We consider the problem of scheduling permanent jobs on related machines
in an on-line fashion. We design a new algorithm that achieves the
competitive ratio of 3+\sqrt{8}\approx 5.828 for the deterministic
version, and 3.31/\ln 2.155 \approx 4.311 for its randomized variant,
improving the previous competitive ratios of 8 and 2e\approx 5.436.
We also prove lower bounds of 2.4380 on the competitive ratio of
deterministic algorithms and 1.8372 on the competitive ratio of
randomized algorithms for this problem.