CPUU%liza%onControlin DistributedRealTimeSystems ChenyangLu - PowerPoint PPT Presentation

CPU
U%liza%on
Control
in
 
 Distributed
Real‐Time
Systems 
 Chenyang
Lu 
 Department
of
Computer
Science
and
Engineering 
 IM
2009:
Recent
Advances
in
the
Applica6on
of
Control
Theory
to
Network
and
Service
Management 


Highlight
  Common
class
of
compu6ng
problems 
  MIMO:
mul6‐input
(knobs),
mul6‐output
(objec6ves)
  Coupling
between
objec6ves.
  Constraints
on
knobs.
  Model
Predic6ve
Control
  Op6miza6on
+
Predic6on
+
Feedback
 IM
2009:
Recent
Advances
in
the
Applica6on
of
Control
Theory
to
Network
and
Service
Management 
 2

Why
CPU
U%liza%on
Control?
  Overload
protec6on
  CPU
over‐u6liza6on
  
system
crash
  Meet
response
6me
requirement
  CPU
u6liza6on
<
bound
  
meet
deadlines
 IM
2009:
Recent
Advances
in
the
Applica6on
of
Control
Theory
to
Network
and
Service
Management 
 3

Challenge:
Uncertain%es
  Execu6on
6mes?
  Unknown
sensor
data
or
user
input
  Request
arrival
rate?
  Aperiodic
events
  Bursty
service
requests
  Disturbance?
  Denial
of
Service
aYacks
 Control‐theore6c
approach
  Robust
u6liza6on
control
in
face
of
workload
uncertainty
 IM
2009:
Recent
Advances
in
the
Applica6on
of
Control
Theory
to
Network
and
Service
Management 
 4

End‐to‐End
Tasks
 Distributed
Real‐Time
Systems
  Periodic
task
T i 
=
sequence
of
subtasks
{T ij }
on
different
 processors
  All
the
subtasks
of
a
task
run
at
a
same
rate
  Task
rate
can
be
adjusted
  Within
a
range
  Higher
rate
  
higher
u6lity
 T 1 T 11 T 12 T 13 T 3 Remote Invocation T 2 Subtask P 2 P 3 P 1 IM
2009:
Recent
Advances
in
the
Applica6on
of
Control
Theory
to
Network
and
Service
Management 
 5

Problem
Formula%on
  B i :
U6liza6on
set
point
of
processor
P i
 (1
≤
i
≤
n)

  u i (k):
U6liza6on
of
P i 
in
the
k th 
sampling
period

  r j (k):
Rate
of
task
T j
 (1
≤
j
≤
m)
in
the
k th 
sampling
period 
 n ∑ ( B i − u i ( k )) 2 min { r j ( k )|1 ≤ j ≤ n } i = 1 subject
to
rate
constraint:
 R min,j 
 ≤ 
r j (k)
 ≤ 
R max,j 
(1
≤
j
≤
m)
 IM
2009:
Recent
Advances
in
the
Applica6on
of
Control
Theory
to
Network
and
Service
Management 
 6

Single‐Input‐Single‐Output
(SISO)
Control
 Single
Processor
 Sensor Inputs {r(k+1)} Set point Application Controller Actuator U s = 69% Middleware u(k) Task Rates R 1 : [1, 5] Hz Monitor OS R 2 : [10, 20] Hz 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. IM
2009:
Recent
Advances
in
the
Applica6on
of
Control
Theory
to
Network
and
Service
Management 
 7

New
in
Distributed
Systems
  Need
to
control
u6liza6on
of
mul6ple
processors
  U6liza6on
of
different
processors
are
coupled
with
each
 other
due
to
end‐to‐end
tasks
  Replica6ng
a
SISO
controller
on
all
processors
does
not
work!
  Constraints
on
task
rates 
 T 1 T 11 T 12 T 13 T 3 T 2 P 2 P 3 P 1 IM
2009:
Recent
Advances
in
the
Applica6on
of
Control
Theory
to
Network
and
Service
Management 
 8

EUCON:
Mul%‐Input‐Mul%‐Output
Control
 Measured Output Distributed System (m tasks, n processors) Utilization UM UM Monitor Model Predictive Rate Controller Modulator RM RM Feedback Loop Control Remote Invocation Input 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. IM
2009:
Recent
Advances
in
the
Applica6on
of
Control
Theory
to
Network
and
Service
Management 
 9

Control
Theore%c
Methodology
 1. Derive
a
dynamic
model
of
the
system
 2. Design
a
controller
 3. Analyze
stability
 IM
2009:
Recent
Advances
in
the
Applica6on
of
Control
Theory
to
Network
and
Service
Management 
 10

Dynamic
Model:
One
Processor
 ∑ u i ( k ) = u i ( k − 1) + g i c jl Δ r j ( k − 1) T jl ∈ S i  S i :
set
of
subtasks
on
P i
  c jl :
es6mated
execu6on
6me
of
T il 
  g i :
u6liza6on
gain
of
P i 
  ra6o
between
actual
and
es6mated
change
in
u6liza6on
  models
 uncertainty
 in
execu6on
6mes


 IM
2009:
Recent
Advances
in
the
Applica6on
of
Control
Theory
to
Network
and
Service
Management 
 11

Dynamic
Model:
Mul%ple
Processors
 u ( k ) = u ( k -1) + GF Δ r ( k -1)  G: 
diagonal
matrix
of
u6liza6on
gains
  F :
subtask
alloca6on
matrix
  models
the
coupling
among
processors 
  f ij 
=
c jl 
if
task
T j 
has
a
subtask
T jl 
on
processor
P i 

  f ij 
=
0
if
T j 
has
no
subtask
on
P i 

 T 1 T 11 T 22 T 3 T 2 T 21 T 31 P 1 P 2 IM
2009:
Recent
Advances
in
the
Applica6on
of
Control
Theory
to
Network
and
Service
Management 
 12

Model
Predic%ve
Control
  Suitable
for
coupled
MIMO
control
problems
with
constraints. 
 
  Compute
input
to
minimize
cost
over
a
future
interval.
  Cost
func6on:
tracking
error
and
control
cost.
  Predict
cost
based
on
a
system
model
and
feedback.
  Compute
input
subject
to
constraints.
  Op6miza6on
+
Predic6on
+
Feedback
 IM
2009:
Recent
Advances
in
the
Applica6on
of
Control
Theory
to
Network
and
Service
Management 
 13

Cost
Func%on
  Cost
 P M − 1 2 2 ∑ ∑ V ( k ) = u ( k + i ) − ref ( k + i ) Δ r ( k + i ) − Δ r ( k + i − 1) + i = 1 i = 0 Tracking
Error
 Control
Cost
  Reference
trajectory:
exponen6al
convergence
to
 B
 − T s i T ref ref ( k + i ) = B − e ( B − u ( k )) IM
2009:
Recent
Advances
in
the
Applica6on
of
Control
Theory
to
Network
and
Service
Management 
 14

Model
Predic%ve
Controller
 At
the
end
of
each
sampling
period
 Compute
inputs
in
future
sampling
periods
  
 Δ r (k),
 Δ r (k+1),
...
 Δ r (k+M‐1)
 
to
minimize
the
cost
func6on
 Cost
is
predicted
using
  
(1)
feedback
u(k‐1)
 
(2)
approximate
dynamic
model
 Apply
 Δ r (k)
to
the
system
  At
the
end
of
the
next
sampling
period
 Shid
6me
window
and
re‐compute
 Δ r (k+1),
 Δ r (k+2),
...
 Δ r (k+M)
based
  on
feedback
 IM
2009:
Recent
Advances
in
the
Applica6on
of
Control
Theory
to
Network
and
Service
Management 
 15

EUCON
Controller
 Constrained
 op6miza6on
 solver
 Desired
trajectory
for
 Difference
from
 u (k)
to
converge
to
 B 

 reference
 trajectory
 IM
2009:
Recent
Advances
in
the
Applica6on
of
Control
Theory
to
Network
and
Service
Management 
 16

Stability
Analysis
  Stability:
u6liza6on
of
all
processors
converge
to
set
points
  Derive
stability
condi6on
  
range
of
 G 
  Tolerable
varia6on
of
execu6on
6mes
  Provides
analy6cal
assurance
despite
uncertainty

 IM
2009:
Recent
Advances
in
the
Applica6on
of
Control
Theory
to
Network
and
Service
Management 
 17

Stable
System
 execu6on
6me
factor
=
0.5 
 (actual
execu6on
6mes
=
½
of
es6mates) 
 IM
2009:
Recent
Advances
in
the
Applica6on
of
Control
Theory
to
Network
and
Service
Management 
 18

Unstable
System
 execu6on
6me
factor
=
7 
 (actual
execu6on
6mes
=
7
6mes
es6mates) 
 IM
2009:
Recent
Advances
in
the
Applica6on
of
Control
Theory
to
Network
and
Service
Management 
 19

Stability
  Stability
condi6on
  
tolerable
range
of
execu6on
6mes
 Analy6cal
assurance
on
u6liza6ons
despite
uncertainty

 Overes%ma%on
 Predicted
 of
execu%on
 bound
for
 %mes
prevents
 stability
 oscilla%on
 actual execution time / estimation IM
2009:
Recent
Advances
in
the
Applica6on
of
Control
Theory
to
Network
and
Service
Management 
 20