Robust function deployment against uncertain recovery time in different protection types with workload-dependent failure probability

Abstract

Modern network services and functions, such as firewalls, load balancers, and network address translators, are virtualized to virtual network functions (VNFs) and run in virtual machines and containers. This paper proposes a robust VNF placement model against uncertain recovery time with satisfying an expected recovery time guarantee in a cost-efficient manner. We consider that each node fails with a workload-dependent failure probability, which is a non-decreasing function that reveals the empirical relationship between the workload and the failure probability. The preventively deployed backup resources can recover an unavailable function hosted by a failed node in a period of time, which is related to the backup strategies and protection types. Multiple functions protected by a node can share the backup resources to reduce the number of active nodes to save cost, which also affects the recovery time if the number of unavailable functions is so large that the remaining capacity cannot recover them and causes a waiting procedure of an unavailable function before being recovered. We introduce an uncertainty set that considers the upper and lower bounds of the recovery time of a function protected by each node and the upper bound of the average recovery time among nodes. We consider the expected remaining capacity of a node and the expected number of unavailable functions hosted by the node to approximate the waiting time in the shared protection. The robust optimization technique is applied to obtain the worst-case expected recovery time under an uncertain recovery time set. With this technique, the model is formulated as a mixed integer linear programming problem. To solve the problem in a practical time, a heuristic algorithm is developed. It reduces the number of active nodes while decreasing the worst-case expected recovery time within the uncertainty set by converting the linear programming problem to a graph problem. The numerical results reveal the superiority of the proposed model by considering the recovery time guarantee, uncertainty set, and shared protection; we investigate the dependency on the bounds of recovery time.