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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)
slide12

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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