  The problem of scheduling jobs and choosing their respective speeds with
multiple servers under a sum power constraint to minimize the flow time +
energy is considered. This problem is a generalization of the flow time
minimization problem with multiple unit-speed servers, when jobs can be
parallelized, however, with a sub-linear, concave speedup function
$k^{1/\alpha}, \alpha>1$ when allocated $k$ servers, i.e., jobs experience
diminishing returns from being allocated additional servers. When all jobs are
available at time $0$, we show that a very simple algorithm EQUI, that
processes all available jobs at the same speed is
$\left(2-\frac{1}{\alpha}\right)
\frac{2}{\left(1-\left(\frac{1}{\alpha}\right)\right)}$-competitive, while in
the general case, when jobs arrive over time, an LCFS based algorithm is shown
to have a constant (dependent only on $\alpha$) competitive ratio.
