Fault-tolerant resource allocation model for service function chains with joint diversity and redundancy

This paper proposes an optimization model to derive a resilient virtual network function allocation in service function chains aiming to reduce the end-to-end (E2E) latency during the migrations from the primary functions to backup functions. The model considers k-fault tolerance assurance and the satisfactions of service requirements under different error patterns in this model. The allocation provided by the proposed model ensures that the processing ability satisfies the requirements even though there are k failed nodes in the network. Diversity splits a single virtual network function (VNF) into a pool of replicas with different specifications. The diversity of both primary and backup functions is considered. Redundancy is used for recovering the failed functions. We formulate the proposed model as a mixed integer linear programming problem to select suitable replicas from the pools of replicas and decide the locations of these replicas for both primary and backup functions. The objective of the proposed model is to minimize the sum of the maximum E2E latencies among functions under all possible failure patterns which have k node failures. The numerical results show that the proposed model reduces the E2E latency between the pair of primary and backup VNFs with ensuring the resiliency of the functions compared with baseline models in the examined cases. Two approximate approaches are developed to reduce the computation time of solving the proposed model with a limited performance penalty. We derive theorems to give the bounds of maximum resiliency in the proposed model.