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Few works consider both the utility of the tasks and jobs.
Such modification consider the extra utility of the scheduled jobs and also the utility of the tasks of the scheduled jobs.
It can improve the result derived by the DP algorithm when the utility of the tasks takes a large proportion comparing with the extra utility.
For simplicity, we only consider the problem where every task has uniform resource requirement, but the utility of the tasks could be different.
Most state of art works study the problem considering either the utility of the tasks or the utility of the jobs.
However, our utility model is general enough to permit the replacement of these assigned utilities with values that better reflect the actual utility of the tasks, for example, by assigning utility based on perceptual values of video quality derived from human trials.
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The main purpose of this article is to describe the utility of the task for studying different behavioral components and demonstrate the time course to achievement of criteria.
However the future utility of the task rests upon our ability to isolate the potential causes of impaired performance in specific clinical populations and syndromes.
Otherwise, even one task of a job is not completed, the utility gain is the sum of the utility of the completed tasks, without the extra job utility, i.e. (u(i)={sum nolimits }_{j=1,I_{ij}neq emptyset }^{n_{i}}u_{ij}).
We now only need to prove that the EDF-based algorithm maximizes the total utility of the scheduled tasks.
Assume the EDF-based algorithm maximizes the total utility of the scheduled tasks when there are k jobs, i.e., n=k.
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