Robust Function Deployment against Uncertain Recovery Time with Workload-Dependent Failure Probability
Mengfei Zhu, Fujun He, Eiji Oki · 2022
This paper proposes a robust function deployment 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 failure and recovery scenarios. We introduce an uncertainty set that considers the upper and lower bounds of the recovery time of a function by each node that protects it and the upper bound of the average recovery time among nodes. The robust optimization technique is applied to handle the worst case of expected recovery time satisfying a time guarantee under an uncertain recovery time. With this technique, the model is formulated as a mixed integer linear programming problem. The numerical results reveal that the proposed model saves the deployment cost on average 24% compared to a baseline that uses the deterministic recovery time in our tested cases.