  With multiple identical unit speed servers, the online problem of scheduling
jobs that migrate between two phases, limitedly parallelizable or completely
sequential, and choosing their respective speeds to minimize the total flow
time is considered. In the limited parallelizable regime, allocating $k$
servers to a job, the speed extracted is $k^{1/\alpha}, \alpha>1$, a
sub-linear, concave speedup function, while in the sequential phase, a job can
be processed by at most one server with a maximum speed of unity. A LCFS based
algorithm is proposed for scheduling jobs which always assigns equal speed to
the jobs that are in the same phase (limitedly parallelizable/sequential), and
is shown to have a constant (dependent only on $\alpha > 1$) competitive ratio.
For the special case when all jobs are available beforehand, improved
competitive ratio is obtained.
