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) . Performance comparison is made by illustrative numerical example. We conclude with a discussion of scheduling problems for a public cloud with heterogeneous instances and servers .
After revision:  Assuming linearly elastic IT resource needs, we extend prior results on proportional fair and max-min and proportional fair scheduling to t his constrained multiresource and multiserver case for generi c fair scheduling criteria. The task efficiencies (a metric r elated to proportional fairness) of max-min fair allocations found b y progressive filling are compared by illustrative examples . They show that "server specific" fairness criteria and those that are b ased on residual (unreserved) resources are more efficient .