Rationale: reserve the behavior folder for trace-based semantics.

These lemmas really constitute an analysis of the basic consequences
arising from the chosen semantics and hence logically belong to the
"analysis" part of Prosa.

Sergey Bozhko authored 5 years ago and Björn Brandenburg committed 5 years ago

Also removes an unnecessary module in rt.util.epsilon.

Make it a statement about scheduled jobs, to match the neighboring
definitions.

Add a [job_ready] parameter to the job model, akin to [pending], that
defines whether a job can be scheduled at a given time in a given schedule.

Then use this new general notion of readiness to define [backlogged].

A pending job may not be ready, whereas (under any reasonable
definition) a ready job ought to be pending, so this definition is
more precise and captures effects such as jitter and self-suspensions.

Sergey Bozhko authored 5 years ago and Björn Brandenburg committed 5 years ago

When we were writing the paper on Abstract RTA, we noticed that the response-time recurrence for EDF does not match the known bound.

This merge request tightens the analysis in Prosa to match the known bound.

This patch adds the classic EDF optimality argument: by swapping
allocations, any schedule in which no job misses a deadline can be
transformed into an EDF schedule in which also no job misses a deadline.

Given an interval [a, b), a function f: nat -> T, a predicate P, and a
total, reflexive, transitive relation R, [search_arg f P R a b] will
find the x in [a, b) that is an extremum w.r.t. R among all elements x
in [a, b) for which (f x) satisfies P.

For example, this can be used to search in a schedule for a scheduled
job released before some reference time with the earliest deadline.

This patch adds functions for transforming a given schedule either by
replacing the allocation at a given point, or by swapping the allocations
at two points, together with a bunch of supporting lemmas and service
invariants.

Points before or after an interval are not in the interval...

n + a - b + b - a = n if n >= b

...to match leq_ltn_trans in ssrnat

To allow reasoning about an entire class of types of schedules /
processor modules, it's useful to have named definitions for various
invariants that processor models ensure. Let's collect these centrally
where we introduce processor models and schedules.

Maxime Lesourd authored 5 years ago and Björn Brandenburg committed 5 years ago

Add model definitions for work-conserving and priority-based preemptive schedules.

Maxime Lesourd authored 5 years ago and Björn Brandenburg committed 5 years ago

This is a port (+additions) of the definitions and semantics for arrival curves (model/arrival/curves.v). As a prerequisite, this includes definitions about activations of a task (model/task_arrivals.v).

Two additional definitions which were not found in the original library but will be useful to us in the future:

* in schedule.v : completes_at
* in task_arrivals.v : arrivals_come_from_taskset