This paper proposes a virtual network function placement and routing model for multicast service chaining based on merging multiple service paths (MSC-M). The multicast service chaining (MSC) is used for providing a network-virtualization based multicast service. The MSC sets up a multicast path, which connects a source node and multiple destination nodes. Virtual network functions (VNFs) are placed on the path so that users on the destination nodes receive their desired services. The conventional MSC model configures multicast paths for services, each of which has the same source data and the same set of VNFs in a predefined order. In the MSC-M model, if paths of different services carry the same data on the same link, these paths are allowed to be merged into one path at that link, which improves the utilization of network resources. The MSC-M model determines the placement of VNFs and the route of paths so that the total cost associated with VNF placement and link usage is minimized. The MSC-M model is formulated as an integer linear programming (ILP) Problem. We prove that the decision version of VNF placement and routing problem based on the MSC-M model is NP-complete. A heuristic algorithm is introduced for the case that the ILP problem is intractable. Numerical results show that the MSC-M model reduces the total cost required to accommodate service chaining requests compared to the conventional MSC model. We discuss directions for extending the MSC-M model to an optical domain.

本文提出了一种基于多服务路径（MSC-M）融合的虚拟网络功能布局和路由模型，用于组播服务链。多播服务链（MSC）用于提供基于网络虚拟化的多播服务。MSC设置了一条多播路径，该路径连接了一个源节点和多个目标节点。虚拟网络功能（VNF）放置在路径上，以便目标节点上的用户获得所需的服务。常规的MSC模型为服务配置多播路径，每个服务具有相同的源数据和按预定义顺序的相同VNF集。在MSC-M模型中，如果不同服务的路径在同一链路上承载相同的数据，则允许将这些路径合并为该链路上的一条路径，从而提高了网络资源的利用率。MSC-M模型确定VNF的放置和路径的路由，从而使与VNF放置和链路使用相关的总成本最小化。MSC-M模型被表述为整数线性规划（ILP）问题。我们证明基于MSC-M模型的VNF放置和路由问题的决策版本是NP完全的。针对ILP问题难以解决的情况，引入了启发式算法。数值结果表明，与传统的MSC模型相比，MSC-M模型减少了满足服务链请求所需的总成本。我们讨论了将MSC-M模型扩展到光域的方向。MSC-M模型被表述为整数线性规划（ILP）问题。我们证明基于MSC-M模型的VNF放置和路由问题的决策版本是NP完全的。针对ILP问题难以解决的情况，引入了启发式算法。数值结果表明，与传统的MSC模型相比，MSC-M模型减少了满足服务链请求所需的总成本。我们讨论了将MSC-M模型扩展到光域的方向。MSC-M模型被表述为整数线性规划（ILP）问题。我们证明基于MSC-M模型的VNF放置和路由问题的决策版本是NP完全的。针对ILP问题难以解决的情况，引入了启发式算法。数值结果表明，与传统的MSC模型相比，MSC-M模型减少了满足服务链请求所需的总成本。我们讨论了将MSC-M模型扩展到光域的方向。数值结果表明，与传统的MSC模型相比，MSC-M模型减少了满足服务链请求所需的总成本。我们讨论了将MSC-M模型扩展到光域的方向。数值结果表明，与传统的MSC模型相比，MSC-M模型减少了满足服务链请求所需的总成本。我们讨论了将MSC-M模型扩展到光域的方向。