  We first consider the static problem of allocating resources to ( i.e. ,
scheduling) multiple distributed application framework s, possibly with
different priorities 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 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.
