Feedback Control Real-time Scheduling

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Feedback Control Real-time Scheduling

• James Yang, Hehe Li,
• Xinguang Sheng
• CIS 642, Spring 2001
• Professor Insup Lee

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Agenda

• Motivation.
• Feedback control system overview.
• Important Issues of Feedback control real-time
  scheduling.
• FC-EDF by UVA.
• Conclusion.

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Motivation

• Static real-time scheduling algorithms
• Requires complete knowledge of task set and
  constraints.
• eg. RM algorithm
• Dynamic algorithms
• Does not have complete knowledge of task set.
• Resource sufficient Vs. insufficient.
• eg. Earliest Deadline first, spring algorithm

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Problems

• They are all open-loop algorithms.
• Works poorly in unpredictable dynamic systems.
  Because they are usually based on worse-case
  work-load parameters.
• Most dynamic real world applications have
  insufficient resources and unpredictable
  workload.
• Assumes that timing requirements(such as
  deadline)are known and fixed.

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Agenda

• Motivation.
• Feedback control system overview.
• Important Issues of Feedback control real-time
  scheduling.
• FC-EDF by UVA.
• Conclusion.

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Feedback Control Scheduling

• Defines error terms for schedules, monitor the
  error, and continuously adjust the schedule to
  maintain satisfactory performance.
• Based on adaptive control theory, stochastic
  control.
• The result would be that many applications meet
  significantly more deadlines thereby improving
  the productivity.

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Approach

• Controlled Variable.
• Set point.
• Error set point current value of CV.
• Manipulated Variable.
• Feedback Loop.

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Agenda

• Motivation.
• Feedback control system overview.
• Important Issues of Feedback control real-time
  scheduling.
• FC-EDF by UVA.
• Conclusion.

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Feedback control real-time scheduling

• Choices for control variables, manipulated
  variables, set points.
• Choice of appropriate Control functions. Is PID
  enough?
• Stability Problem of feedback control in the
  context of real-time scheduling?
• How to tune Control parameters?
• How significant is the overhead and how to
  minimize it?
• How to integrate a runtime analysis of time
  constraints with scheduling algorithms?

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Agenda

• Motivation.
• Feedback control system overview.
• Important Issues of Feedback control real-time
  scheduling.
• FC-EDF by UVA.
• Conclusion.

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FC-EDF algorithm

• Control Variable miss rate of admitted tasks
  MissRatio(t)
• Set Point 1.
• Manipulated Variable System Load(requested CPU
  utilization).
• Controller PID Controller.
• Scheduler EDF algorithm.
• Actuators Service level Controller, admission
  Controller

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FC-EDF Architecture
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Task Model

• Imprecise Computation Model
• Ti (Ii, ETi, VALi, Si, Di)
• I Logical Versions of Ti ( Ti1, Ti2, , Tik)
• ET Execution time (ETi1, ETi2, , ETik_)
• VAL values of different implementations.
• Si Start time, DiSoft deadlines
• Different Version of task are called service
  levels.
• In the future, extend deadlines.

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PID Controller

• Maps the miss ratio of accepted tasks to the
  change in requested utilization so as to drive
  the miss ratio back to set point.
• Cp, Ci, Cd , are tunable parameters.

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PID Controller cont.
/ called every sampling period PS / void
PID() Get Error(t) during last sampling
period P S /PID control function/
?CPU(t) Cp Error(t) Ci IW Error(t) CD
(Error(t-DW) - Error(t))/DW /
greedily increase system load when lightly loaded
/ if(?CPU(t) ³ 0) ?CPU(t) ?CPU(t)
?CPU A / call the Service Level Controller,
which returns the portion of ?CPU(t)
that is not completed in it / ?CPU0
SLC(?CPU(t)) / call the admission controller
to accommodate the portion of ?CPU(t) that is
not completed by SLC, if there is any /
if(?CPU0 ! 0) ACadjust(?CPU0)  
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Service Level Controller
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Admission Controller

• Decides whether accepts a task or not.
• If ETik lt 1- CPU(t) accept, else reject.
• CPU(t) maybe adjusted when SLC controller cannot
  completely accommodate ?CPU(t)
• void Acadjust(?CPU0)
• CPU(t) CPU(t) - ?CPU0
• Given an example.

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Admission Controller(example)

• Suppose CPU(t) 80,
• SLC could increase 10 of the cpu use.
• AC could only admit tasks with 10 usage of cpu
  time, instead of 20

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Experiment Results

• Simulation Model
• Workload Model
• Implementation of FC-EDF
• Performance Matrices
• Experiment A Steady Execution time
• Experiment B Dynamic Execution Time

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Simulation Model
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Workload Model

• Each source is characterized with a period (P)
  (the deadline of each task instance equals its
  period),
• Worst case execution times WCETi, best case
  execution times BCETi, estimated execution
  times EETi, average execution times AETi
• Each tuple (P, WCETi,BCETi, EETi, AETi, VALi)
  characterizes a service level
• EETi (WCETiBCETi)0.5
• AETi EETietf
• etf execution time factor denotes the accuracy
  of the estimation.

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Implementation of FC-EDF
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Performance Matrices

• MRA Miss Ration among admitted tasks.
• CPU utilization how much the CPU is used.
• HRS hit ratio among submitted tasks is a measure
  of throughput.
• VCR Value completion ratio quality of results.
  Task with lower service level contributes to
  lower value.

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Performance Conclusion

• FC-EDF provides soft performance guarantee for
  admitted tasks.
• Achieving high system utilization.
• High throughput.
• Effectively adapts to the radical changes in the
  execution time and system load and maintains
  satisfactory performance.

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Overhead
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Conclusion

• Presented the need for feedback control
  scheduling
• Presented a system developed by UVA.
• Questions?

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Control Theory Terminology

• Process Variable
• Error
• Overshoot
• Steady state error
• Settling time

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PID Controller

• PID Proportional, Integral, Derivative
• Proportional the controller output is
  proportional to the error.
• Integral output is proportional to the amount of
  time the error is present.
• Derivative output is proportional to the rate of
  change of the measurement of error.

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PID Controller (cont.)