  The average coflow completion time (CCT) is the standard performance metric
in coflow scheduling. However, standard CCT minimization may introduce
unfairness between the data transfer phase of different computing jobs. Thus,
while progress guarantees have been introduced in the literature to mitigate
this fairness issue, the trade-off between fairness and efficiency of data
transfer is hard to control. This paper introduces a fairness framework for
coflow scheduling based on the concept of slowdown, i.e., the performance loss
of a coflow compared to isolation. By controlling the slowdown it is possible
to enforce a target coflow progress while minimizing the average CCT. In the
proposed framework, the minimum slowdown for a batch of coflows can be
determined in polynomial time. By showing the equivalence with Gaussian
elimination, slowdown constraints are introduced into primal-dual iterations of
the CoFair algorithm. The algorithm extends the class of the sigma-order
schedulers to solve the fair coflow scheduling problem in polynomial time. It
provides a 4-approximation of the average CCT w.r.t. an optimal scheduler.
Extensive numerical results demonstrate that this approach can trade off
average CCT for slowdown more efficiently than existing state of the art
schedulers.
