An On-line Approach to Reduce Delay Variations on Real-Time Operating Systems

1
An On-line Approach to Reduce Delay Variations on
Real-Time Operating Systems

• Shengyan Hong

2
Problem

• Reduce Delay Variations of Tasks

3
Why Important?

• Delay Variations degrade hardware performance,
  e.g. sluggish response, erroneous behavior.

4
Task Model

• Original Task Model (Ci, Di, Pi)
• IMF Task Model
• initial subtask (Cii, Dii, Pi, Oii0)
• mandatory subtask (Cim, Dim, Pi, Oim0)
• final subtask (Cif, Dif, Pi, Oif)
• ADR Task Model
• initial subtask (Cii, Diinew, PiinewPi/Mi)
• mandatory subtask (Cimnew, Dimnew, Pi)
• C represents execution time, D represents
  deadline, P represents period, O represents
  release time.

5
A Trick in Problem

• Suppose we have a task in original model, how to
  split mandatory subtask in IMF model to form ADR
  model?
• Example, a task (Ci5000,Di27000,Pi27000), and
  Cii and Cif consumes 10 of Ci,
• The optimal scheme is to cut 8 splits from the
  mandatory subtask in IMF model.

The constraints (1), (2) and (3) help us get it.
(1)
(2)
(3)
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Quadratic Programming Problem
Objective Function
(4)
,where each term is an approximation of
.
(5)
Schedulability Constraint
or
Constraints (5), (6), (7) guarantees the correct
running of Real-Time Operating Systems.
(6)
Deadline Constraints
(7)
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ADR Algorithm Flow
Adjust deadlines of mandatory subtasks, and
search a new solution, and the process is
repeated until the algorithm converges.
Search an initial feasible solution with optimal
model transformation.
For any fixed deadlines of mandatory subtasks,
compute an updated feasible solution, i.e.
deadlines of initial subtasks.
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Initial Results

• A custom simulator by C running on Linux
• A task set with first two tasks decomposable
• Compare results with original Delay Variations,
  and two representative methods
• The smaller DV, the better the method is.
• When workload changes, see which method can adapt
  to it.

Task Name Decomp. Exec. Time Deadline Period
Speed Yes 5000 27000 27000
Strength Yes 8000 30000 32000
Position No 10000 45000 500000
Sense No 13000 60000 70000
Task Name Decomp. Exec. Time Deadline Period
Speed Yes 5000 27000 27000
Strength Yes 8000 30000 32000
Position No 10000 45000 50000
Sense No 13000 60000 70000
Task Name Delay Variations of Orig/DRB/TBB/ADR
Speed 33.33/41.48/16.67/ 2.96
Strength 28.13/31.25/22.50/ 0.08
Position 4.40/ 3.40/02.60/06.28
Sense 48.57/32.86/33.57/15.57
Task Name Delay Variations of Orig/DRB/TBB/ADR
Speed 33.33/41.48/16.67/ 2.96
Strength 28.13/31.25/22.50/ 0.08
Position 44.00/34.00/26.00/62.80
Sense 48.57/32.86/33.57/15.57
Task Name Delay Variations of Orig/DRB/TBB/ADR
Speed 33.33/41.48/16.67/ 7.7
Strength 28.13/31.25/22.50/ 0.87
Position 44.00/34.00/26.00/22.09
Sense 48.57/32.86/33.57/39.86
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The Road Ahead

• If initial subtask and final subtask do not have
  the same execution time, what to do?
• If mandatory subtask can not be divided, what to
  do?
• Test more task sets in the simulator.
• Show the performance of the proposed approach and
  the existing methods.

10
Questions?
11
Second Trick in Problem
(6)
(7)

• Deadline constraints (6) and (7) incorporate the
  subtask dependencies to schedulability test
  without being overly pessimistic.
• From (6), we can derive another constraint for Mi
  .

(8)