Library prosa.model.schedule.priority_driven

Priority-Driven Schedules

We now define what it means for a schedule to respect a priority in the presence of jobs with non-preemptive segments. We only specify a definition for JLDP policies since JLFP and FP policies can be used with this definition through the canonical conversions (see model.priority.classes).
NB: For legacy reasons, the below definition is currently specific to ideal uniprocessor schedules. Removal of this limitation is future work.

Section Priority.

Consider any type of tasks ...
  Context {Task : TaskType}.

... and any type of jobs associated with these tasks.
  Context {Job : JobType}.
  Context `{JobTask Job Task}.

Suppose jobs have an arrival time, a cost, ...
  Context `{JobArrival Job}.
  Context `{JobCost Job}.

... and consider any preemption model and notion of readiness.
  Context `{JobPreemptable Job}.
  Context {jr : JobReady Job (ideal.processor_state Job)}.

Given any job arrival sequence...
  Variable arr_seq : arrival_sequence Job.

...and an ideal uniprocessor schedule of these jobs,
we say that a priority policy is respected by the schedule iff, at every preemption point, the priority of the scheduled job is higher than or equal to the priority of any backlogged job. We define three separate notions of priority policy compliance based on the three types of scheduling policies : JLDP...
  Definition respects_JLDP_policy_at_preemption_point (policy: JLDP_policy Job) :=
     j j_hp t,
      arrives_in arr_seq j
      preemption_time sched t
      backlogged sched j t
      scheduled_at sched j_hp t
      hep_job_at t j_hp j.

... JLFP, and...