G572 Real-time Systems

1. G572 Real-time Systems Rate Monotonic Analysis Xinrong Zhou (xzhou@abo.fi)

2. RMA • RMA is one quantitative method which makes it possible to analyze if the system can be scheduled • With the help of RMA it is possible to: • select the best task priority allocation • select the best scheduling protocol • Select the best implementation scheme for aperiodic reality • If RMA rules are followed mechanically, the optimal implementation (where all hard deadlines are met) is reached with the highest possibility

3. RMA • System model • scheduler selects tasks by priority • if a task with higher priority comes available, task currently running will be interrupt and the task with higher priority will be run (preemption) • Rate Monotonic:priority controls • monotonic, • frequency (rate) of a periodic process

4. Contents • Under what conditions a system can be scheduled when priorities are allocated by RMA? • Periodic tasks • Blocking • Random deadlines • Aperiodic activities

5. Why are deadlines missed? • Two factors: • The amount of computation capacity that is globally available, and • how this is used • Factor 1 can be easily quantified • MIPS • Max bandwidth of LAN • Factor 2 contains • Processing capacity that is used by the operating system • Distribution between tasks • RMA goals: • Optimize distribution in such a way that deadlines will be met; • or ”provide for graceful degradation”

6. Utilization • Task Ti is dependent on: • Preemption of tasks with higher priority • describes relative usability grade of tasks with higher priority • Its own running time • ci • blocking by tasks with lower priority • Lower priority tasks contain critical resources

7. Example Total utilization U = 88,39% 23 10 20 Missed deadline

8. Harmonic period helps • Application is harmonic if every task’s period is exact portion of a longer period Total utilization U = 88,32% 10 20 30 36

9. Liu & Layland • Suppose that: • Every task can be interrupted (preemption) • Tasks can be ordered by inverted period: • pr(Ti) < pr(Tj) iff Pj<Pi • Every task is independent and periodic • Tasks relative deadlines are similar to tasks’ periods • Only one iteration of all tasks is active at one time!

10. Liu & Layland • When a group of tasks can be scheduled by RMA? • RMA 1 • If total utilization of tasks tasks can be scheduled so that every deadline will be met e.g. When the number of tasks increases, processor will be idling 32% of time!

11. Variation of U(n) by n

12. Example • In example below, we get utilization6/15+4/20+5/30 = 0,767 • because U(3) = 0,780, application can be scheduled

13. 10 0 5 non RMA RMA Why shorter periods are prioritized? In realistic application. c is small compared with T. Shortest T first ensures that negative preemption effects will be minimized T2 T1 T1 misses deadline

14. Why shorter periods are prioritized? • Slack: T-c = S • In example is c2 > T1 – c1 • In practice is c<< T e.g. slack is proportional to the period • By selecting the shortest period first, the preemption effect will be minimized • NOTE: • We are primarly interesting in shortening deadlines by priorities!

15. How 100% utilization can be achieved? • Critical zone theorem: • If some number of independent periodic tasks start synchronously and every task meets its first deadline, then every future deadline will be met • Worst-case: task starts at the same time with higher-priority task • Scheduling points for task Ti: Ti’s first deadline, and the end of periods within Ti’s first deadline for every task with higher priority than Ti • If we can show that there are at least one scheduling point for one task, then if that task have time to run one time, this task can be scheduled

16. Overhead • Periodic overhead • overhead to make tasks periodic • overhead to switch between tasks • System overhead • overhead of operating system • UNIX, Windows NT: difficult to know what happens in background

17. Periodic Overhead • To execute a task periodically, the clock must be read and the next execution time must be calculated Next_Time = Clock; loop Next_Time = Next_Time + Period; { ... periodic task code here ... } delay Next_Time – Clock; end loop • task switch: • saving and recalling tasks ”context” • add two task switches to the running queue

18. Periodic Overhead • Data can be gathered by benchmarking • for eCOS operating system with: • Board: ARM AEB-1 Evaluation Board • CPU : Sharp LH77790A 24MHz

19. Bad points of ”classic” RMA • It requires preemptive scheduler • blocking can stop the system • aperiodic activities must be ”normalized” • tasks which have jitter must be specially handled • RMA can’t analyze multiprocessor systems

20. Blocking • If two tasks share the same resource, those tasks are dependent • Resources are serially and mutually exclusive used • Shared resources are often implemented using semaphores (mutex): • 2 operations • get • release • Blocking causes two problems: • priority inversion • deadlocks

21. R reserved T1 Terminates Allocates R T2 Release R Terminates Interrupt T3 Blocking time Interrupt Try to allocate R Interrupt and allocates R Priority inversion • Priority inversion happens when a task with a lower priority blocks a task with a higher priority • e.g. Mars Rover was lost because of priority inversion Release R

22. Deadlock • Deadlock means that there are circular resource allocation: • T1 allocates R1 • T2 interrupt T1 • T2 allocates R2 • T2 try to allocate R1 but blocks  T1 will be run • T1 try to allocate R2 but blocks • Both tasks are now blocked • deadlock

23. Deadlock • Deadlocks are always design faults • Deadlocks can be avoided by • Special resource allocation algorithms • deadlock-detection algoritms • static analysis of the system • Resource allocation graphs • Matrix method • Deadlocks will be discussed more thoroughly with parallel programming

24. Priority inversion: control of blocking time • It is difficult to avoid priority inversion when blocking happens • Scheduling using fixed priorities produces unlimited blocking time • 3 algorithms for minimization of blocking time: • PIP: Priority inheritance • PCP: Prioirity ceiling • HL: Highest locker

25. Priority Inheritance • 3 rules: • Blocked task inherits a temporary priority from the blocking task with a higher priority (priority-inheritance rule) • Task can lock a resource only if no other task has locked the resource. Task blocks until resources are released, after which task will continue running on its original priority (allocation rule) • Inheritance is transitive: • T1 blocks T2, and T2 blocks T3 • T1 inherits T3’s priority

26. Priority inheritance In the example Alowest priority Chighest priority

27. Priority inheritance • Blocking time will be now shorter • Maximum blocking time for a task • Length of min(m,n) critical section • m = number of critical sections in application • n = number of tasks with higher priority • ”chain blocking” • PIP can’t prevent deadlock in all cases • priority ceiling algorithm can prevent deadlock and reduce the blocking time

28. Priority Inheritance

29. Priority Ceiling • Every resource has the highest priority level (”ceiling”): • Highest priority level of task which can lock (or require) the resource • Highest ceiling value (currently used) is stored in a system variable called system ceiling • A task can lock or release a resource if • It already has locked a resource which has ceiling=system ceiling, or • Task’s priority is higher than system ceiling • A task blocks until resource will be available and system ceiling variable decrements • Blocking task inherits its priority from that blocking task which has highest priority • Inheritance is transitive

30. Priority Ceiling R1 ceiling = Prio B R2 ceiling = Prio C system ceiling = R1 ceiling

31. Priority Ceiling • blocking time forc is now 0 • no ”chain blocking” possible • deadlock not possible in any cases • Complicated implementation

32. Highest locker • Every resource has highest priority level (”ceiling”): highest priority of a task which can lock the resource • Task can lock or release resource and inherit resources ceiling + 1 as its new priority level • Simpler than PCP to implement • In practice same properties than PCP • ”best” alternative

33. Highest Locker

34. Cost of implementation • PIP protocol • Task generates a context-switch when it blocks • Task generates a context-switch when it becomes executable • Scheduler must keep one queue for semaphores of tasks ordered by priorities • Every time new task needs a semaphore, scheduler must adjust tasks priority to the resource owner’s priority • Owner (task) must possible inherit the priority • Every times resource is released, disinheritance procedure is executed

35. Costs of implementation • PIWG ( Performance Issues Working Group) has developed benchmarks for comparing scheduling algorithms

36. Cost of implementation • Note: • If the protocol is not in operating system, it must not be implemented by itself. (application level=>huge overhead) • ”No silver bullet” • Scheduling protocol can only minimize the possibility of blocking • Blocking must be prevented by improved design

37. Similarities of scheduling protocols

38. Algorithms in commercial RTOS • Priority inheritance • WindRiver Tornado/VxWorks • LynxOs • OSE • eCOS • Priority Ceiling • OS-9 • pSOS+

39. Deadline Monotonic Priority Assignment • RM: • Shortest period gets the highest priority • DM: • Shortest deadline gets the highest priority • DM gives higher utilization • Get first the analysis using RM, allocate then priorities using DM

40. Dynamic scheduling • Priorities are calculated at run time • Earliest deadline first (EDF): • Task with shortest time to the deadline executed first • It is always possible to transform timing plan which meets deadlines to the timing plan under EDF • EDF is an optimal scheduling algorithm • It is not simple to show that the system is schedulable using EDF • RMA is enough in practice • tasks need not to be periodic!

41. EDF: Example • When t=0 can only T1 run. • When t=4 has T2 higher priority because d2 < d1 • When t=5 has T2 higher priority than T3 • When t=7 stops T2 and T3 has higher priority • When t=17 stops T3 and T1 executes

42. EDF: test of schedulability • In general case, we must simulate the system to show that it is schedulable • finity criterion gives limits to the simulation • Let hT(t) be the sum of running times of those tasks in unit T which have an absolute deadline

43. Aperiodic activities • In practice not every event is periodic • Aperiodic activities are often I/O activities • Connected to the interrupt lines of the CPU • Processors’ interrupt has always higher priority than the scheduler of the operating system • How could the aperiodic events be connected that the system will be schedulable?

44. Aperiodic activities • Look 5 different implementation models: • Interrupt handled at hardware priority level • Cyclic polling (handled at the os-schedulers priority level) • Combination of 1 and 2 (deferred aperiodic handling) • Interrupt handled partially at hardware level and partially at OS level with a deferred server • Interrupt handled partially at hardware level and partially OS level with a sporadic server

45. Hardware handling • Interrupt handled wholy by interrupt service routine (ISR)

46. Event period n period n+1 Processering 5 0 1 10 D Cyclic polling • One task allocate for handling of events • Hardware must buffer • Requirements: • Only one event should happens between two cycles • Event must be handled before its deadline • If polling task is not executed with the highest priority, its period should be highest half of the events deadline

47. Cyclic polling

48. Delayed handling • Partition handling to two parts: • ISR: handle those tasks that must be handled immediately: • Reading of hardware registers • .... • ”deferred handler” (DH) will be activated that handles the rest of task

49. Deferred Server • Delayed handling is still aperiodic • Idea: make DH periodic • Server process • period • for prevention that server takes all processing capacity, server under period is given limited execution capacity • After server goes idle, the consumed processor capacity can be restored (replenishment period) • deferred server restores its processing capacity at the beginning of period

50. Event A Event B Event C Event D 15 10 5 12 8 4 0 Deferred server • execution capacity 1 (one event/period) • period 4 • server is redo when t=0, but runs first when t=3 e.g. phase = 3 • RMA analysis needs that every task should be executable at the beginning of the cycle