FaultTolerant RateMonotonic Scheduling

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Fault-Tolerant Rate-Monotonic Scheduling

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

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Outline

• Background
• System, task and fault models
• IBRMS
• FTRMS
• Conditions bounds
• Simulation conclusion

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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.

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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

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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

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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

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An example of IBRMS schedule

• C11.5, T15, U130, C22,T28, U225
• Assume UB30

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Conditions (recovery from a single fault)

• S1 For every task Si, a slack of at least Ci
  should be present between kTi and (k1)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.

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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.

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Recovery algorithm
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Schedulability test

• If the total utilization is lower than the bound(
  least upper bound), then the task set is
  schedulable.
• Unaive ULL-UB( UB maxUi)
• UG-FT-RMSULL(1-UB)

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• Minimum fault interval
• proved one fault can be tolerated within
  TnTn-1 if the backup task with
  and the recovery scheme RS is used
• Recovery from multiple faults
• UBTmmaxCi/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 maxUi
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example

• Three tasks
• T1 10, T215, T324
• C12.5, C23, C33.6
• Then U125, U220, U315
• Fault tolerance requirement
• Each task should tolerate one transient fault
• task 3 should tolerate one additional transient
  fault within TnTn-1
• UB1maxUi25, UB215.

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Simulation conclusion

• Using an event-driven simulator to compare pure
  RMS and FTRMS
• ?Schedulability
• ?Utilization
• ?Lost tasks