Feedback Control in Quality of Services

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Feedback Control in Quality of Services

• Zengzhong Li
• zengzhong_at_cs.virginia.edu

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Outline

• What is feedback control in software system?
• How to map the QoS to feedback control?
• Any implementation example?
• How to build by computer engineers?
• Why feedback control in QoS?

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What is feedback control
closed loop
Controller
System

input
output
error
-

• using difference signals, determined by comparing
  the actual values of system variables to their
  desired values, as a means of controlling a
  system
• ----F.L. Lewis, Applied Optimal Control and
  Estimation

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More detail in software system
System
Controller
control function
control input
manipulated variable
Actuator
error
sample
controlled variable
Monitor

-
reference

• Monitor(sensor) measure system performance
  metric
• Actuator manage resource allocation
• Reference desired performance metric

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Control design methodology

• Classical Control
• Mainly in the frequency domain and the s-plane
• Relying on transform methods
• Primarily applicable for linear time-invariant
  systems
• Expression example Y(s)U(s)G(s)
• Modern Control
• a time-domain technique
• An exact state-space model describing the
  internal state of the system
• Expression example dx/dt Ax Bu
• y Cx

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QoS Mapping (Cont.)

• What is QoS Mapping?
• Describe how to use feedback control to solve a
  particular QoS control problem, associated with a
  control loop template
• Different guarantee, different template
• Absolute Convergence Guarantee
• Resource Reservation Guarantee
• Prioritization Guarantee
• Statistical Multiplexing Guarantee
• Relative Guarantee
• Utility Optimization Guarantee

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QoS Mapping (Cont.)

• Absolute Convergence Guarantee
• Converges within a specified exponentially
  decaying envelope to a fixed value, Rdes.
• the maximum deviation Rdes. R is bounded at all
  times

• Classification
• Rate and queue-length control
• proportional
• Delay Control
• inversion

-
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QoS Mapping

• Relative guarantee
• Keep the ratio between the performance levels of
  different traffic classed fixed, namely, make

• Total amount of allocated resource remains
  constant, if the controller is linear
• The controller can be linear, but the loop is
  nonlinear
• What about the nonlinear controller?
• Modify the meaning of controller output
• Change the controller to linear

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Too abstract? Example!
A web server case for guaranteeing relative
delays
?
Controlled variable?
?
Controller reference?
monitor
controller
Manipulated variable?
?
TCP connection requests
Server Process
TCP listen queue
connection scheduler
HTTP response
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Feedback architecture (cont.)

• Delay definition
• Connection delay
• Process delay
• Server process
• Fixed pool of size M
• Communication with connection scheduler
• Monitor
• Sampling the average connection delays for all
  classes
• Connection scheduler
• FIFO connection queue for different classes
• Class ks relative share
• The most processes be allocated to class k
• Dispatch connection at the front of the highest
  priority class
• Decide process proportion by desired relative
  delay
• Static mapping wont work well!

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Feedback architecture
Math description of controller - Controller
design
Sampling average connection delay
Math description of system - System
identification
monitor
controller
Server Process
TCP listen queue
connection scheduler
FIFO connection queue
Fixed process pool
HTTP response
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Controller (cont.) - for relative guarantee
Controller
System

reference
error
-

• Reference
• Desired delay ratio between class k and k-1
• Feedback Input
• Sampled delay ratio between class k and k-1
• Controller input
• Delay error
• Controller Output
• Current process ratio to drive the connection
  scheduler
• Inversion relationship between error and current
  process ratio
• Do not expect a inversion controller
• N-1 basic controller for N classes general
  controller

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Controller - for relative guarantee

• Math description
• Control method
• Proportional control
• may have non-zero steady-state error
• Integral control
• improves steady-state tracking
• PI control
• Discrete form of basic controller
• g controller gain
• r controller zero
• The performance of web server significantly
  depends on the controller parameters

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System Identification
Model parameters
White-noise generator
Least squared estimator
monitor
Server Process
TCP listen queue
connection scheduler
HTTP response

• Model structure
• White noise input
• Least squares estimator
• iteratively update the parameter estimates such
  that accumulative error is minimized

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Controller tuning (cont.)

• Close-loop transfer function

ci are poles of the function and decide the
system behavior -We can tune controller gain g
and controller zero r to change the poles
distribution and so satisfy the performance specs
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Controller tuning

• Root locus design
• graphical technique that plots the traces of
  poles of a closed-loop system on the z-plane
• Attributes
• Stability boundary z1 (Unit circle)
• Settling time distance from Origin
• Speed location relative to Im axis
• Right half slower
• Left half faster
• Results
• Tune the g0.3, r0.05, P00.70,P10.38i,P20.38-
  i
• Stability all the closed-loop poles are in the
  unit cycle
• Settling time270 sec
• Steady state error zero

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Evaluation of a Server with two classes

• Workload
• 4 client machines, each had 100 users. At start,
  only one machine from class 0 and two machine
  from class 1 generated HTTP requests. The second
  machine from class 0 started after 870 sec
• Close-loop server
• W1/W03, P0(m)/P1(m) initialized to 1
• Open-loop server
• Fine-tuned based on the original workload
• Evaluation
• Robust to workloads varying

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Design summary
For control engineer or computer engineer?

• QoS specification
• QoS mapping to Control loop
• Connect all components
• Controller modeling
• Open loop system identification
• Controller parameter tuning

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Controlware Architecture

• Isolating the application programmer from
  control-theoretic concerns
• -Interface between the service software and
  middleware control loops
• -software sensor and actuator design

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Communication backbone - Soft Bus

• Interface modules
• Passive vs. Active
• Registrar
• Save components info for local machine
• Directory Server
• Save global components info
• Data Agent
• Make remote communication transparent

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Resource management

• Sensor
• available at controlled software service or the
  operation system

• Actuator
• Queue manager
• Control enqueue and dequeue and queue space
• Queue policy
• FIFO, priority and proportional
• Quota manager
• Control resource usage or dequeue ratio
• Preempt or non-preempt
• Mapping of quota to physical resource allocation

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Comparison with QuO (cont.)
?

• Algorithm implementation of QuO
• Region not predefined
• Continues contract evaluation

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Comparison with QuO

• System condition
• Gather system information
• Contracts
• Summarize current region and trigger adaptive
  behavior based upon current regions
• Delegates
• Execute alternative behavior
• Specialized ORB

• Sensor/monitor
• Controller
• GRM
• Soft Bus

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Why feedback control

• Handling unpredicted environment
• Requests from clients not known a priori
• Handling accumulative factors
• Smooth resource adjustment
• Robust
• System model unavailable
• For real-time system?
• Not rapid response

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Thank you for your patience!