Robust Optimization for Probabilistic Protection with Multiple Types of Resources in Cloud

This paper proposes a robust optimization model for probabilistic protection with multiple types of resources to minimize the required backup capacity for each type of resource against multiple random failures of physical machines in a cloud provider. If random failures occur, the required capacities for virtual machines are allocated to the dedicated backup physical machines, which are determined in advance. Probabilistic protection restricts the probability that the workload caused by failures exceeds the backup capacity by a given survivability parameter. We introduce three survivability parameters for central processing unit (CPU), memory, and the entire cloud provider considering both CPU and memory. By using the relationship between the three survivability parameters, the proposed model guarantees probabilistic protection for each resource, CPU and memory, and the entire cloud provider. By adopting the robust optimization technique, we formulate the proposed model as a multi-objective mixed integer linear programming problem. To deal with the multi-objective optimization problem, we apply the lexicographic weighted Tchebycheff method with which a Pareto optimal solution is obtained. Our proposed model reduces the average value between the backup capacity ratios of CPU and memory compared with the conventional model.