Robust Optimization Model for Probabilistic Protection under Uncertain Virtual Machine Capacity in Cloud

This paper presents robust optimization models for minimizing the required backup capacity with probabilistic protection against multiple simultaneous 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. We consider two uncertainties, failure event and virtual machine capacity. By adopting the robust optimization technique, we formulate three mixed integer linear programming problems. There are differences of robustness between the three models. Then we provide theorems concerned with the differences and prove them. The theorems are supported by numerical results. Our three presented models are applicable to the case that virtual machine capacities are uncertain, and by using these models, we can obtain the optimal solution of the allocation of virtual machines under the uncertainty.