Bandwidth-centric allocation of independent tasks on heterogeneous platforms

We consider the problem of allocating a large number of independent, equal-sized tasks to a heterogeneous "grid" computing platform. We use a tree to model a grid, where resources can have different speeds of computation and communication, as well as different overlap capabilities. We define a base model, and show how to determine the maximum steady-state throughput of a node in the base model, assuming we already know the throughput of the subtrees rooted at the node's children. Thus, a bottom-up traversal of the tree determines the rate at which tasks can be processed in the full tree. The best allocation is bandwidth-centric: if enough bandwidth is available, then all nodes are kept busy; if bandwidth is limited, then tasks should be allocated only to the children which have sufficiently small communication times, regardless of their computation power.