Outcomes for the net setting
The true complexity lies within the on-line setting, the place jobs arrive dynamically and the scheduler should make speedy, irrevocable choices with out realizing what jobs will arrive subsequent. We quantified the efficiency of a web-based 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 a protracted job can damage the potential of scheduling many future smaller jobs. On this instance, should you think about that every accomplished job brings equal weight, no matter its size, finishing many quick jobs is far more worthwhile than finishing one lengthy job.
To make the net downside solvable and mirror real-world flexibility, we studied two fashions that enable an lively job to be interrupted if a greater alternative arises (although solely jobs restarted and later accomplished non-preemptively rely as profitable).
Interruption with restarts
On this mannequin, a web-based 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 will be retried.
We discovered that the pliability supplied by permitting job restarts is extremely useful. A variant of Grasping that iteratively schedules the job that finishes earliest continues to attain a 1/2-competitive ratio, matching the outcome 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 endlessly. 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 far more work sooner or later. As soon as once more, the aggressive ratio of all on-line algorithms approaches zero. Analyzing the above onerous situations led us to give attention to the sensible state of affairs the place all jobs share a standard deadline (e.g., all information processing should end by the nightly batch run). For such widespread deadline situations, we devise novel fixed aggressive algorithms. Our algorithm could be very intuitive and we describe the algorithm right here for the easy setting of a unit capability profile, i.e., we will 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:
