With the penetration of Network Function Virtualization (NFV), network functions, traditionally deployed as proprietary physical equipment like firewalls, Network Address Translations (NATs), are gradually being implemented as software and deployed on standardized hardware. One of the crucial challenges in this paradigm is how to place the software implemented network functions to minimize the number of used physical servers. In this paper, we study the problem of how to optimally place Virtual Network Functions (VNFs) in networks where it is allowed to migrate already placed VNFs to decrease used servers. We first formulate the offline problem as an Integer Linear Programming (ILP) problem, and then propose a semi-online algorithm to solve the online variant of the problem. We name the proposed algorithm Semi-onlIne Vnf plAcement (SIVA). In particular, SIVA is based on a bin packing algorithm that solves online bin packing problem while taking care of migrations. According to our theoretical analysis, SIVA migrates at most \(\lambda\) VNFs each step, and it has Asymptotic Competitive Ratio (ACR) of 3/2 if \(k \rightarrow \infty\), where \(\lambda = k \cdot |N|\), k is a tunable parameter, and \(|N|\) is the the number of supported VNF types. We conduct extensive numerical simulations to evaluate the performances of SIVA. The experiment results validate the theoretical analysis and show that SIVA outperforms the state-of-the-art algorithms by achieving near-optimal performance with minor VNF migrations.

随着网络功能虚拟化（NFV）的渗透，传统上作为防火墙，网络地址转换（NAT）等专有物理设备部署的网络功能逐渐被实现为软件并部署在标准化硬件上。此范例中的关键挑战之一是如何放置软件实现的网络功能，以最大程度地减少所使用的物理服务器的数量。在本文中，我们研究了如何在允许迁移已放置的VNF减少使用的服务器的网络中最佳放置虚拟网络功能（VNF）的问题。我们首先将离线问题表述为整数线性规划（ILP）问题，然后提出一种半在线算法来解决该问题的在线变体。我们将提出的算法命名为Semi-onlIne Vnf PlaAcement（SIVA）。特别是，SIVA基于垃圾箱打包算法，该算法在解决迁移问题的同时解决了在线垃圾箱打包问题。根据我们的理论分析，SIVA最多会迁移\（\ lambda \） VNF每一步，如果\（krightrightarrow \ infty \），则VNF的渐近竞争比（ACR）为3/2 ，其中\（\ lambda = k \ cdot | N | \），k是可调参数，\（| N | \）是受支持的VNF类型的数量。我们进行了广泛的数值模拟，以评估SIVA的性能。实验结果验证了理论分析的有效性，并表明SIVA在较小的VNF迁移下达到了近乎最佳的性能，其性能优于最新的算法。