Online Throughput Maximization on Unrelated Machines: Commitment is No Burden

We consider a fundamental online scheduling problem in which jobs with processing times and deadlines arrive over time at their release dates. The task is to determine feasible preemptive schedule on single or multiple possibly unrelated machines that maximizes the number of complete before deadline. Due strong impossibility results for competitive analysis machine, we require contain some slack ɛ > 0, means window job least 1+ɛ its each eligible machine. Our contribution two-fold: (i) give first non-trivial algorithms throughput maximization machines, (ii), this main focus our paper, answer question how handle commitment requirements enforce scheduler has guarantee certain point completion admitted jobs. This very relevant, e.g., providing cloud-computing services, disallows last-minute rejections critical tasks. present an algorithm \(\Theta (\frac{1}{\varepsilon })\) -competitive when must commit upon starting job. Somewhat surprisingly, same optimal performance bound (up constants) as without If decisions be made job’s becomes less than δ-fraction size, prove ratio \(\mathcal {O}(\frac{1}{\varepsilon - \delta 0 < δ ɛ. result nicely interpolates between arrival. For latter model, it known no (randomized) admits any bounded ratio. While mainly migration, also hold comparing against migratory solution case identical machines.