On-Line Load Balancing for Related Machines

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+8?5.828 for the deterministic version, and 3.31/ln2.155?4.311 for its randomized variant, improving the previous competitive ratios of 8 and 2e?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.