In the problem of online load balancing on uniformly related machines with
bounded migration, jobs arrive online one after another and have to be
immediately placed on one of a given set of machines without knowledge about
jobs that may arrive later on. Each job has a size and each machine has a
speed, and the load due to a job assigned to a machine is obtained by dividing
the first value by the second. The goal is to minimize the maximum overall load
any machine receives. However, unlike in the pure online case, each time a new
job arrives it contributes a migration potential equal to the product of its
size and a certain migration factor. This potential can be spend to reassign
jobs either right away (non-amortized case) or at any later time (amortized
case). Semi-online models of this flavor have been studied intensively for
several fundamental problems, e.g., load balancing on identical machines and
bin packing, but uniformly related machines have not been considered up to now.
In the present paper, the classical doubling strategy on uniformly related
machines is combined with migration to achieve an
(8/3+ε)-competitive algorithm and a (4+ε)-competitive
algorithm with O(1/ε) amortized and non-amortized migration,
respectively, while the best known competitive ratio in the pure online setting
is roughly 5.828