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CPU Utilization Control in Distributed Real-Time Systems

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Title: CPU Utilization Control in Distributed Real-Time Systems


1
CPU Utilization Control in Distributed Real-Time
Systems
Chenyang Lu Department of Computer Science and
Engineering
2
Why CPU Utilization Control?
  • Overload protection
  • CPU over-utilization ? system crash
  • Nightmare for mission-critical applications and
    always-on E-businesses
  • Meet deadlines
  • CPU utilization lt schedulable utilization bound

3
End-to-End Task Modelin Distributed Real-Time
Systems
  • Periodic task Ti a chain of subtasks Tij
    located on different processors
  • Subtasks run at a same rate
  • Task rate can be adjusted within a range
  • Higher rate ? higher utility

T1
T11
T12
T13
T3
Remote Invocation
T2
Subtask
P2
P3
P1
4
Problem Formulation
  • Bi Utilization set point of processor Pi (1 i
    n)
  • ui(k) Utilization of Pi in kth sampling period
  • rj(k) Rate of task Tj (1 j m) in kth
    sampling period
  • subject to rate constraints
  • Rmin,j ? rj(k) ? Rmax,j (1 j m)

5
Challenge Uncertainties
  • Execution times?
  • Unknown sensor data or user input
  • Request arrival rate?
  • Aperiodic events
  • Bursty service requests
  • Disturbance?
  • Denial of Service Attacks
  • Control-theoretic approaches to adaptive software
  • Robust performance in face of workload uncertainty

6
Single-Processor SolutionFeedback Control
Real-Time Scheduling
  • Adaptation based on single-input-single-output
    control

Sensor Inputs
FCS
r(k1)
Application
Set point Us 69 Task Rates R1 1, 5 Hz R2
10, 20 Hz
Actuator
Controller
Middleware
u(k)
OS
Monitor
Processor
C. Lu, X. Wang, and C. Gill, Feedback Control
Real-Time Scheduling in ORB Middleware, IEEE
Real-Time and Embedded Technology and
Applications Symposium (RTAS'03), May 2003.
7
Whats New in Distributed Systems?
  • Need to control utilization of multiple
    processors
  • Utilization of different processors are coupled
    with each other due to end-to-end tasks
  • Replicating FCS on all processors does not work!
  • Constraints on task rates

8
EUCON Multi-Input-Multi-Output Control
Measured Output
Distributed System (m tasks, n processors)
Utilization Monitor
UM
UM
Model Predictive Controller
Rate Modulator
RM
RM
Feedback Loop
Control Input
Precedence Constraints
Subtask
C. Lu, X. Wang and X. Koutsoukos, Feedback
Utilization Control in Distributed Real-Time
Systems with End-to-End Tasks, IEEE Transactions
on Parallel and Distributed Systems, 16(6)
550-561, June 2005.
9
Control Theoretic Methodology
  • Derive a dynamic model of the controlled system
  • Design a controller
  • Analyze stability

10
Dynamic Model One Processor
  • Si set of subtasks on Pi
  • cjl estimated execution time of Til running on
    Pi
  • may not be correct
  • gi utilization gain of Pi
  • unknown ratio between actual and estimated change
    in utilization
  • models uncertainty in execution times

11
Dynamic Model Multiple Processors
u(k) u(k-1) GF?r(k-1)
  • G diagonal matrix of utilization gains
  • F subtask allocation matrix
  • models the coupling among processors
  • fij cjl task Tj has a subtask Tjl on processor
    Pi
  • fij 0 if Tj has no subtask on Pi

T1
T11
T22
T3
T2
T21
T31
P2
P1
12
Model Predictive Control
  • Advanced control technique for coupled MIMO
    control problems with actuator constraints.
  • Minimize a cost function over an interval in the
    future.
  • Compute an input trajectory that minimizes cost
    subject to actuator constraints.
  • Predict cost based on a system model and
    feedback.
  • Combines optimization, model-based prediction,
    and feedback.

13
Model Predictive Controller
  • At a sampling instant
  • Compute inputs in future sampling periods
  • ?r(k), ?r(k1), ... ?r(kM-1)
  • to minimize a cost function
  • Cost is predicted using
  • (1) feedback u(k-1)
  • (2) approximate dynamic model
  • Apply ?r(k) to the system
  • At the next sampling instant
  • Shift time window and re-compute ?r(k1),
    ?r(k2), ... ?r(kM) based on feedback

14
Model Predictive Controller in EUCON
Constrained optimization solver
Desired trajectory for u(k) to converge to B
Difference with reference trajectory
15
Stability Analysis
  • Stability system converges to equilibrium point
    from any initial condition
  • Equilibrium point utilization set points B
  • If stable, utilization of all processors converge
    to their set points whenever feasible
  • Derive stability condition ? tolerable range of G
  • tolerable variation of execution times
  • Stability analysis establishes analytical
    guarantees on utilization despite uncertainty

16
Simulation Stable System
execution time factor 0.5 (actual execution
times ½ of estimates)
17
Simulation Unstable System
execution time factor 7 (actual execution times
7 times estimates)
18
Stability
  • Stability system converges to desired
    utilizations from any initial condition
  • Derive stability condition ? tolerable range of
    execution times
  • Analytical assurance on utilizations despite
    uncertainty

Overestimation of execution times prevents
oscillation
Predicted bound for stability
actual execution time / estimation
19
FC-ORB Middleware
X. Wang, C. Lu and X. Koutsoukos, Enhancing the
Robustness of Distributed Real-Time Middleware
via End-to-End Utilization Control, IEEE
Real-Time Systems Symposium (RTSS'05), December
2005.
20
Workload Uncertainty
disturbance from periodic tasks
time-varying execution times
21
Processor Failure
  1. Norbert fails.
  2. move its tasks to other processors.
  3. reconfigure controller
  4. control utilization by adjusting task rates

22
Summary Model Predictive Control
  • Robust utilization control for distributed
    systems
  • Handles coupling among processors
  • Enforce constraints on task rates
  • Analyze tolerable range of execution times

23
References
  • Centralized control EUCON
  • C. Lu, X. Wang and X. Koutsoukos, Feedback
    Utilization Control in Distributed Real-Time
    Systems with End-to-End Tasks, IEEE Transactions
    on Parallel and Distributed Systems, 16(6)
    550-561, June 2005.
  • Decentralized control DEUCON
  • X. Wang, D. Jia, C. Lu and X. Koutsoukos, DEUCON
    Decentralized End-to-End Utilization Control for
    Distributed Real-Time Systems, IEEE Transactions
    on Parallel and Distributed Systems, 18(7)
    996-1009, July 2007.
  • Middleware FC-ORB
  • X. Wang, C. Lu and X. Koutsoukos, Enhancing the
    Robustness of Distributed Real-Time Middleware
    via End-to-End Utilization Control, IEEE
    Real-Time Systems Symposium (RTSS'05), December
    2005.
  • Controllability and feasibility
  • X. Wang, Y. Chen, C. Lu and X. Koutsoukos, On
    Controllability and Feasibility of Utilization
    Control in Distributed Real-Time
    Systems, Euromicro Conference on Real-Time
    Systems (ECRTS'07), July 2007.
  • Project page http//www.cse.wustl.edu/lu/aqc.htm
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