  We study the problem of allocating multiple types of resources to agents with
Leontief preferences. The classic Dominant Resource Fairness (DRF) mechanism
satisfies several desired fairness and incentive properties, but is known to
have poor performance in terms of social welfare approximation ratio. In this
work, we propose a new approximation ratio measure, called \emph{\fratio},
which is defined as the worst-case ratio between the optimal social welfare
(resp. utilization) among all \emph{fair} allocations and that by the
mechanism, allowing us to break the lower bound barrier under the classic
approximation ratio. We then generalize DRF and present several new mechanisms
with two and multiple types of resources that satisfy the same set of
properties as DRF but with better social welfare and utilization guarantees
under the new benchmark. We also demonstrate the effectiveness of these
mechanisms through experiments on both synthetic and real-world datasets.
