Cumulative Workload of Sets of Jobs

In this module, we define the notion of the cumulative workload of a set of jobs.

Consider any type of tasks ...

... and any type of jobs with execution costs that are associated with these tasks.

Consider any job arrival sequence.

First, we define the workload for generic sets of jobs.

Given any computable predicate on jobs, ...

... and any (finite) set of jobs, ...

... we define the total workload of the jobs that satisfy predicate P.

Next, we define the workload of jobs with higher or equal priority under JLFP policies.

Consider any JLFP policy that indicates whether a job has higher or equal priority.

Let j be the job to be analyzed.

Recall the notion of a job of higher or equal priority.

Then, we define the workload of higher or equal priority of all jobs with higher-or-equal priority than j.

We also define workload of a task.

Let tsk be the task to be analyzed.

We define the task workload as the workload of jobs of task tsk.

Finally, we define the task's workload in a given interval [t1, t2)].