We consider the problem of on-line scheduling of jobs arriving one by one o
n uniformly related machines, with or without preemption. We prove a lower
bound of 2, both with and without preemption, for randomized algorithms wor
king for an arbitrary number of machines. For a constant number of machines
we give new lower bounds for the preemptive case. (C) 2000 Elsevier Scienc
e B.V. All rights reserved.