1. University of Virginia CS 6501 Module Feedback Control of Computing Systems Spring 2015 Jack Stankovic

2. University of Virginia Outline Goals Motivation Examples

3. University of Virginia Outline - continued Modeling and System ID Z-transforms and transfer functions (Briefly) First and Second Order Systems P control – shows how it all works (Briefly) I, PI, D, PD and PID control

4. University of Virginia Goals Learn the basics of (discrete time) Feedback Control (FC) Understand the application of the concepts of FC to computer systems Be able to read CPS performance control papers that use FC – more and more are appearing! Understand how to design performance controllers to meet objectives

5. University of Virginia Goals (cont.) If ambitious – learn Matlab on your own –Supports all techniques discussed here and “more” –Toolbox for FC Have a basis in knowledge for more advanced FC techniques that will be needed in CPS

6. University of Virginia Miscellaneous Recommended Text: –Feedback Control of Computer Systems, J. Hellerstein, et.al. –Excellent text Some chapters to be zeroxed (handout) Slides posted – more than used in class High Level Notes Papers: –(Follow on) Use of control in CPS

7. University of Virginia Assignment If you buy recommended text Read Chapters 1, 2, 3, 5, 8, 9 Else read handouts See/read the slides There will be a homework

8. University of Virginia Motivation Design and Implement SW/Systems –Correctness/Meet Performance Requirements –Difficult for large, distributed, open CPS –What analysis techniques do we have? Performance Evaluation Techniques –Queuing Theory? –Formal Correctness? –Performance Control »Feedback Control (Robustness!!!)

9. University of Virginia Motivation Classical Control Applications –Mathematical basis –Tremendous amounts of experience on electro-mechanical systems –In practice - Simple solutions => PID control Rules of thumb –P, PI, PID control (but not restricted to this) »Does not require precise analytical model of the system being controlled »Solutions are typically highly robust »Not ad hoc either As opposed to solutions like - MLFQ found in OSs

10. University of Virginia How has FC/CS been used? Real-time systems (most prominently in RT scheduling) –The fourth paradigm for RTS Congestion control Networking Power control (in cpu) Wireless Sensor Networks OS resource management Middleware Multimedia (streams) Web servers RT Databases

11. University of Virginia Control Applying input to cause system variables to conform to desired values called the reference. –Cruise-control car: f_engine(t)=?  speed=60 mph –E-commerce server: Resource allocation=?  T_response=5 sec –Networking: Flow rate=?  Delay = 1 sec

12. University of Virginia FC Using Differential Equations U(t) R a (t) C? UsUs CPU R c (t) Model (differential equation): Error: E(t)=U s -U(t) Controller C? Convert E(t)  R a (t)

13. University of Virginia Open-Loop Control Compute control input without continuous variable measurement –Simple –Need to know EVERYTHING ACCURATELY to work right »Cruise-control car: friction(t), ramp_angle(t) »E-commerce server: Workload (request arrival rate? resource consumption?); system (service time? fa ilures ?) Open-loop control fails when –We don’t know everything –We make errors in modeling –Things change

14. University of Virginia Questions Is RMA an open loop system? –Yes, you assume you know “everything” and prove it works –What if WCET was wrong? Is basic EDF an open loop system? –Yes, normally assume you know all about the task set, but not arrival times –However, you still have no FC Is EDF with planning an open loop system? –Yes, planning is done at arrival time but no feedback

15. University of Virginia Feedback (closed-loop) Control Actuator Monitor reference control input controlled variable manipulated variable Controlled System + - error control function Controller sample What can this be? SISO vs MIMO

16. University of Virginia Examples - Controlled Variable Response Time Throughput Utilization Deadline Miss Ratio

17. University of Virginia Examples - Manipulated Variable Queue size/Buffer size Scheduling policy Concurrency level Max number of users Max cpu for a process Flow rate Size of timeslice …

18. IBM logo must not be moved, added to, or altered in any way. Background should not be modified. Title/subtitle/confidentiality line: 10pt Arial Regular, white Maximum length: 1 line Information separated by vertical strokes, with two spaces on either side Slide heading: 28pt Arial Regular, blue R120 | G137 | B251 Maximum length: 2 lines Slide body: 18pt Arial Regular, black Square bullet color: teal R045 | G182 | B179 Recommended maximum text length: 5 principal points Group name: 14pt Arial Regular, white Maximum length: 1 line Copyright: 10pt Arial Regular, white Template release: Oct 02 For the latest, go to http://w3.ibm.com/ibm/presentations © 2004 Hellerstein Optional slide number: 10pt Arial Bold, white Indications in green = Live content Indications in white = Edit in master Indications in blue = Locked elements Indications in black = Optional elements Feedback Control of Computing Systems: M1 - Introduction Example: Control of Lotus Notes Architecture RIS = RPCs in System Actual RIS Desired RIS RPCs MaxUsers Server Controller Admin Control Model Controller Notes Server MaxUsers Desired RIS Actual RIS   r(k) e(k) u(k)y(k) Control error: e(k)=r(k)-y(k) System model: y(k)=(0.43)y(k-1) +(0.47)u(k-1)

19. IBM logo must not be moved, added to, or altered in any way. Background should not be modified. Title/subtitle/confidentiality line: 10pt Arial Regular, white Maximum length: 1 line Information separated by vertical strokes, with two spaces on either side Slide heading: 28pt Arial Regular, blue R120 | G137 | B251 Maximum length: 2 lines Slide body: 18pt Arial Regular, black Square bullet color: teal R045 | G182 | B179 Recommended maximum text length: 5 principal points Group name: 14pt Arial Regular, white Maximum length: 1 line Copyright: 10pt Arial Regular, white Template release: Oct 02 For the latest, go to http://w3.ibm.com/ibm/presentations © 2004 Hellerstein Optional slide number: 10pt Arial Bold, white Indications in green = Live content Indications in white = Edit in master Indications in blue = Locked elements Indications in black = Optional elements Feedback Control of Computing Systems: M1 - Introduction Application of Control Theory to a DBMS Database Server Agents Buffer Pools, Sorts, Cache, etc. Disks Statistics Collector Memory Tuner Without Controller T S =26,342 With Controller T S =10,680 59% Reduction in Total RT Good Controller Unstable

20. IBM logo must not be moved, added to, or altered in any way. Background should not be modified. Title/subtitle/confidentiality line: 10pt Arial Regular, white Maximum length: 1 line Information separated by vertical strokes, with two spaces on either side Slide heading: 28pt Arial Regular, blue R120 | G137 | B251 Maximum length: 2 lines Slide body: 18pt Arial Regular, black Square bullet color: teal R045 | G182 | B179 Recommended maximum text length: 5 principal points Group name: 14pt Arial Regular, white Maximum length: 1 line Copyright: 10pt Arial Regular, white Template release: Oct 02 For the latest, go to http://w3.ibm.com/ibm/presentations © 2004 Hellerstein Optional slide number: 10pt Arial Bold, white Indications in green = Live content Indications in white = Edit in master Indications in blue = Locked elements Indications in black = Optional elements Canonical Feedback Loop K(z) G(z)   Controller Target System   D(z) T(z) R(z) E(z) U(z)V(z) H(z) Transducer W(z)   N(z) Y(z) Measured Output Noise Input Disturbance Input Reference Input Want to analyze characteristics of the entire system: its stability, accuracy, settling time, and overshoot (ability to achieve the reference input). SASO It’s all done with transfer functions!

21. University of Virginia Examples - Disturbances Workload (users) Execution of backups Execution of virus scans Or make part of system

22. University of Virginia Examples -Noise Reading output variables via “sensors” has noise –Example: Temperature –Example: Utilization

23. University of Virginia Transducers Converts measured outputs to units expected for inputs (i.e., the units expected by the controller) –Example: convert from queue length to response time by using Little’s formula Response time Number in System Arrival rate Will see other transducers later

24. University of Virginia Advantages of Feedback Control Theory Adaptive resource management heuristics –Laborious design/tuning/testing iterations –Not enough confidence in face of untested workloads Queuing theory –Doesn’t handle feedback –Not good at characterizing transient behavior –Primarily descriptive BUT Feedback Control Theory –Systematic theoretical approach for analysis and design »Methodology to create control algorithm itself –Predict system response and stability to input

25. University of Virginia Control Design Methodology Controller Design Root-Locus PI Control Requirement Analysis Modeling -Analytical - System ID Dynamic model Control algorithm Performance Specifications Satisfy

26. University of Virginia Properties of Controllers Stable (S) Accurate (A) Settling Time (S) Overshoot (O) SASO Robustness – sensitivity analysis (Model is only an approximation) –System model: y(k)=(0.43)y(k-1) +(0.47)u(k-1) -- Parameters of the model:.43 and.47 -- Order of the model (first order – back one unit of time)

27. University of Virginia Performance Specifications (SASO) Settling time Overshoot Controlled variable Time Reference  % Steady StateTransient State Steady state error (Accuracy)

28. University of Virginia System Models Linear vs. non-linear (differential eqns) –Based on electromagnetic laws, Newton’s laws, … –Computer system laws? »Yes – examples … »Primarily use System Identification (empirical technique) Deterministic vs. Stochastic Time-invariant vs. Time-varying Continuous-time vs. Discrete-time

29. University of Virginia Example: Control & Response in an Email Server (IBM) Control (MaxUsers) Response (queue length) Good Slow Bad Useless

30. University of Virginia Real-Time Example There are many soft real-time systems in unpredictable environments –agile manufacturing –command and control or other defense applications –web browsers (audio and video) –real-time database systems

31. University of Virginia Application Requirements Missing some deadlines inevitable and OK –Agile manufacturing »part or product is produced wrong Worst Case Assumptions 100 products/day No errors $10 profit/product Profit - $1,000 Plant Average Case + FC Scheduling Plant 1000 products/day 10 errors ($2 penalty) $10 profit/product Profit - $9,880

32. University of Virginia Example (cont.) For Dynamic RTS in unpredictable environments (some CPS) –WCET too pessimistic, high variance in execution time, unbounded arrival rate, overload unavoidable

33. University of Virginia Motivation - What’s Available RT Scheduling Paradigms –Static - predictable »all is known a priori (WCET, invocation times or worst case rates, resource needs, precedence, etc.) »Cyclic scheduling, RM, table driven, … »open loop –Dynamic - high degree of predictability »all is known except invocation times/rates (use WCET) »Spring algorithm - admission control and planning, or EDF »open loop

34. University of Virginia Claims Despite the significant body of results in real-time scheduling many real world problems and NOT easily supported! We need a new real-time scheduling paradigm based on feedback !!!

35. University of Virginia Feedback Front-End –feedback loops based on real world control –generate timing requirements/rates –generally fixed –handed to scheduling algorithm P1 P2 P3 P4 SchedulingAlgSchedulingAlg

36. University of Virginia Feedback Control System (for the SW side) Controller Actuator Process Sensor feedback System set point controlled variable manipulated variable

37. University of Virginia FC-EDF Scheduling Algorithm PID Controller Service Level Controller Admission Controller EDF Scheduler CPU FC-EDF Accepted Tasks Submitted Tasks MissRatio s MissRatio(t)  CPU o Completed Tasks  CPU i

38. University of Virginia PID controller The PID controller periodically (sampling period) maps the error in term of the deadline miss ratio to the control signal - the required change in the requested CPU utilization P I D

39. University of Virginia Control Questions Decide on PID versus other control algorithm types Determine coefficients of PID control terms –To meet performance specs Establish link between Miss Ratio and Delta CPU –System model

40. University of Virginia Challenges What are the techniques/principles of control theory that can apply to computer systems? How to generate models and laws for computer systems? How to handle stochastics and non-linearities? Note: No new control theory – just – novel ways of applying it => will new control theory emerge?

41. University of Virginia CPS Challenges How to handle distributed systems How to handle systems of systems How to handle excessive delays How to handle missing data How to handle humans in the loop