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Maxime Lesourd
rtproofs
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425ff442
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425ff442
authored
Aug 23, 2019
by
Martin PORTALIER
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# Formal proof for maximisation of job response time in real time systems
Those files provide a proof that,
under some hypothesis, if the workload bound has a fixpoint,
then it bounds the job response time and there exists a case where it is reached.
Those files provide a proof that,
considering one job, if the workload bound has a fixpoint
then it bounds the job response time
of the considered job
and there exists a case where it is reached.
This proof is supposed to be as direct as possible.
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@@ 21,10 +21,10 @@ This proof supposes that :

the arrival sequence model is sporadic (there exists a task minimal period)

the deadline are implicit (the task deadline is equal to the task minimal period)

the policy is with fixed preemptives priorities

the system is schedulable (all jobs complete
s
before their deadline)

the system is schedulable (all jobs complete before their deadline)
Then the main hypothesis :
their exists a fixpoint for the workload bound
, and the smallest one is reached
.
their exists a fixpoint for the workload bound.
WARNING : A tricky hypothesis supposes that all jobs terminate.
I give some ideas to prove it in the section "To go further".
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