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
