A Statistical Framework for Optimal Workload Consolidation with Application to Capacity Planning for On-Demand Computing

In on-demand computing services, the customer pays based on actual usage and the service provider is free to allocate unused capacity to other customers. Capacity planning becomes an important issue in such a shared environment. It is desirable that a portfolio effect takes place so that less total capacity would be required in a shared system than in a dedicated one. In this article, a quantile-based statistical approach is proposed to quantify the portfolio effect and the associated risks. It is shown that the portfolio effect may or may not exist for a given set of workloads, depending crucially on their joint distribution and the assumed risk levels. For Gaussian workloads, the portfolio effect almost always exists regardless of the statistical correlation and the risk level. For non-Gaussian workloads, the portfolio effect is not guaranteed and can even be negative, even if they are negatively correlated or statistically independent. However, when simultaneously recorded workload history is available, the portfolio effect can be estimated directly from the data. Based on the data-driven approach, an optimization problem is formulated for capacity planning with the aim of maximizing the portfolio effect for a given set of workloads. It calls for a consolidation of the workloads into one or more portfolios so that each portfolio can be served satisfactorily by a dedicated system and the total capacity requirement is minimized. Iterative algorithms are proposed to solve the optimization problem numerically. The method is applied to a server consolidation problem with real workload data.

By: Ta-Hsin Li

Published in: American Statistical Association. Journal, volume 102, (no 479), pages 841-855 in 2007

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