The invention comprises a computer-implemented process for managing computing resources provided to customers in an on-demand data center. The process comprises: providing a shared computing environment; providing to each customer one or more logical partitions of computing resources within the shared computing environment; allocat ing at least one processing engine to each logical partition; modeling a selected customer's resource utilization as a beta distribution; iteratively select ing a random resource utilization value from the beta distribution and, for each logical partition, calculating a processing engine differential; for each iteration, calculating a collective processing engine differential until the collective processing engine differential converges on an optimal processing engine differential; and adjusting the number of processing engines by the optimal processing engine differential to achieve an optimal free pool size.