Library prosa.model.priority.elf

Require Export prosa.model.priority.classes.
Require Export prosa.model.priority.gel.

ELF Priority Policy

We define the class of "EDF-Like-within-Fixed-priority (ELF)" scheduling policies. ELF scheduling is a (large) subset of the class of JLFP scheduling policies that can be structurally viewed as a combination of the fixed-priority and GEL scheduling policies. In ELF scheduling, we take an FP policy as an argument, and each task has a constant "priority-point offset". Each job's (absolute) "priority point" is given by its arrival time plus its task's priority-point offset.
Given two jobs, their relative priority order is first determined by the fixed- priority policy, i.e., the priority order of their respective tasks. However, if their tasks have equal fixed priority, then it is determined by the jobs' priority points (GEL), with the interpretation that an earlier priority point implies higher priority. It can be viewed as an FP Policy with the GEL scheduling policy employed to resolve ties.
The FP policy is a particular case of ELF if all the tasks are assigned distinct priorities. GEL (and hence, FIFO and EDF) are special cases of ELF if all tasks have equal priority according to the FP policy.
In order to define the policy, we introduce the required context.
Section ELF.

Consider any type of tasks with relative priority points...
  Context {Task : TaskType} `{PriorityPoint Task}.

...and jobs of these tasks.
  Context {Job : JobType} `{JobArrival Job} `{JobTask Job Task} .
We parameterize the ELF priority policy based on a fixed-priority policy. Job j1 is assigned a higher priority than job j2 if either the task associated with j1 has a strictly higher priority than the task associated with j2, or if their tasks have equal priorities and the relative priority point of j1 is less than or equal to the relative priority point of j2, similar to the GEL policy.
NB: The | 0 at the end of the next line is a priority hint for type-class resolution, meaning this type class should be picked with highest priority in ambiguous contexts.
  #[export] Instance ELF (fp : FP_policy Task) : JLFP_policy Job | 0:=
      hep_job (j1 j2 : Job) :=
Recall the notion of a higher-priority job under the GEL policy as gel_hep_job.
        let gel_hep_job := @hep_job _ (GEL Job Task) in
Under the ELF policy, job j1 has higher-or-equal priority than job j2 if (1) j1's task has higher priority than j2's task...
          hp_task (job_task j1) (job_task j2)
...or (2) if the two tasks have the same priority and j1 has higher priority than j2 according to the GEL policy.
            || (hep_task (job_task j1) (job_task j2)
               && gel_hep_job j1 j2)

End ELF.