Robust Optimization for Probabilistic Protection with Primary and Backup Allocations under Uncertain Demands

Abstract

This paper proposes a robust optimization model for probabilistic protection under uncertain capacity demands to minimize the total required backup capacity against multiple simultaneous failures of physical machines. Probabilistic protection restricts the probability that the workload caused by failures exceeds the backup capacity by a given survivability parameter. The proposed model determines both primary and backup virtual machine allocations simultaneously under the probabilistic protection guarantee. To express the uncertainty of capacity demands, we introduce an uncertainty set which considers the upper bound of the total demand and the upper and lower bounds of each demand. The robust optimization technique is applied to the optimization model to deal with two uncertainties, failure event and capacity demand. With this technique, the model is formulated as a mixed integer linear programming problem. Our proposed model reduces the total required backup capacity compared with the conventional model by determining both primary and backup VM allocations simultaneously.