  Makespan minimization on identical parallel machines is a classical
scheduling problem. We consider the online scenario where a sequence of $n$
jobs has to be scheduled non-preemptively on $m$ machines so as to minimize the
maximum completion time of any job. The best competitive ratio that can be
achieved by deterministic online algorithms is in the range $[1.88,1.9201]$.
Currently no randomized online algorithm with a smaller competitiveness is
known, for general $m$.
  In this paper we explore the power of job migration, i.e.\ an online
scheduler is allowed to perform a limited number of job reassignments.
Migration is a common technique used in theory and practice to balance load in
parallel processing environments. As our main result we settle the performance
that can be achieved by deterministic online algorithms. We develop an
algorithm that is $\alpha_m$-competitive, for any $m\geq 2$, where $\alpha_m$
is the solution of a certain equation. For $m=2$, $\alpha_2 = 4/3$ and
$\lim_{m\rightarrow \infty} \alpha_m = W_{-1}(-1/e^2)/(1+ W_{-1}(-1/e^2))
\approx 1.4659$. Here $W_{-1}$ is the lower branch of the Lambert $W$ function.
For $m\geq 11$, the algorithm uses at most $7m$ migration operations. For
smaller $m$, $8m$ to $10m$ operations may be performed. We complement this
result by a matching lower bound: No online algorithm that uses $o(n)$ job
migrations can achieve a competitive ratio smaller than $\alpha_m$. We finally
trade performance for migrations. We give a family of algorithms that is
$c$-competitive, for any $5/3\leq c \leq 2$. For $c= 5/3$, the strategy uses at
most $4m$ job migrations. For $c=1.75$, at most $2.5m$ migrations are used.
