Library prosa.analysis.definitions.carry_in

From mathcomp Require Import ssreflect ssrbool eqtype ssrnat seq fintype bigop.
Require Export prosa.model.priority.classes.

No Carry-In

In this module, we define the notion of a time without any carry-in work.
Section NoCarryIn.

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

... and any type of jobs associated with these tasks, where each job has an arrival time and a cost.
  Context {Job : JobType} `{JobTask Job Task} `{JobArrival Job} `{JobCost Job}.

Consider any arrival sequence of such jobs with consistent arrivals ...
  Variable arr_seq : arrival_sequence Job.
  Hypothesis H_arrival_times_are_consistent : consistent_arrival_times arr_seq.

... and the resultant schedule.
  Context {PState : ProcessorState Job}.
  Variable sched : schedule PState.

There is no carry-in at time t iff every job (regardless of priority) from the arrival sequence released before t has completed by that time.
  Definition no_carry_in (t : instant) :=
    ∀ j_o,
      arrives_in arr_seq j_o →
      arrived_before j_o t →
      completed_by sched j_o t.

End NoCarryIn.