Before revision:  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:  Assuming linearly elastic IT resource needs, we extend prior results on proportional fair and server preferences , in a private cloud with heterogeneous servers. Several fai r scheduling mechanisms have been proposed for this purpose. We extend pr ior results on 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) .