Post on 29-Mar-2015
Feedback Control Real-time Scheduling
James Yang, Hehe Li, Xinguang Sheng
CIS 642, Spring 2001Professor Insup Lee
Agenda
• Motivation.• Feedback control system overview.• Important Issues of Feedback
control real-time scheduling.• FC-EDF by UVA.• Conclusion.
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
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.
Agenda
• Motivation.• Feedback control system overview.• Important Issues of Feedback
control real-time scheduling.• FC-EDF by UVA.• Conclusion.
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.
Approach
• Controlled Variable.
• Set point.• Error = set point
– current value of CV.
• Manipulated Variable.
• Feedback Loop.
Agenda
• Motivation.• Feedback control system overview.• Important Issues of Feedback
control real-time scheduling.• FC-EDF by UVA.• Conclusion.
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?
Agenda
• Motivation.• Feedback control system overview.• Important Issues of Feedback
control real-time scheduling.• FC-EDF by UVA.• Conclusion.
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
FC-EDF Architecture
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.
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.
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) 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); }
Service Level Controller
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.
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%
Experiment Results
• Simulation Model• Workload Model• Implementation of FC-EDF• Performance Matrices• Experiment A: Steady Execution time• Experiment B: Dynamic Execution
Time
Simulation Model
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)*0.5AETi = EETi*etf
• etf : execution time factor denotes the accuracy of the estimation.
Implementation of FC-EDF
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.
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.
Overhead
Conclusion
• Presented the need for feedback control scheduling
• Presented a system developed by UVA.
• Questions?
Control Theory Terminology
• Process Variable• Error• Overshoot• Steady state error• Settling time
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.
PID Controller (cont.)