Feedback%20Control%20Real-Time%20Scheduling - PowerPoint PPT Presentation

About This Presentation
Title:

Feedback%20Control%20Real-Time%20Scheduling

Description:

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 ... – PowerPoint PPT presentation

Number of Views:149
Avg rating:3.0/5.0
Slides: 48
Provided by: kang98
Category:

less

Transcript and Presenter's Notes

Title: Feedback%20Control%20Real-Time%20Scheduling


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
  • Doesnt 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
Measured Perf.
Control Signal
Setpoint
Error

Controller
Controlled RT System
-
  • 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

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 gt 1
  • Turn on/off util/MR controller when U 1
  • Turn on/off MR/util controller when U gt 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,
  • -gt Precise workload/system model unknown a
    priori
  • Failure to meet QoS requirements -gt 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?
  • -gt 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 -gt 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 ltlt 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 12 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 31
  • Hi measured perf of class i
  • Ci weight of class i
  • Relative guarantee specifies H1H2 13
  • 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
  • -gt Claim connection delay dominates service
    response time
  • -gt 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/zah
    er/
  • 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?
Write a Comment
User Comments (0)
About PowerShow.com