Harini Ramaprasad, Frank Mueller North Carolina State University Center for Embedded Systems Researc

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Harini Ramaprasad, Frank MuellerNorth Carolina
State UniversityCenter for Embedded Systems
Research
Tightening the Bounds on Feasible Preemption
Points
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Motivation

• Timing Analysis
• Calculation of Worst Case Execution Times (WCETs)
  of tasks
• Required for scheduling of real-time tasks
• Schedulability theory requires a-priori
  knowledge of WCET
• Estimates need to be safe
• Static Timing Analysis an efficient method to
  calculate WCET of a program!
• Data caches (D) introduce unpredictability in
  timing analysis

• Data caches
• Improve Performance Significantly
• Complicate Static Timing Analysis for a task

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Preemptive scheduling

• Practical Real-Time systems
• Multiple tasks with varying priorities
• Higher prio. task may preempt a lower prio. task
  at any time
• Additional misses occur when lower prio. task
  restarted
• WCET with preemption delay required

Static Timing Analysis becomes even more
complicated!
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Data Cache Reference Patterns (Prior Work)

• Data Cache Analyzer added to Static Timing
  Analysis framework
• Enhanced Cache Miss Equations (Ghosh et al.)
  framework
• ? D miss/hit patterns for memory references
• Used for loop-nest oriented code
• Scalar and array references analyzed
• Considers only a single task with no preemptions
• Patterns fed to timing analyzer to tighten WCET
  estimate
• Necessary terminology
• Iteration point
• Represents an iteration of a loop-nest
• Set of all iteration points Iteration Space

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Static Timing Analyzer Framework
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Methodology

• Task Schedulability ? Response Time Analysis used
• Steps involved in calculation of WCET with
  preemption delay
• Calculate max. of preemptions possible for a
  task
• Identify placement of preemption points in
  iteration space
• Calculate preemption delay at a certain point

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Methodology Analysis Phases

• Phase 1 Single-Task Analysis
• For every task
• Build D Reference Patterns assuming NO
  preemptions
• Calculate stand-alone WCET and BCET
• Performed once for each task using
• D analyzer static timing analyzer
• Phase 2 Preemption Delay Calculation (in
  task-set context)
• Per-job analysis done
• All jobs within hyperperiod considered
• Proof of correctness is in paper

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Identification of Preemption Points

• Identification of preemption points for a job
• All higher priority (hp) jobs can potentially
  preempt
• Eliminate infeasible points
• In every interval between potential preemption
  points
• Check whether job can be scheduled
• ? use BCET and WCET of hp jobs
• Check whether portion of job remains beyond
  interval
• Count preemption point only if both criteria
  satisfied

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Eliminating Infeasible Preemption Points
T1
T1
T0
T0
T0
BEST CASE
WORST CASE
0
10
20
30
40
50
Partial timeline for task T1
Infeasible since T1 is already done before point
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Eliminating Infeasible Preemption Points
Max exec time for T2 in interval
T2
T1
T1
T0
T0
T0
T0
BEST CASE
WORST CASE
0
10
20
30
40
50
60
Partial timeline for task T2
Min exec time for T2 in interval
Infeasible since T2 not scheduled in interval ?
cannot be preempted
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Placement of Points within Job

• Identification of worst-case scenario
• Preemption point placement
• Bound by range of exec. time available for task
  in interval
• Interact with Timing Analyzer
• ? find iteration point corresponding to point in
  time

• Min iter point reached in shortest possible time
• Min iter point reached in longest possible time
• Max iter point reached in shortest possible time
• Max iter point reached in longest possible time

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Preemption Delay at a Point

• Access Chain building
• Build time-ordered list of all mem. refs in task
• Connect all refs accessing same D set to form
  chain
• Different cache sets shown with different colors
• Assign weights to every access point
• Weight
• distinctly colored chains that cross the point
• indicates misses if preemption at that point
• Count only chains for D sets used by a higher
  prio. task
• Count only if next point in chain is a HIT

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Experimental Results
Task set with U 0.8, hyperperiod 5000000
Our new method gives the tightest bound on of
preemptions in all cases
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Maximum of preemptions (U 0.8)
Our method gives tightest bound on preemptions
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WCET w/ delay (U 0.8)

• Our method gives lowest preemption delay and
  hence WCET
• Since WCET is unique to task, theres no pattern
  of increase/decrease

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Response Time (U 0.8)

• Response times monotonically increase as task
  priority decreases
• Our method has least rate of increase
• All task-sets deemed schedulable by our method

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Varying WCET/BCET Ratios

• Our method produces significantly lower
  preemptions
• As WCET/BCET increases
• preemptions increases upto a point
• preemptions decreases slightly beyond point
• preemptions is lowest when WCET/BCET 1
• Max increase beyond lowest 30

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Critical Instant

• Does Critical instant (CI) occur on simultaneous
  task release?
• Not when preemption delay is considered!
• When preemption delay is considered
• CI occurs when tasks are released in reverse
  priority order
• Similar to effect of critical sections/blocking!
• Considering all jobs in hyperperiod eliminates
  safety concerns

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Critical Instant
RT 12
Task Set
1. Preemption with WCET - no phasing

• In 1, response time of T3 is more
• In 1, response time of T4 is shorter

RT 12.25
2. Preemption with WCET - phasing
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Conclusions

• Contributions
• Determination of critical instant under cache
  preemption
• Calculation of tighter bound on max preemptions
• Construction of realistic worst-case scenario for
  preemptions
• Results show significant improvements in
• Max preemptions
• WCET with preemption delay
• Response time
• Improvements
• Order of magnitude over simplistic methods
• Half an order of magnitude over best prior method
• Observations
• As WCET/BCET increases, preemptions increases
  by 30
• Some tools dont provide BCET
• Compromise ? use BCET 0, get slightly
  pessimistic results

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Future Work

• Consider phased task-sets in experiments
• Extend framework to deal with dynamic scheduling
  policies
• Recalculate priority at every interval

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Related Work

• C.-G. Lee et al.
• 1. Analysis of cache-related preemption delay in
  Fixed-priority preemptive scheduling.
• 2. Bounding cache related preemption delay for
  real-time systems.
• Basic ideas involved in calculating cache related
  preemption delay
• Works only with instruction caches
• J. Staschulat et al.
• 1. Multiple process execution in cache related
  preemption delay analysis.
• 2. Scheduling analysis of real-time systems with
  precise modeling of cache related preemption
  delay.
• Complete framework to calculate cache related
  preemption delay
• Works only with instruction caches
• Takes indirect preemption effects into
  consideration

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Thank you!

• Questions?