Resource Management of Highly Configurable Tasks April 26
Resource Management of Highly Configurable Tasks April 26, 2004 Jeffery P. Hansen Sourav Ghosh Rajkumar John P. Lehoczky Carnegie Mellon University
Outline • • • 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% Qo. S-Based Optimization 100% 50% 0% • Qo. S-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.
Qo. S Optimization with Q-RAM • • Qo. S 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 Qo. S set-point can be realized by multiple “Resource Options”. – Resource trade-offs – Qo. S 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 Qo. S setpoint combinations found in under 1 sec. Frames/sec. • Image Resolution
Qo. S Model of Radar Tracking Problem Threat Assessment Resources Marginal Utility • Distance • Speed • Direction • Maneuvering • Counter Measures ol ntr Co • Radar bandwidth • Short-term power • Long-term power • CPUs • Memory Environment Qo. S Dimensions • Track Error • Target Drop Probability • Reliability Operational Dimensions • Dwell Period • Dwell Time • Transmit Power • Tracking Algorithm • # of task replicas
Qo. S Setpoints Resource Option 1 Qo. S 0. 999 CPU Resource Option 2 Utility CPU (0. 0) 0. 99999 CPU CPU (0. 4) CPU 0. 999 CPU (0. 6) 0. 99999 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 R 1 R 2 Global Constraints: Power (Pmax) – Limit on power that can be provided to power radars. Computing (Cmax) – Limit on processing capabilities for tracking targets. …
Radar Model Error Estimation Radar tracking error is estimated by a function: Dwell Time Tx Dwell Period Time Tx Power Environmental Distance Dimensions Target Type Operational Dimensions Velocity Tracking Acceleration Alg. Tx Rx w Noise r a Tx Rx w Radar Usage v n ξ 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. 100 ms 1. 3 k. W 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 Qo. S 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 “non. Dwell 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 Utility U • FOFT: First Order Fast Traversal Algorithm: U U R* R* U U U R* R* Dwell Period Compound Resource R* – Make the minimum Qo. S 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 Qo. S 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 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.
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