Network Function Placement (NFP) involves placing virtual network functions (VNFs) on the nodes of a network such that the data that flow through the network are processed by a chain of service functions along their path from source to destination. There are three aspects to this problem: (i) routing the flows efficiently through the network, (ii) placement of the VNFs on the nodes and (iii) steering each flow through a chain of VNFs, known as the service function chain (SFC). Routing must attempt to find “optimal” paths through the network (for e.g., shortest paths), possibly subject to constraints such as path latency and link bandwidth. The VNFs consume resources on the nodes where they are placed and are constrained by the capacity of the nodes. Steering must ensure that each flow has along its path a sequence of VNFs, likely in a certain order. One way to specify this problem is to define a multi-commodity flow problem with additional constraints based on the steering and placement requirements. Simultaneously solving all three aspects of this problem, trying to optimize various parameters and within the various constraints, is a hard problem, with even a simplified version shown to be NP-complete in this paper. Attempting to optimally solve this problem in real time while flows are getting provisioned and de-provisioned in parallel is an intractable problem, especially in large networks. Hence various types of heuristics have been used to solve this problem. In this paper we introduce a distributed, online solution that employs a message-passing protocol for nodes to negotiate the placement of the VNFs, with the minimization of the number of VNF instances being the primary objective. We compare the performance of the solution to that of the theoretically optimal solution and other proposed heuristics on both the Fat-tree topology and the BCube topology. The results show that this solution performs better than other heuristics. The average ratio of the result of the proposed solution to that of the optimal solution, taken as the approximation ratio, is found to be 1.5 for the tested scenarios.

网络功能放置（NFP）涉及将虚拟网络功能（VNF）放置在网络的节点上，以便流经网络的数据由服务功能链沿其从源到目的地的路径进行处理。这个问题包括三个方面：（i）通过网络有效地路由流；（ii）在节点上放置VNF；以及（iii）引导每个流都经过称为服务功能链（SFC）的VNF链。路由必须尝试通过网络找到“最佳”路径（例如，最短路径），可能会受到诸如路径等待时间和链路带宽之类的约束。VNF消耗了放置它们的节点上的资源，并受节点容量的限制。转向必须确保每个流在其路径上都有可能以一定顺序排列的一系列VNF。指定此问题的一种方法是根据操纵和放置要求定义具有附加约束的多商品流问题。同时解决此问题的所有三个方面，试图优化各种参数并在各种约束内，这是一个难题，即使是简化版本也显示为NP完全的。在并行配置和取消配置流量时，尝试实时地以最佳方式解决此问题是一个棘手的问题，尤其是在大型网络中。因此，已经使用各种启发式方法来解决该问题。在本文中，我们介绍了一种分布式的在线解决方案，该解决方案对节点采用消息传递协议来协商VNF的放置，而将VNF实例的数量减到最少是主要目标。我们在胖树拓扑和BCube拓扑上将解决方案的性能与理论上最优的解决方案以及其他提议的启发式方法进行了比较。结果表明，该解决方案的性能优于其他启发式方法。拟议解决方案的结果与最优解决方案的结果的平均比率，作为近似比率，