1. Feedback Control Real-time Scheduling
James Yang, Hehe Li,
Xinguang Sheng
CIS 642, Spring 2001
Professor Insup Lee

2. Agenda Motivation. Feedback control system overview.
Important Issues of Feedback control real-time scheduling.
FC-EDF by UVA.
Conclusion.
I am going to start with motivation for feedback realtime control systems, then I am going to give an overview of feedback control systems, for those who are not familiar with it. Then I will discuss important issues and questions to answer when designing the system, I’ll use FC-EDF developed by University of Virginia to illustrate these issues. Finally is the conclusion

3. Motivation Static real-time scheduling algorithms Dynamic 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
Real time scheudling algorithms fall into two categories: static scheduling and dynamic scheduling.
Static scheduling constraints: deadlines, computation times.
RM algorithm represents a major paradigm in static scheduling
Dynamic: for example new tasks may arrive at any future unknown time and request to be scheduled.
It could be further divided into: algorithms that works in resource sufficient and insufficient environments.

4. 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.
Open loop refers to the fact that once schedules are created, they are not adjusted based on continous feedback.
Eg: systems with open-loop scheulders such as EDF or spring are usually designed based on worst-case worklod parameters. When the workload of the system are not available, they could result in highly underutilized system based on extremly persimistic estimation of workload.
Timing requirements:

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

6. 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.

7. Approach Controlled Variable. Set point.
Error = set point – current value of CV.
Manipulated Variable.
Feedback Loop.
Controlled variable: the quantity of the output that is measured and controlled.
Set point represents the correct value for controlled variable.
Manipulated variable: the quantity that are changed by controller to affect the value of the controlled variable.

8. Agenda Motivation. Feedback control system overview.
Important Issues of Feedback control real-time scheduling.
FC-EDF by UVA.
Conclusion.
In real-time scheduling, a scheduling system is a feedback control system, the scheduler is the controller, and it utilizes the control techniques to achieve satisfied system performance.

9. 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?

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

11. 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

12. FC-EDF Architecture

13. 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, Di:Soft deadlines
Different Version of task are called service levels.
In the future, extend deadlines.
Imprecise computation model: break down the task into mandatory and optional.

14. 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.

15. 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);  }

16. Service Level Controller

17. Admission Controller Decides whether accepts a task or not.
If ETik < 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.
-20% cpu(t),

18. 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%

19. Experiment Results Simulation Model Workload Model
Implementation of FC-EDF
Performance Matrices
Experiment A: Steady Execution time
Experiment B: Dynamic Execution Time

20. Simulation Model

21. 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 =(WCETi+BCETi)*0.5
AETi = EETi*etf
etf : execution time factor denotes the accuracy of the estimation.

22. Implementation of FC-EDF

23. 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.

24. 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.
Value completion ration: VCR quality of results.

26. 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.

27. Overhead

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

29. Control Theory Terminology
Process Variable
Error
Overshoot
Steady state error
Settling time

30. 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.

31. PID Controller (cont.)