Abstract As cloud computing gains in popularity, understanding the patterns and structure of its loads is increasingly important in order to drive effective resource allocation, scheduling and pricing decisions. These efficiency increases are then associated with a reduction in the data center environmental footprint. Existing models have only treated a single resource type, such as CPU, or memory, at a time. We offer a sophisticated machine learning approach to capture the joint-distribution. We capture the relationship among multiple resources by carefully fitting both the marginal distributions of each resource type as well as the non-linear structure of their correlation via a copula distribution. We investigate several choices for both models by studying a public data set of Google datacenter usage. We show the Burr XII distribution to be a particularly effective choice for modeling the marginals and the Frank copula to be the best choice for stitching these together into a joint distribution. Our approach offers a significant fidelity improvement and generalizes directly to higher dimensions. In use, this improvement will translate directly to reductions in energy consumption.