Before revision: We consider the problem of scheduling a group of heterogeneous, distributed processes, with different relative priorities and service preferences , to a group of heterogeneous virtual machines. Assuming linearly elastic IT resource needs, we extend prior results on proportional fair and  max-min fair scheduling to a constrained multiresource case for a fam- ily of fairness criteria(including our recently proposed Per- Server Dominant-Share Fairness) .
After revision: We first consider the static problem of allocating resources to ( i.e. , scheduling) multiple distributed application framework s, possibly with different priorities and max-min fair scheduling to a constrained multiresource case for a fam- ily of fairness criteria(including our recently proposed Per- Server Dominant-Share Fairness) .