1. A system comprising: computing resources for running computer workloads; a workload manager for planning an allocation for each of a series of allocation periods of said resources to candidate recipient computer workloads at least in part as a function of expected marginal utilities of allocating resource units of said resources to said workloads, each of said expected marginal utilities corresponding to an expected change in utility resulting from allocating at least one of said resource units to a non-negative number of resource units already allocated to one of said workloads, said workload manager including, a workload monitor for generating utilization data indicating for at least some of said workloads the extent to which that workload utilizes resources assigned to it; a prediction engine for providing probability distributions for expected demands by said workloads for said resources for future allocation periods; a workload utility function for at least some of said workloads, each workload utility function specifying for its respective workloads a value of a utility parameter at least in part as a function of a demand level and an allocation level, said expected marginal utilities being determined at least in part from said workload utility functions and said probability distributions; and a container hierarchy of containers to which said resources can be assigned, said container hierarchy including a root container, intermediate-level containers, and base-level containers within each of which at most one of said workloads runs, said root container containing all other of said containers and said workloads, each of said intermediate-level containers including one or more of said base-level containers, said resources being allocable to at least some of said intermediate-level containers in gross units of said resources, said resources being allocable to said workloads and base-level containers in fine units of said resources, wherein each of said gross units corresponds to multiple fine units.