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G53SRP: Feasibility analysis

G53SRP: Feasibility analysis. Chris Greenhalgh School of Computer Science. 1. Contents. Introduction Process and scheduling model Utilisation tests Response time analysis Run-time feasibility testing in RTSJ Summary

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G53SRP: Feasibility analysis

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  1. G53SRP: Feasibility analysis Chris Greenhalgh School of Computer Science 1

  2. Contents • Introduction • Process and scheduling model • Utilisation tests • Response time analysis • Run-time feasibility testing in RTSJ • Summary • Book: Wellings Ch. 10 (part), Burns & Wellings 12.5-12.6; 13.1-13.5, 13.7, 13.9, 13.10 (part) 2

  3. Introduction • Feasibility = whether a set of processes, if scheduled correctly, will meet their deadlines • RTSJ: all active RealtimeThreads and AsyncEventHandlers (i.e. Schedulables) • Also known as “Schedulability” • Can be determined analytically given enough information about the system…

  4. (Simple) Process and scheduling model • Fixed set of processes • Known worst-case execution times • Independent processes • See later notes for some information on dealing with competition between threads • Periodic; known deadlines • Zero time context switch • Correctness = meet deadlines • Priority-based scheduling • Pre-emptive • No timeslicing

  5. Process parameters: • D = deadline (time period) • RTSJ: ReleaseParameters deadline • T = period of periodic process • RTSJ: PeriodicParameters period • Sporadic process minimum interarrival time • RTSJ: SporadicParameters minimumInterarrival • Feasibility analysis not possible for aperiodic processes, i.e. no process set with an aperiodic process is feasible • C = worst case execution time • RTSJ: ReleaseParameters cost

  6. Scheduling approach • Fixed Priority Scheduling (FPS) • RTSJ: PriorityScheduler • Single fixed priority allocated in advance for each process • Runnable processes executed in order of priority • Deadline Monotonic Priority Order (DMPO) • Allocate highest priority to shortest deadline • Provably optimal for FPS • RTSJ: Priorities specified by programmer via SchedulerParameters (PriorityParameters)

  7. Fraction of CPU used by process Total CPU (no. of CPUs) Schedulability (1): Utilisation tests • Is there enough CPU capacity? • Sum(Ci/Ti) <= 1 • But: • Necessary (not sufficient) • D=T only

  8. Process set Proc. T C 1 5 2 2 4 2 Utilization = 2/5+2/4 = 0.85 Might be schedulable :-/ Process set Proc. T C 1 5 3 2 4 2 Utilization = 3/5+2/4 = 1.10 Definitely not schedulable For example:

  9. (consider P1 cost=2.01 => U = 0.852!) 0 1 2 3 4 5 6 Example time-line (first case) Process Process Release Time Process Completion Time Deadline Met 1 2/2 Process Completion Time Deadline Missed Preempted 2 2/2 2/2 Executing Time

  10. 0 1 2 3 4 5 6 Example time-line (second case) Process Process Release Time Process Completion Time Deadline Met 1 2/3 Process Completion Time Deadline Missed Preempted 2 2/2 2/2 Executing Time

  11. Jolly clever formula worked out by Liu & Leylard (see Burns & Wellings) Schedulability (2): Utilisation bound test (Liu & Leyland) • Is there enough CPU capacity? • Sum(Ci/Ti) <= N(2(1/N)-1) • But: • Sufficient (not necessary) • D=T only • 1 CPU

  12. For example: • Process set • Proc. T C • 1 5 2 • 2 4 1 • Utilization = 2/5+1/4 = 0.65 • Bound 2 processes = 0.828 • Schedulable!

  13. 0 1 2 3 4 5 6 Example time-line Process Process Release Time Process Completion Time Deadline Met 1 … 2/2 Process Completion Time Deadline Missed Preempted 2 1/1 1/1 Executing Time

  14. Another example Process Set Process Period ComputationTime Priority Utilization T C P U a 50 12 1 0.24 b 40 10 2 0.25 c 30 10 3 0.33 • The combined utilization is 0.82 (or 82%) • This is above the threshold for three processes (0.78) and, hence, this process set fails the utilization test

  15. 0 10 20 30 40 50 60 Example time-line Process a 10 2 Process Release Time Process Completion Time Deadline Met b 10 10 Process Completion Time Deadline Missed Preempted c 10 10 Executing Time

  16. Example Gantt Chart c b a c b 0 10 20 30 40 50 Time

  17. Schedulability (3): Response time analysis • Consider a worst-case scenario: • Every process is released at the same moment • Will they all meet their deadlines? • i.e. is the worst-case response time (completion time) for each process <= its deadline?

  18. Release of process (nominal start time) Interference from higher priority processes, Ii a With preemptive fixed priority scheduling the only reason we aren’t actually running (given assumptions) b c Time execution time Ci = a + b +c End of process execution -> response time, Ri=Ci+Ii Units of execution Deadline

  19. Response time analysis (1) • Necessary and sufficient • D <= T • (i) Ri = Ci+Ii • Ri = response time • Ci = worst case execution time • Ii = interference • (ii) Ri = Ci+SUMj (ceil(Ri/Tj)*Cj) • where j : Pj>Pi • ceil(Ri/Tj) = max. number of times that process j released in time during i

  20. Response time analysis (2) • Solve by: • wi(0) = Ci • wi(n+1) = Ci +SUM j (ceil(wi(n)/Tj )*Cj) • where j : Pj >Pi • From highest priority to lowest • until converges • Schedulable iff • Ri <= Di

  21. For example: • Process set • Proc. T C D P • 1 5 2 3 1 • 2 4 1 2 2 • Process 2: • w2(0) = C2 = 1 • R2 = w2(0) = 1

  22. R2 < D2 ! • Process 1: • w1(0) = C1 = 2 • w1(1) = C1+ceil(w1(0)/T2)*C2 = 3 • w1(2) = C1+ceil(w1(1)/T2)*C2 = 3 • R1 = w1(2) = 3 • R1 < D1 ! • Schedulable!

  23. Past paper questions • 2004 Q2, 2003 Q2, 2002 Q3, 2001 Q4, 2000 Q2.

  24. Run-time feasibility testing in RTSJ • RTSJ Scheduler may implement run-time feasibility checking • Default PriorityScheduler just assumes any process set without aperiodic processes is feasible • Scheduler manages a “feasibility set” of Schedulables • i.e. RealtimeThreads and AsyncEventHandlers • To which any schedulability analysis is applied • Scheduler abstract class and Schedulable interface include various methods for checking feasibility and conditionally changing parameters…

  25. Now feasible? Scheduler class (part) package javax.realtime; public abstract class Scheduler {` … protected boolean addToFeasibility(Schedulable s); protected boolean removeFromFeasibility(Schedulable s); public boolean isFeasible(); public boolean setIfFeasible(Schedulable s, ReleaseParameter r, MemoryParameters m, ProcessingGroupParameters g); … }

  26. Schedulable class (part) package javax.realtime; public interface Schedulable extends Runnable { … public boolean addIfFeasible(); public boolean addToFeasibility(); public boolean removeFromFeasibility(); public boolean setIfFeasible( SchedulableParameters s, ReleaseParameter r, MemoryParameters m, ProcessingGroupParameters g); public boolean setSchedulingParametersIfFeasible( SchedulableParameters s); … }

  27. Summary (1) • Feasibility = schedulability, i.e. whether a set of processes should meet its deadlines • Typically requires simplifying assumptions • E.g. zero time context switch • Simple tests based on CPU utilisation • Total CPU requirements • Liu & Leyland’s utilisation bound • => necessary or sufficient but not both

  28. Summary (2) • Response time analysis • Models worst case simultaneous release of all processes • Simple case models pre-emption by higher priority processes only • Can be extended to consider process conflict (e.g. resource sharing) • RTSJ provides an API for run-time feasibility testing • In Scheduler & Schedulable • Scheduler maintains feasibility set • “Process” = Schedulable, i.e. RealtimeThread or AsyncEventHandler

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