On-line load balancing

The setup for the authors´ problem consists of n servers that must complete a set of tasks. Each task can be handled only by a subset of the servers, requires a different level of service, and once assigned can not be re-assigned. They make the natural assumption that the level of service is known at arrival time, but that the duration of service is not. The on-line load balancing problem is to assign each task to an appropriate server in such a way that the maximum load on the servers is minimized. The authors derive matching upper and lower bounds for the competitive ratio of the on-line greedy algorithm for this problem, namely ^(3n)2/3/₂(1+o(1)), and derive a lower bound, Ω(√n), for any other deterministic or randomized on-line algorithm