Robust Optimization Model for Primary and Backup Resource Allocation in Cloud Providers

Abstract

This article proposes a primary and backup resource allocation model that provides a probabilistic protection guarantee for virtual machines against multiple failures of physical machines in a cloud provider to minimize the required total capacity. A physical machine allocates both primary and backup computing resources for virtual machines. When any failure occurs, the survived physical machines with preplanned backup resources recover the virtual machines on the failed physical machines and take over the workloads. The probability that the protection provided by a physical machine does not succeed is guaranteed within a given number. Providing the probabilistic protection can reduce the required backup capacity by allowing backup resource sharing, but it leads to a nonlinear programing problem in a general-capacity case against multiple failures. We apply robust optimization with extensive mathematical operations to formulate the primary and backup resource allocation problem as a mixed integer linear programming problem, where capacity fragmentation is suppressed. We prove the NP-hardness of considered problem. A heuristic is introduced to solve the optimization problem. The results reveal that the proposed model saves about one-third of the total capacity in our examined cases; it outperforms the conventional models in terms of both blocking probability and resource utilization.