Fault-Tolerant Rate-Monotonic Scheduling

1. Fault-Tolerant Rate-Monotonic Scheduling Sunondo Ghosh, Rami Melhem, Daniel Mosse and Joydeep Sen Sarma

2. Outline • Background • System, task and fault models • IBRMS • FTRMS • Conditions & bounds • Simulation & conclusion

3. 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.

4. 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

5. 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

6. 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

7. An example of IBRMS schedule • C1=1.5, T1=5, U1=30%, C2=2,T2=8, U2=25% • Assume UB=30%

8. 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.

9. 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.

10. Recovery algorithm

11. 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)

12. 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}

13. 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%.

16. Simulation & conclusion • Using an event-driven simulator to compare pure RMS and FT+RMS ☻Schedulability ☻Utilization ☺Lost tasks