Dispatching Equal-Length Jobs to Parallel Machines to Maximize Throughput

We consider online, non preemptive scheduling of equal-length jobs on parallel machines jobs have arbitrary release times and deadlines and a scheduler's goal is to maximize the number of completed jobs (Pm vertical bar r(j), p(j) = p vertical bar Sigma 1 - U-j). This problem has been previously studied under two distinct models. In the first, a scheduler must provide immediate notification to a released job as to whether it is accepted into the system. In a stricter model, a scheduler must provide an immediate decision, for an accepted job, selecting both the time interval and machine on which it will run. We examine an intermediate model in which a scheduler immediately dispatches an accepted job to a machine, but without committing it to a specific time interval. We present a natural algorithm that is optimally competitive for m = 2. For the special case of unit-length jobs, it achieves competitive ratios for m >= 2 that are strictly better than lower bounds for the immediate decision model.