Cloud computing applications must be allocated sufficient resources to comply with Service Level Agreements (SLAs). This paper considers data-driven probabilistic modeling of application resource demand for resource allocation. The modeling method is focused on peak demand and SLA violations and relies on a branch of statistics known as extreme value theory (EVT). Rigorous statistical validation of the proposed model shows that it generalizes better than the alternative. The paper presents a resource allocation algorithm using the model to ensure a given small SLA violation rate. For resource allocation in Yahoo data center, over 50 percent savings are demonstrated using the proposed approach.

This letter develops a method for estimating trends of extreme events statistics across multiple time periods. Some of the periods might have no extreme events and some might have much data. The extreme event distribution is modeled with a Pareto or exponential tail. The method requires selecting an extreme event threshold and then solving two convex problems for the tail parameters. Solving one provides a smoothed tail rate trend, solving another, the smoothed trend of the tail quantile level. The approach is illustrated by trending the 10-year extreme event risks for S&P 500 index daily losses and for peak power load in electrical utility data.