Resource Management of
Highly Configurable Tasks
April 26, 2004
Jeffery P. Hansen
Sourav Ghosh
Raj Rajkumar
John P. Lehoczky
Carnegie Mellon University
Outline
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•
•
•
•
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Radar Tracking Problem
Introduction to Q-RAM
Application of Q-RAM to Radar Tracking
Slope-Based Traversal
Fast Traversal
Experimental Results
Resource Management for Radar Tracking
• For each target we need to choose:
– Radar parameters such as dwell
period, dwell time and transmit power.
– Ship/antenna to use.
– Signal processing algorithm to use.
– CPU from processing bank to use.
• While satisfying constraints on:
– Power dissipation
– Radar and CPU Utilization
– Scheduling
• We must quickly respond to:
– Changes in target position
– New target arrivals
– Target departures
Radar Resource Management Approaches
Priority-Based Allocation
•
100%
Existing solutions use operational doctrine
to make resource allocation decisions.
– Resources allocated to tasks in order of
importance based only on each task’s
characteristics.
– Some problems with this approach are:
• Important tasks can starve tasks of slightly
lower priority.
• Does not make best use of resources.
• Difficulty in predicting viable scenarios.
50%
0%
QoS-Based Optimization
100%
50%
0%
•
QoS-based optimization considers resource
tradeoffs and relative task importance.
– Resources allocated in proportion to importance.
– Tasks can have unlimited access to resource
when demand is low.
– Tasks can not starve other tasks of similar
importance.
– Operator can dynamically change importance.
QoS Optimization with Q-RAM
•
•
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QoS modeled as an n-dimensional space
– Each set-point in the space has an associated
“utility” value representing user satisfaction.
– Utility values can be assigned individually or
via dimension-wise utility functions.
A single QoS set-point can be realized by multiple
“Resource Options”.
– Resource trade-offs
– QoS Routing
Optimization goal is to maximize total system utility
while meeting resource constraints.
Per-user weights give higher priority to “important”
users.
Near optimal solution for search space of over a
trillion QoS setpoint combinations found in under 1
sec.
Frames/sec.
•
Image Resolution
QoS Model of Radar Tracking Problem
Threat
Assessment
Resources
Marginal
Utility
• Radar bandwidth
• Short-term power
• Long-term power
• CPUs
• Memory
Environment
• Distance
• Speed
• Direction
• Maneuvering
• Counter Measures
Operational Dimensions
QoS Dimensions
• Track Error
• Target Drop Probability
• Reliability
• Dwell Period
• Dwell Time
• Transmit Power
• Tracking Algorithm
• # of task replicas
QoS Setpoints
Resource
Option 1
QoS
0.999
CPU
Resource
Option 2
Utility
CPU
(0.0)
0.99999
CPU
CPU
CPU
(0.4)
CPU
0.999
CPU
CPU
(0.6)
0.99999
CPU
CPU
CPU
CPU
(1.0)
Radar Constraint/Resource Model
Per Antenna Constraints:
Utilization(Ui ) – Limit on
fraction of time radar can
be in continuous use.
Heat (Hi ) – Limit on
heat that can be
dissipated per unit time.
Global Constraints:
Power (Pmax) – Limit
on power that can be
provided to power
radars.
Computing (Cmax) –
Limit on processing
capabilities for tracking
targets.
Global
Pmax Cmax
R1
R2
U2
U1
H1
H2
…
Radar Model Error Estimation
Radar tracking error is estimated by a function:
Dwell
  E ( , r , v, a, n, P, C , C ' , A,  )Period
Dwell
Time
Tx
Time
Environmental Distance
Dimensions
Target
Type
r
a
v
n
P
C
Velocity C 
Tracking
Acceleration
Alg.
A
Tx Rx
w
Noise
ξ
Tx
Power
~
C

Operational
Dimensions
Tx
Rx
w
Radar Usage

CPU Usage
Setpoint Explosion Problem
One Dimension
Two Dimensions
• Concave majorant algorithm used by Q-RAM
requires O(n ln n) and must examine every
setpoint.
• For applications with more than a few operational
dimensions, the number of setpoints can be very
large
– With k dimensions having m settings, there
are mk setpoints.
– Even a linear algorithm may take a long time.
Three Dimensions
Four Dimensions
– Generate concave majorant of
utility/resource curve for each target.
– Assign minimum resource allocation to
all targets.
Dwellwith
Period:
– Increase allocation for target
the
highest marginal utility. Dwell Time:
Power:
– Repeat until all resources
have been
Tracking
Alg.:
allocated.
100ms
1ms
1.3 kW
Kalman
Utility
• Optimization goal: Maximize total
system utility while meeting resource
constraints.
• Algorithm:
Utility
Q-RAM Overview
Track 1
Resources
Track 2
• Solution Properties
– Optimal in continuous case
– Within a fixed distance of optimal in
discrete case.
Resources
Slope Based Traversal
• Algorithm
Utility
– Determine minimum and maximum
QoS points.
– Eliminate points under the line
connecting them.
– Apply concave majorant to remaining
points.
• Initial scan is linear
Compound Resource
– Reduces number of points to which
we must apply the concave majorant
algorithm.
– Some reduction in execution time.
– But, still must examine every setpoint.
Transmit Power
Fast Convex Hull Algorithms
RU
RU
• Resource/utility values associated with
setpoints are not random.
• Utilize structure in the resource
management problem to reduce this
complexity.
• For most operational dimensions, an
increase in quality on any dimension results
in:
– Non-decreasing resource consumption.
– Non-decreasing utility.
RU
• We call dimensions with the above property
“monotonic” dimensions.
• All other dimensions are called “nonDwell Period
monotonic” dimensions.
Fast Traversal Methods
Utility
<3,*> <3,5>
<2,*> <3,4>
<1,4> <2,4>
<1,*>
<*,4>
<1,3>
<*,5>
<*,3>
<*,2>
<1,2>
<*,1>
Compound Resource
<1,1>
Observations of the points
on the concave majorant
have revealed that for
monotonic dimensions:
– Concave majorant is usually
composed of sub-sequences
of points differing in only one
quality index.
– Dimension that is changing
may shift as the concave
majorant is traversed.
– May need to treat “nonmonotonic” dimensions
separately.
Transmit Power
Fast Traversal Algorithms
U
U
• FOFT: First Order Fast Traversal
Algorithm:
U
U
R*
U
R*
R*
R*
R*
Utility
U
U
U
U
U
R*
R*
R*
R*
Dwell Period
Compound Resource
R*
– Make the minimum QoS point the
current point.
– Examine points adjacent in the
quality index space to the current
point.
– Choose next point with highest
marginal utility.
– Repeat until reaching maximum
QoS point.
– Apply concave majorant to resulting
set of points.
• Generates nearly the same set of
points as full concave majorant.
• Explicitly examines only a small
subset of the possible setpoints.
• Utility values within a few percent of
standard Q-RAM algorithm.
SOFT - Second Order Fast Traversal
• Same as FOFT, but we include setpoints
that increase in up to two dimensions.
• Experimental results show that
– SOFT requires more execution time than
FOFT.
– Resulting concave majorant is actually
worse than FOFT.
Transmit Power
Higher Order Traversal Algorithms
Dwell Period
Transmit Power
SOFT* - Modified Second Order Fast Traversal
• Same as SOFT, but include points which
increase in at least one dimension, but may
decrease in the other.
•
Dwell Period
Experimental results show that
– SOFT* requires more execution time than FOFT
and SOFT.
– Resulting concave majorant is slightly better than
FOFT.
Optimization with Non-Monotonic Dimensions
Algorithm
αβγ
Transmit Power
Transmit Power
Kalman
Dwell Period
Utility
Dwell Period
Compound Resource
Concave Majorant Generation with
Non-Monotonic Dimensions
• For each combination of nonmonotonic parameters, apply the
traversal algorithm.
• Generate the concave majorant
from the combined set of setpoints.
Utility
Concave Majorant
Compound Resource
Slope-Based Concave Majorant
FOFT Concave Majorant Approximation
2-FOFT Concave Majorant Approximation
Global Utility
Number of Setpoint per Task
Total Optimization Time
Conclusion
• Approach Overview
– Leverage structure in the setpoint space to generate concave majorant
approximation.
– Concave majorant estimated by following the adjacent point on the
monotonic dimension with the highest marginal utility.
– Algorithm repeated for all combinations of non-monotonic dimensions.
• Benefits of Approach
– Significantly reduces the number of setpoints that must be examined to
obtain a concave majorant estimate.
– Complexity is sub-linear in the number of setpoints.
– Works best when most operational dimensions are monotonic.
• Results
– No significant reduction in solution quality.
– Order of magnitude reduction in optimization time.