Speedy and Efficient Service Chaining and Function Placement Based on Lagrangian Heuristics for Capacitated Shortest Path Tour Problem

Network functions virtualization (NFV) can realize flexible and diverse network services by replacing the conventional network equipment with the combination of virtual network functions (VNFs) and commodity servers. A certain network service can be composed of a sequence of VNFs, i.e., service (function) chain. The service chaining (SC) problem aims to establish an appropriate service path from the origin node to the destination node, which holds both the resource constraints and service chain requirements of executing the required VNFs in the designated order. SC belongs to the complexity class NP -hard. In the previous work, inspired by the similarity between the SC problem and the shortest path tour problem (SPTP), we showed the capacitated SPTP (CSPTP) based ILP for the SC problem, where CSPTP is a generalized version of the SPTP with both the node and link capacity constraints. In this paper, we propose Lagrangian heuristics to solve the CSPTP-based ILP for the SC in a speedy and efficient manner. We further present that the proposed heuristics can also solve both the service chaining and function placement by slightly extending the network model called an augmented network. Through numerical results, we show that the proposed heuristics for the SC is competitive with the optimal resource allocation while executing much faster than the combination of the CSPTP-based ILP and the existing solver, i.e., CPLEX. Furthermore, we also show that the proposed heuristics for both the service chaining and function placement can still balance the solution optimality and computational complexity, thanks to the parallel computation architectures.