为流量提供了重要的增值服务，因此中间盒越来越受欢迎。策略感知流量通常需要以预定义的顺序遍历多个中间盒以满足其关联的策略，也称为服务功能链。通常，中间箱在专用硬件上运行，这使得它们在处理不可预测和波动的流量方面非常不灵活，并有助于大量资本和运营支出（Cap-ex 和 Op-ex）来提供、容纳和维护它们。网络功能虚拟化是一项很有前途的技术，有可能解决上述硬件中间盒的局限性。然而，NFV仍处于起步阶段，并且存在几个需要解决的技术挑战，其中，虚拟网络功能分配问题位居榜首。VNF 分配问题源于新获得的在网络中任何地方实例化 VNF（按需）的灵活性。随后，网络提供商必须决定 VNF 实例的最佳位置，以最大限度地增加通过其网络的策略感知流量的数量。现有的工作包括整数线性规划 (ILP) 模型，这些模型是相当不可扩展的，或者基于启发式的方法，无法保证获得的解决方案的质量。这项工作提出了一种新颖的基于逻辑的弯曲分解 (LBBD) 方法来解决 VNF 分配问题。它包括将问题分解为两个子问题：主问题和子问题；并且在每次迭代中，都会向主节点引入建设性的 Benders 切割以收紧其搜索空间。我们将 LBBD 方法与 ILP 和启发式方法进行了比较，结果表明，我们的方法获得最佳解决方案（与基于启发式的方法相反）比 ILP 快 700 倍。