Outcomes for the net setting

The actual complexity lies within the on-line setting, the place jobs arrive dynamically and the scheduler should make rapid, irrevocable choices with out understanding what jobs will arrive subsequent. We quantified the efficiency of an internet algorithm through its aggressive ratio, which is the worst case comparability between the throughput of our on-line algorithm and the throughput of an optimum algorithm that’s conscious of all the roles apriori.

The usual non-preemptive algorithms fail utterly right here as their aggressive ratio approaches zero. This occurs as a result of a single dangerous resolution of scheduling an extended job can smash the potential of scheduling many future smaller jobs. On this instance, in case you think about that every accomplished job brings equal weight, no matter its size, finishing many brief jobs is rather more worthwhile than finishing one lengthy job.

To make the net downside solvable and mirror real-world flexibility, we studied two fashions that permit an lively job to be interrupted if a greater alternative arises (although solely jobs restarted and later accomplished non-preemptively depend as profitable).

Interruption with restarts

On this mannequin, an internet algorithm is allowed to interrupt a at the moment executing job. Whereas the partial work already carried out on the interrupted job is misplaced, the job itself stays within the system and might be retried.

We discovered that the pliability supplied by permitting job restarts is very useful. A variant of Grasping that iteratively schedules the job that finishes earliest continues to realize a 1/2-competitive ratio, matching the end result within the offline setting.

Interruption with out restarts

On this stricter mannequin, all work carried out on the interrupted job is misplaced and the job itself is discarded eternally. Sadly, we discover that on this strict mannequin, any on-line algorithm can encounter a sequence of jobs that forces it into choices which forestall it from satisfying rather more work sooner or later. As soon as once more, the aggressive ratio of all on-line algorithms approaches zero. Analyzing the above laborious cases led us to concentrate on the sensible situation the place all jobs share a standard deadline (e.g., all information processing should end by the nightly batch run). For such widespread deadline cases, we devise novel fixed aggressive algorithms. Our algorithm could be very intuitive and we describe the algorithm right here for the straightforward setting of a unit capability profile, i.e., we are able to schedule a single job at any time.

On this setting, our algorithm maintains a tentative schedule by assigning the roles which have already arrived to disjoint time intervals. When a brand new job arrives, the algorithm modifies the tentative schedule by taking the primary relevant motion out of the next 4 actions: