Online scheduling of equal-length jobs on parallel machines

We study on-line scheduling of equal-length jobs on parallel machines. Our main result is an algorithm with competitive ratio decreasing to e/(e - 1), approximate to 1.58 as the number of machine increases. For m >= 3, this is the first algorithm better than 2-competitive greedy algorithms: Our algorithm has an additional property called immediate decision: at each time, it is immediately decided for each newly released job if it will be scheduled, and if so, then also the time interval and machine where it is scheduled is fixed and cannot be changed later. We show that for two machines, no deterministic algorithm with immediate decision is better than 1.8-competitive; this lower bound shows that our algorithm is optimal for m = 2 in this restricted model. We give some additional lower bounds for algorithms with immediate decision.