Feedback Control Real- time Scheduling James Yang, Hehe Li, Xinguang Sheng CIS 642, Spring 2001 Professor 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 T i – (I i, ET i, VAL i, S i, D i ) –I: Logical Versions of T i =( T i1, T i2, …, T ik) –ET: Execution time (ET i1, ET i2, …, ET ik_ ) –VAL: values of different implementations. –S i : Start time, D i :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. C p, C i, C d, 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) = C p *Error(t) + C i IW Error(t) + C D *(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 */ CPU 0 =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( CPU 0 != 0) ACadjust( CPU 0 ); }

Service Level Controller

Admission Controller Decides whether accepts a task or not. If ET ik < 1- CPU(t) accept, else reject. CPU(t) maybe adjusted when SLC controller cannot completely accommodate CPU(t) void Acadjust( CPU 0 ) {CPU(t) = CPU(t) - CPU 0 ; } 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)*0.5 AETi = 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.)