A modern Network Function Virtualization (NFV) service is usually expressed in a service chain that contains a list of ordered network functions, each can run in one or multiple virtual machines. Although lots of efforts have been devoted to service chain deployment, the researchers normally consider a simple model of network functions where different service chains have their own network functions no matter whether some of the network function appliances are interdependent. In this paper, we study the service chain deployment by exploiting two types of correlations between network functions: the Coordination Effect due to information exchanges among multiple VMs running the same network function, and the Traffic-Change Effect where the volume of outgoing traffic is not necessarily equal to the volume of its incoming traffic at each network function because of packet manipulations such as compression and encryption. These two effects have not been studied simultaneously in the context of service chaining. With theobjective to maximize the profit measured by the admitted traffic minus the implementation cost, we first formulate a joint service-function deployment and traffic scheduling (SUPER) problem that is proved to be NP-hard. We then devise an approximation algorithm based on the Markov approximation technique and analyze its theoretical bound on the convergence time. Simulation results show that the proposed algorithm outperforms two existing benchmark algorithms significantly.

中文翻译：

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通过利用网络功能之间的相关性来近乎最优地部署服务链

现代网络功能虚拟化 (NFV) 服务通常表示为包含有序网络功能列表的服务链，每个功能都可以在一个或多个虚拟机中运行。尽管在服务链部署方面付出了很多努力，但研究人员通常会考虑一个简单的网络功能模型，即无论某些网络功能设备是否相互依赖，不同的服务链都有自己的网络功能。在本文中，我们通过利用网络功能之间的两种相关性来研究服务链部署：由于运行相同网络功能的多个虚拟机之间的信息交换而产生的协调效应，以及流量变化效应，其中由于压缩和加密等数据包操作，每个网络功能的传出流量不一定等于传入流量。尚未在服务链的背景下同时研究这两种影响。为了最大化由接纳流量减去实施成本衡量的利润，我们首先制定了一个联合服务功能部署和流量调度（SUPER）问题，该问题被证明是 NP-hard。然后，我们设计了一种基于马尔可夫逼近技术的逼近算法，并分析了其收敛时间的理论界限。仿真结果表明，该算法明显优于现有的两种基准算法。