Dispatching Equal-Length Jobs to Parallel Machines to Maximize Throughput

Abstract

Abstract. We consider online, nonpreemptive 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 (P m | rj, pj = p | P 1 − Uj). 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.

Maximizing Online Utilization with Commitment

“…If the system allows preemption (pmtn) then we can interrupt the execution of any job and immediately or later resume it on a possibly different machine without any penalty. In the non-preemptive case, we combine the acceptance commitment with a machine and start time commitment (immediate decision, see Bunde and Goldwasser [6]).…”

Online Scheduling of Unit Length Jobs with Commitment and Penalties

“…A e/(e − 1) lower bound (again for large m) from [10] shows that this algorithm is optimal; in fact the lower bound holds even for unit length jobs. In [2] an immediate dispatch model was proposed, in which the machine allocated for an accepted job must be announced upfront but the machine is free to move these jobs around. In [3] an online scheduling problem with commitment (IMM NOTIF) was studied where the penalty is equal to the length of the unfinished part of the job, with application in the charging of electric vehicles.…”