  In this report we demonstrate the potential utility of resource allocation
management systems that use virtual machine technology for sharing parallel
computing resources among competing jobs. We formalize the resource allocation
problem with a number of underlying assumptions, determine its complexity,
propose several heuristic algorithms to find near-optimal solutions, and
evaluate these algorithms in simulation. We find that among our algorithms one
is very efficient and also leads to the best resource allocations. We then
describe how our approach can be made more general by removing several of the
underlying assumptions.
