Fault tolerant rate monotonic scheduling
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Fault-Tolerant Rate-Monotonic Scheduling. Sunondo Ghosh, Rami Melhem, Daniel Mosse and Joydeep Sen Sarma. Outline. Background System, task and fault models IBRMS FTRMS Conditions & bounds Simulation & conclusion. Definitions & classifications. Real-time scheduling algorithms

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Fault tolerant rate monotonic scheduling

Fault-Tolerant Rate-Monotonic Scheduling

Sunondo Ghosh, Rami Melhem, Daniel Mosse and Joydeep Sen Sarma


Outline
Outline

  • Background

  • System, task and fault models

  • IBRMS

  • FTRMS

  • Conditions & bounds

  • Simulation & conclusion


Definitions classifications
Definitions & classifications

  • Real-time scheduling algorithms

    • Preemptive & non-preemptive

  • Tasks

    • Periodic & aperiodic

  • Real-time systems

    • Static & dynamic

  • Three kinds of hardware faults

    • Permanent, transient or intermittent

      This paper focus on adding time redundancy to a schedule of preemptive, periodic real-time tasks such that faults can be tolerated.


System task fault models
System, task & fault models

  • Sets of independent, periodic, preemptive tasks are considered.

  • A task is eligible for execution at the beginning of its period and has to complete before the end of its period.

    • The computation time Ci

    • Period Ti

    • Utilization Ui = Ci/Ti

    • Total utilization of n tasks


Rate monotonic scheduling
Rate monotonic scheduling

  • Task with higher request rates will have higher priority assignment.

    Proved result:

    • such a priority assignment is optimum

    • utilization bound: any set of n tasks with a total utilization below is schedulable on a uniprocessor system.

      for large values of n, the RMS bound


Inserted backup rms
Inserted-Backup RMS

  • General fault tolerance approach is to insert enough slack in the schedule to guarantee re-execution.

  • The amount of slack available over an interval of time is proportional to the length of that interval.

    • Treat it as a backup task B with backup utilization UB

    • The same reserved time is being used as the backup for all the tasks in the system


An example of ibrms schedule
An example of IBRMS schedule

  • C1=1.5, T1=5, U1=30%, C2=2,T2=8, U2=25%

  • Assume UB=30%


Conditions recovery from a single fault
Conditions (recovery from a single fault)

  • [S1]: For every task Si, a slack of at least Ci should be present between kTi and (k+1)Ti

  • [S2]: If there is a fault during the execution of task Sr then the recovery scheme should enable task Sr to re-execute for a duration Cr before its deadline

  • [S3]: When a task re-execution, it should not cause any other task to miss its deadline.

    If the task set satisfies [S1], then following recovery scheme ensure that both [S2] and [S3] are satisfied.


Recovery scheme
Recovery scheme

  • Recovery mode:

    • Any instance of a task that has a priority higher than that of re-execute task t and a deadline greater than Dt will be delayed until recovery is complete.



Schedulability test
Schedulability test

  • If the total utilization is lower than the bound( least upper bound), then the task set is schedulable.

    • Unaive = ULL-UB( UB = max{Ui})

    • UG-FT-RMS=ULL(1-UB)


  • Minimum fault interval:

  • proved: one fault can be tolerated within Tn+Tn-1 if the backup task with and the recovery scheme RS is used

  • Recovery from multiple faults

    • UBT=m*max{Ci/Ti}, at least m faults can be tolerate.

  • FTRMS bounds can be further improved by making assumption about task utilizations. please search it in paper if you are interested 

UB = max{Ui}


Example
example

  • Three tasks

    • T1= 10, T2=15, T3=24

    • C1=2.5, C2=3, C3=3.6

    • Then U1=25%, U2=20%, U3=15%

  • Fault tolerance requirement:

    • Each task should tolerate one transient fault

    • task 3 should tolerate one additional transient fault within Tn+Tn-1

      UB1=max{Ui}=25%, UB2=15%.


Simulation conclusion
Simulation & conclusion

  • Using an event-driven simulator to compare pure RMS and FT+RMS

    ☻Schedulability

    ☻Utilization

    ☺Lost tasks


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