Backup Resource Allocation of Virtual Machines With Two-Stage Probabilistic Protection

In a cloud, protection through backup of virtual machines contained in physical machines (PMs) reduces damage to users due to failure of PMs, such as hardware malfunctions. However, from a resource cost perspective, it is necessary to reduce the amount of capacity for backup while limiting the probability of unsuccessful protection. Existing studies suggest the method of sharing backup capacity among primary resources, but the amount of capacity reduction required to protect is limited. This paper proposes a backup resource allocation model with two-stage probabilistic protection to minimize the total required backup capacity for multiple simultaneous failures of PMs. In probabilistic protection, backup resources are allocated so that the probability of backup failure does not exceed a given survivability parameter which represents the acceptable probability of backup failure. Probabilistic protection which achieves efficient sharing of backup capacity enables flexible allocation and reduces the required backup capacity. In order to increase the flexibility of backup capacity allocation, the proposed model extends the probabilistic protection to two stages. By dividing the protection into two stages, the weight of probability between stages can be adjusted, enabling more effective capacity sharing. Since it is uncertain which primary PMs fail, we apply robust optimization to the probabilistic protection. By using a table that takes into account the survivability parameter and the failure probability of PMs, the proposed model is formulated as a mixed integer linear programming problem. We prove the NP-hardness of considered problem. A heuristic is introduced to solve the optimization problem. The proposed model can reduce the total required backup capacity compared to the models with dedicated protection and one-stage probabilistic protection. The model can also provide protection in a range of survivability parameters that the model with one-stage probabilistic protection cannot satisfy.