Chenyang Lu Highlight Commonclassofcompu5ngproblems - PDF document

Chenyang Lu Highlight
  Common
class
of
compu5ng
problems
 CPU
U%liza%on
Control
in

 • MIMO:
mul5‐input
(knobs),
mul5‐output
(objec5ves)
 Distributed
Real‐Time
Systems
 • Coupling
between
objec5ves.
 • Constraints
on
knobs.
  Model
Predic5ve
Control
 Chenyang
Lu
 • Op5miza5on
+
Predic5on
+
Feedback
 CSE
520S
 2 
 Why
CPU
U%liza%on
Control?
 Challenge:
Uncertain%es
  Overload
protec5on
  Execu5on
5mes?
 Unknown
sensor
data
or
user
input
  CPU
over‐u5liza5on
  
system
crash
   Request
arrival
rate?
 Aperiodic
events
   Meet
response
5me
requirement
 Bursty
service
requests
   CPU
u5liza5on
<
bound
  
meet
deadlines
  Disturbance?
 Denial
of
Service
a^acks
  Control‐theore5c
approach
  Robust
u5liza5on
control
in
face
of
workload
uncertainty
 3 
 4 
 End‐to‐End
Tasks
 Problem
Formula%on
 Distributed
Real‐Time
Systems
  B i :
U5liza5on
set
point
of
processor
P i
 (1
≤
i
≤
n)

  Periodic
task
T i 
=
sequence
of
subtasks
{T ij }
on
different
  u i (k):
U5liza5on
of
P i 
in
the
k th 
sampling
period

 processors
  r j (k):
Rate
of
task
T j
 (1
≤
j
≤
m)
in
the
k th 
sampling
period 
 All
the
subtasks
of
a
task
run
at
a
same
rate
   Task
rate
can
be
adjusted
 n Within
a
range
  ∑ ( B i − u i ( k )) 2 min Higher
rate
  
higher
u5lity
  { r j ( k )|1 ≤ j ≤ n } i = 1 subject
to
rate
constraint:
 T 1 T 11 T 12 T 13 R min,j 
 ≤ 
r j (k)
 ≤ 
R max,j 
(1
≤
j
≤
m)
 T 3 T 2 Remote Invocation Subtask P 2 P 3 P 1 5 
 6 
 SIGMETRICS
2008:
Introduc5on
to
Control
 Theory.
Abdelzaher,
Diao,
Hellerstein,
Lu,
and
 1 Zhu.


Chenyang Lu Single‐Input‐Single‐Output
(SISO)
Control
 New
in
Distributed
Systems
 Single
Processor
  Need
to
control
u5liza5on
of
mul5ple
processors
  U5liza5on
of
different
processors
are
coupled
with
each
 other
due
to
end‐to‐end
tasks
 Sensor Inputs Replica5ng
a
SISO
controller
on
all
processors
does
not
work!
   Constraints
on
task
rates 
 {r(k+1)} Set point Application Controller Actuator U s = 69% Middleware u(k) Task Rates T 1 T 11 T 12 T 13 R 1 : [1, 5] Hz Monitor OS R 2 : [10, 20] Hz T 3 Processor T 2 P 2 P 3 P 1 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 
 8 
 EUCON:
Mul%‐Input‐Mul%‐Output
Control
 Control
Theore%c
Methodology
 1. Derive
a
dynamic
model
of
the
system
 Measured Output 2. Design
a
controller
 Distributed System 3. Analyze
stability
 (m tasks, n processors) Utilization UM UM Model Monitor 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. 9 
 10 
 Dynamic
Model:
One
Processor
 Dynamic
Model:
Mul%ple
Processors
 u ( k ) = u ( k -1) + GF Δ r ( k -1) ∑ u i ( k ) = u i ( k − 1) + g i c jl Δ r j ( k − 1)  G: 
diagonal
matrix
of
u5liza5on
gains
 T jl ∈ S i  F :
subtask
alloca5on
matrix
  models
the
coupling
among
processors 
  S i :
set
of
subtasks
on
P i
 f ij 
=
c jl 
if
task
T j 
has
a
subtask
T jl 
on
processor
P i 

   c jl :
es5mated
execu5on
5me
of
T il 
 f ij 
=
0
if
T j 
has
no
subtask
on
P i 

   g i :
u5liza5on
gain
of
P i 
 T 1 T 11  ra5o
between
actual
and
es5mated
change
in
u5liza5on
 T 22  models
 uncertainty
 in
execu5on
5mes


 T 3 T 2 T 21 T 31 P 1 P 2 11 
 12 
 SIGMETRICS
2008:
Introduc5on
to
Control
 Theory.
Abdelzaher,
Diao,
Hellerstein,
Lu,
and
 2 Zhu.


Chenyang Lu Model
Predic%ve
Control
 Cost
Func%on
  Cost
  Suitable
for
coupled
MIMO
control
problems
with
 constraints.

 P M − 1  Compute
input
to
minimize
cost
over
a
future
interval.
 2 2 ∑ ∑ V ( k ) = u ( k + i ) − ref ( k + i ) + Δ r ( k + i ) − Δ r ( k + i − 1) Cost
func5on:
tracking
error
and
control
cost.
  i = 1 i = 0 Predict
cost
based
on
a
system
model
and
feedback.
  Tracking
Error
 Control
Cost
 Compute
input
subject
to
constraints.
   Op5miza5on
+
Predic5on
+
Feedback
  Reference
trajectory:
exponen5al
convergence
to
 B
 − T s i T ref ref ( k + i ) = B − e ( B − u ( k )) 13 
 14 
 Model
Predic%ve
Controller
 EUCON
Controller
 Constrained
 At
the
end
of
each
sampling
period
 op5miza5on
  Compute
inputs
in
future
sampling
periods
 solver
 
 Δ r (k),
 Δ r (k+1),
...
 Δ r (k+M‐1)
 
to
minimize
the
cost
func5on
  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
 Desired
trajectory
for
  Shil
5me
window
and
re‐compute
 Δ r (k+1),
 Δ r (k+2),
...
 Δ r (k+M)
based
 Difference
from
 u (k)
to
converge
to
 B 

 on
feedback
 reference
 trajectory
 15 
 16 
 Stable
System
 Stability
Analysis
  Stability:
u5liza5on
of
all
processors
converge
to
set
points
  Derive
stability
condi5on
  
range
of
 G 
  Tolerable
varia5on
of
execu5on
5mes
  Provides
analy5cal
assurance
despite
uncertainty

 execu5on
5me
factor
=
0.5 
 (actual
execu5on
5mes
=
½
of
es5mates) 
 17 
 18 
 SIGMETRICS
2008:
Introduc5on
to
Control
 Theory.
Abdelzaher,
Diao,
Hellerstein,
Lu,
and
 3 Zhu.


Chenyang Lu Unstable
System
 Stability
  Stability
condi5on
  
tolerable
range
of
execu5on
5mes
 Analy5cal
assurance
on
u5liza5ons
despite
uncertainty

 Overes%ma%on
 Predicted
 of
execu%on
 bound
for
 %mes
prevents
 stability
 execu5on
5me
factor
=
7 
 oscilla%on
 (actual
execu5on
5mes
=
7
5mes
es5mates) 
 actual execution time / estimation 19 
 20 
 FC‐ORB
Middleware
 FC‐ORB
Features
  End‐to‐end
u5liza5on
control
 Maintains
desired
u5liza5ons
on
all
processors
 Model
  Measured
 Predic%ve
  End‐to‐end
ORB
architecture
 Control
 Output
 Controller
 Input
 Specialized
for
rate
adapta5on
  Feedback
lane
  Task
migra5on
 Reliability
in
terms
of
func5onality
 and 
real‐5me
performance

  Rate
 Rate
 Rate
 Modulator
 Modulator
 Modulator
 Priority
 Priority
 Priority
 Manager
 Manager
 Manager
 U%liza%on
 U%liza%on
 U%liza%on
 Monitor
 Monitor
 Monitor
 Remote
request
lanes
 Remote
request
lanes
 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. 21 
 22 
 End‐to‐End
U%liza%on
Control
Service
 End‐to‐End
Object
Request
Broker �  Release
guard
for
end‐to‐end
tasks
  Implements
EUCON
(End‐to‐end
U5liza5on
CONtrol)

  Provides
func5onal
and
performance
portability
  Priority
management
 Rate
adapta5on
  
con5nuous
priority
changes
  Thread‐per‐priority
  
high
overhead

  Thread‐per‐subtask:
Change
priority
only
when
the
order
of
task
 Controlled  Model Manipulated variables: Predictive variables: rate
changes
 � Controller Utilizations Rate changes Rate Rate Rate Modulator Modulator Modulator Rate Rate Rate Priority Priority Priority Modulator Modulator Modulator Manager Manager Manager Priority Priority Priority Manager Manager Manager Utilization Utilization Utilization Monitor Monitor Monitor Utilization Utilization Utilization Monitor Monitor Monitor Remote request lanes Remote request lanes Remote request lanes Remote request lanes 23 
 24 
 SIGMETRICS
2008:
Introduc5on
to
Control
 Theory.
Abdelzaher,
Diao,
Hellerstein,
Lu,
and
 4 Zhu.