Feedback Control Real-Time Scheduling

1. Feedback Control Real-Time Scheduling C. Lu, J.A. Stankovic, G. Tao, and S.H. Son, Design and Evaluation of a Feedback Control EDF Scheduling Algorithm,  IEEE Real-Time Systems Symposium (RTSS'99), December 1999.

2. Motivation for Feedback control Scheduling • Open-loop scheduling paradigms perform poorly in unpredictable dynamic systems where the workload cannot be accurately modeled • Many complex applications, e.g., robotics and agile manufacturing, are dynamic and operate in a non-deterministic environment where precise workload is not known • Challenging to build real-time systems providing predictable performance in a highly uncertain environment • Feedback control can support the target performance even when the workload varies dynamically via graceful QoS degradation in a closed-loop loop

3. Motivation • Apply control theoretic approaches to real-time performance management • Feedback control is well known for its robustness, e.g., cruise control or chemical reactor control, in the presence of disturbances • Doesn’t need a precise system model • If the precise system model is known, feedback control is not necessary • Dynamically adapt the system behavior to achieve the targe performance (also called set point) in the feedback loop

4. Feedback Control Concepts • Set-point: Target performance to achieve, e.g., 1% deadline miss ratio • Measured perf: Actual perf, e.g., actual (deadline) miss ratio, measured at the current sampling period • Error = set-point – measured perf = target miss ratio – current miss ratio Measured Perf. Control Signal Setpoint Error + Controller Controlled RT System -

5. Feedback Control Loop • Periodically measure and compare the perf to the set point to determine the error • Controller computes the control signal based on the error and controlled system model • Actuator, e.g., admission controller or QoS manager, change the value of the manipulated variable to control the system

6. FC-EDF Architecture

7. Miss Ratio Control Model • At kth sampling instant, miss ratio is: m(k) = m(k-1) + g(k) ∆u(k-1) where • m(k-1): miss ratio at the (k-1)th sampling period • g(k): miss ratio gain • ∆u(k-1): utilization adjustment by admission control and QoS adaptation at the (k-1)th sampling period

8. Miss Ratio Control Model • Instead of considering time-varying miss ratio gain g(k), they took G = maximum (miss ratio/unit load increase) Miss Ratio Miss ratio control is very challenging due to the nonlinear nature of MR increase!! Load 0.9 1 1.1 1.2 1.3 ...

9. Miss Ratio Control Model • Replace g(k) with G m(k) = m(k-1) + g(k)∆u(k-1) → m(k) = m(k-1) + G∆u(k-1) • Take z-transform to convert to frequency domain • Convert from time domain to frequency domain • You can do arithmetic manipulation rather than solving (partial) differential equations

10. Apply z-transform to m(k) = m(k-1) + G∆u(k-1) M(z) = z-1M(z) + z-1∆U(z) M(z) = (G/z-1) ∆U(z) • Transfer function T(z) = output/input = M(z)/U(z) = G/z-1

11. Utilization Control Model • Miss ratio controller itself is not stable • MR controller is saturated when utilization is less than 1 if EDF is used • In their later work, they added utilization controller • Utilization controller works when U ≤ 1, miss ratio controller works when U > 1 • Turn on/off util/MR controller when U ≤ 1 • Turn on/off MR/util controller when U > 1 • Good idea?

12. Controller Tuning • Given the control model shown in the previous slide, apply Root Locus model to graphically tune the controller in Matlab to support the stability & specified transient performance such as the overshoot and settling time

13. Feedback performance control in software services T.F. Abdelzaher, J.A. Stankovic, C. Lu, R. Zhang, and Y. Lu, Feedback Performance Control in Software Services, IEEE Control Systems, 23(3): 74-90, June 2003.

14. Overview • SW systems become larger and bigger • Performance guarantee required, e.g., in web-based e-commerce • Control theory • Promising theoretical foundation for perf control in complex SW applications, e.g., real-time scheduling, web servers, multimedia control, storage mangers, power management, routing in computer networks, …

15. Overview • Software performance assurance problems • Feedback control problems focused on web server performance guarantee problems • Data centers

16. SW performance control • Less rigorous guarantees on perf and quality • Most SW eng. research deals with the development of functionally correct SW • Functional correctness is not enough! • Timeliness in embedded systems • Correct but delayed action can be disastrous • Non-fucntional QoS attributes, e.g., timeliness, security, availability, …

17. Traditional approaches for perf guarantees • Worst case estimates of load & resource availability • Recall EDF, RM, DM, Priority Ceiling Protocol, …

18. New demand for performance assurance • QoS guarantees required in a broader scope of applications run in open, unpredictable environments • Global communication networks enabling online banking, trading, distance learning, … • Points of massive aggregation suffering unpredictable loads, potential bottlenecks, DoS attacks, … -> Precise workload/system model unknown a priori • Failure to meet QoS requirements -> loss of customers or financial damages • Worst case analysis/overdeisgn could be overly pessimistic or wasteful • Solid analytic framework for cost-effective perf assurance required

19. Challenges • How to model SW architecture? • How to map a specific QoS problem into a feedback control system? • How to choose proper SW sensors and actuators to monitor and adjust perf and workloads/resource allocation? • How to design controllers for servers? -> This paper focuses on web servers

20. QoS metrics • Delay metrics • Proportional to time: queuing delays, execution latencies, service response time • Rate metrics • Inversely proportional to time • Connection bandwidth, throughput, packet rate

21. Time-related perf attributes • Can be controlled by adjusting resource allocation • Queuing theory can predict perf given a particular resource allocation or vice versa • Queuing theory only works for Poisson arrival patterns • Queuing theory can only predict average perf even if this assumption holds • Arrival patterns in web applications follow heavy-tailed distribution -> Bursty arrival patterns

22. Service architecture Liquid task model Fig. 1 Server architecture: (a) computing model (b) control-oriented representation

23. Liquid task model • Ci << Di • Takes Ci units of time to serve request i • Di is the max tolerable response time • Tolerable response time is finite • Service times are infinitesimal • Progress of requests through the server queues ≈ Fluid flow • Service rate at stage k = dNk(t)/dt where Nk is #requests processed by stage k

24. Liquid task model • Volume at time T≈ #requests queued at stage k = ∫T(Fin – Fk) • Fk: service rate at stage k • Fin: request arrival rate to this stage • Valves: points of control, i.e., manipulated variables such as the queue length • Liquid model does not describe how individual requests are prioritized • Control theory can be combined with queuing theory or real-time scheduling

25. Server modeling • Difference equation to model web servers • y(k): perf, e.g., delay or throughput, measured at the kth sampling period • U(k): control input at the kth sampling period • ARMA (Auto Regressive Moving Average) model • y(k) = a1y(k-1) + a2y(k-2) + … + any(k-n) + b1u(k-1) + b2u(k-2) + … + bnu(k-n) • n: system order – higher order model is usually (not always!) more accurate but more complex • Transfer function can be derived • Web proxy cache model [4] • TCP dynamics [5]

26. Transfer function • Shows the relation between input and output • Apply z-transform to y(k) in the previous slide • Open loop transfer function vs. closed-loop transfer function

27. Resource allocation for QoS guarantees • Allocate more/less resource = open/close a valve • Need actuators to control resource allocation or QoS provided by the system

28. SW system actuators • Input flow actuators • Admission control • Control queue length, server utilization, … • Reject some requests under overload

29. SW system actuators • Quality adaptation actuators • Change processing requirements to increase server rate under overload • E.g., Return abbreviated web page under overload • Tradeoff btwn delay & quality • Service level m in a range [0, M] where 0 is rejection

30. Resource reallocation actuator • Alter the amount of allocated resources • Usually applicable to multiple classes of clients, e.g., dynamically reallocate disk space for differentiated web caching to support the service delay ratio 1:2 between two service classes [4,7]

31. QoS Mapping • Convert common resource management & SW perf assurance problems to FC problems • Absolute convergence guarantee • Relative guarantee • Resource reservation guarantee • Prioritization guarantee • Statistical multiplexing guarantee • Utility optimization guarantee

32. Absolute convergence guarantee • Convergence to the specified problem • Overshoot: Maximum deviation • Settling time: Time taken to recover the desired perf

33. Absolute convergence guarantee • Rate & queue length control • Result in linear FC • (Flow) rate can be directly controlled by actuators • Queue length can be linearly controlled by controlling the flow • E.g., server utilization control loop

34. Absolute convergence guarantee • Delay control • More difficult • Delay is inversely proportional to flow • Queuing delay d = Q/r where Q is queue length & r is service rate • Nonlinear

35. Relative guarantee • For example, fix the delays of two traffic classes at a ratio 3:1 • Hi: measured perf of class i • Ci: weight of class i • Relative guarantee specifies H1:H2 = 1:3 • Set point = 1/3 • Error e = 1/3 – H1/H2

36. Relative guarantee in Apache web server • Controlled variable: relative delay ratio • Manipulated variable: #allocated processes per class to control connection delay • HTTP protocol summary • A client, e.g., a web browser, establishes a TCP connection with a server process • The client submits an HTTP request to the sever over the TCP connection • The server sends the response back to the client • Keep open the TCP connection for the Keep Alive interval, e.g., 15s -> Claim connection delay dominates service response time -> Scheduling can also significantly affect relative delay ratio, but it is not considered

37. Relative guarantee in Apache web server • System identification based on the ARMA model (Least square method) • Also called System Identification (SYSID) in control theory • Randomly change per class process allocations • Measure response time

38. Relative guarantee in Apache web server • Perf settings • 4 Linux machines run the Surge web workload generator • 1 Linux machine runs the Apache web server • Suddenly increase #premium clients by 100 at time 870s

39. Relative guarantee in Apache web server • Perf results Open Loop Stable? Closed Loop

40. Related work • ControlWare • CPU scheduling • Storage management • Network routers • Power/heat management • RTDB

41. Conclusions • Feedback control is applicable to managing performance in SW systems • Future work • Adaptive/robust control • Predictive control • Apply to other computational systems such as embedded systems

42. Adptive Control: Self-Tuning Regulator • Dynamically estimate a model of the system via the Recursive Least Square method • Controller will accordingly set the actuators to support the desired perf.

43. References (HP Storage Systems Lab) • Designing controllable computer systems, Christos Karamanolis, Magnus Karlsson and Xiaoyun Zhu. USENIX Workshop on Hot Topics in Operating Systems (HotOS), June 2005, pp. 49-54, Santa Fe, NM. • Dynamic black-box performance model estimation for self-tuning regulators, Magnus Karlsson and Michele Covell. International Conference on Autonomic Computing (ICAC), pp. 172-182, June 2005, Seattle, WA.

44. Autonomic Computing • General, broader research issues regarding self-tuning, self-managing, self-* systems • Autonomic computing web site • http://autonomiccomputing.org/ • IBM • http://www.research.ibm.com/autonomic/index.html • Adaptive Systems Department

45. Some University Labs • Tarek Abdelzaher: http://www.cs.uiuc.edu/homes/zaher/ • Chenyang Lu: http://www.cse.wustl.edu/~lu/

46. Next class • We will discuss papers from our RTES Lab on feedback control of software system • K. D. Kang, J. Oh, Y. Zhou, "Backlog Estimation and Management for Real-Time Data Services", 20th Euromicro Conference on Real-Time Systems (ECRTS '08), July 2-4, Prague, Czech Republic. • C. Basaran, K. D. Kang, M. H. Suzer, K. S. Chung, H. R. Lee, K. R. Park, "Bandwidth Consumption Control and Service Differentiation for Video Streaming," 17th International Conference on Computer Communications and Networks (ICCCN '08), August 3 - 7, 2008, St. Thomas U.S. Virgin Islands.

47. Questions?