Online Adaptive Utilization Control for RealTime Embedded Multiprocessor Systems

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Online Adaptive Utilization Control for Real-Time
Embedded Multiprocessor Systems

• Jianguo Yao McGill Univ.
• Xue Liu McGill Univ.
• Mingxuan Yuan HKUST
• Zonghua Gu HKUST

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Motivation of Utilization Control

• CPU utilization a trade-off
• Too high ? system overload ? crash
• OS frozen by higher-priority real-time threads
• Too low ? poor application QoS
• Schedulable utilization bound
• Utilization bound ? meet all deadlines
• Highest possible utilization with deadline
  guarantee
• Uncertainties
• Unpredictable exec times (e.g. influenced by
  sensor data)
• External resource contention (e.g. Denial of
  Service attacks)
• Must maintain desired utilization under
  uncertainty!

Courtesy of Xiaorui Wang
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End-to-End Task Modelin Distributed Real-Time
Systems

• Periodic task Ti a chain of subtasks Tij on
  different processors
• All subtasks run at a same rate
• End-to-end deadline sum of all sub-deadlines
• Task rate can be adjusted within a range
• Higher rate ? better performance

Precedence Constraints
Subtask
P2
P3
P1
Courtesy of Xiaorui Wang
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End-to-End Utilization Control

• Schedule tasks in distributed real-time systems
• Utilization control on all processors
• ? meet all end-to-end deadlines in the whole
  system
• Control approach
• Controlled variable utilizations
• Manipulated variable task rates
• Variations inaccurate and varying task exec
  times
• Adjust task rates to compensate for exec time
  variations

Precedence Constraints
Subtask
P2
P3
P1
Courtesy of Xiaorui Wang
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Challenges of End-to-End Utilization Control
CPU utilization

• Utilizations are coupled due to end-to-end tasks
• Changing rate of a task chain affects utilization
  of all processors in its path
• Multi-Input-Multi-Output (MIMO) control problem
• Constraints on range of task rates
• Linear (e.g., PID) control theory is not
  sufficient

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Controller
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P2
P3
P1
Courtesy of Xiaorui Wang
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Control System Architecture

• Controller invoked periodically to adjust
  utilizations of all processors
• Based on Recursive Least Squares (RLS) Estimator
  Linear Quadratic (LQ) Controller

Controlled Variables CPU utilizations
Schedulable utilization bounds
Utilization Monitor
UM
UM
Controller
Rate Modulator
RM
RM
Manipulated variables Task rate changes
Allowed ranges for task rates
(constraints)
Courtesy of Xiaorui Wang
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Challenge Unknown or Changing Plant Model

• Task execution time is often unknown or have
  large runtime variations
• Plant model is unknown or changing at runtime!

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Controller Internal Design

• Traditional control design requires a priori
  knowledge of plant model
• RLS Estimator
• Online learning and updating of plant model
• Can cope with unknown or changing plant model
  better compared to traditional control design
  with fixed plant model
• LQ Controller
• Compute control inputs by minimizing a quadratic
  cost function

Utilization Set point
LQ Controller
RLS-based Model Estimator
-
CPU Utilizations (output)
Computing System (plant)
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Simulation Setup

• Matlab simulation
• 2 CPUs, 4 tasks
• Reference utilization 0.828,
• Based on Liu and Layland bound
  
• Controller execution time10ms in Matlab
• Also tried larger examples with similar
  performance
• 5 CPUs, 11 tasks, 6 chains

T1
T21
T22
T2
T3
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Simulation Results Large Execution Time
Estimation Error

• Constant gain

MPC Controller
RLS-based LQ Controller
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Simulation Results Varying Execution Times

• At start,
• At the 400th step
• At the 800th time step

MPC Controller
RLS-based LQ Controller
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Simulation and Evaluation (5)

• Metric aggregate error
• Sum of squared errors between desired and actual
  utilizations in the steady state.
• Time steps 200, 1000

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Related Work

• Single processor feedback control
• Feedback real-rate scheduler Steere 99Goel
  04,
• Feedback control real-time scheduling Lu 99
• Reservation-based scheduler Abeni 02
• Control tasks Cervin 02Marti 02Marti 04
• Real-time databases Kang 04Amirijoo 05
• Power management Sharma 03Zhu 04
• Not applicable to distributed systems
• Feedback control in distributed systems
• DFCS Stankovic 01, DRTS Lin 03
• Cannot handle coupling between processors due to
  end-to-end tasks
• MPC-based control Lu 05
• Can handle limited plant model errors or runtime
  changes

Courtesy of Xiaorui Wang
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Conclusion

• Utilization control for distributed embedded
  systems
• Provides performance guarantees despite unknown
  or uncertain execution times using online plant
  model estimation
• Handles coupling between processors
• Can enforce min, max constraints on task rates

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Future Work Decentralized End-to-End Utilization
Control
?

• Limitations of centralized control in large
  system
• Computation bottleneck
• Communication delay
• Single point of failure
• Decentralized control
• Localized control decision
• Neighborhood coordination
• Consider other metrics
• End-to-end latency
• Power consumption with DVS

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Courtesy of Xiaorui Wang
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Backup Slides
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Online Model Parameter Estimation (1)
MIMO System
RLS-friendly Model
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Online Model Parameter Estimation (2)
RLS
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Linear Quadratic Optimal Controller Design for
MIMO System

• Goal Minimize the quadratic cost function
• Solution