2. Resource Management of Highly Configurable Tasks April 26, 2004 Jeffery P. HansenSourav Ghosh Raj RajkumarJohn P. Lehoczky Carnegie Mellon University

3. Outline Radar Tracking Problem Introduction to Q-RAM Application of Q-RAM to Radar Tracking Slope-Based Traversal Fast Traversal Experimental Results

4. 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 Resource Management for Radar Tracking

5. 0% 50% 100% 0% 50% 100% Radar Resource Management Approaches 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. 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. Priority-Based Allocation QoS-Based Optimization

6. QoS Optimization with Q-RAM Image Resolution Frames/sec. 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.

7. QoS Model of Radar Tracking Problem Resources Radar bandwidth Short-term power Long-term power CPUs Memory Operational Dimensions Dwell Period Dwell Time Transmit Power Tracking Algorithm # of task replicas Environment Distance Speed Direction Maneuvering Counter Measures Threat Assessment QoS Dimensions Track Error Target Drop Probability Reliability Marginal Utility Control

8. QoS Setpoints QoS Resource Option 1 Resource Option 2 Utility (0.0) (0.4) (0.6) (1.0) CPU 0.999 CPU 0.99999 CPU

9. Radar Constraint/Resource Model Per Antenna Constraints: Global Constraints: … R1R2Global Computing (C max ) – Limit on processing capabilities for tracking targets. Power (P max ) – Limit on power that can be provided to power radars. Heat (H i ) – Limit on heat that can be dissipated per unit time. Utilization(U i ) – Limit on fraction of time radar can be in continuous use.

10. Radar Model Error Estimation Radar tracking error is estimated by a function: Environmental Dimensions r v a ξ n CPU Usage Radar Usage Operational Dimensions w Tx Rx w Tx Rx Target Type Distance Velocity Acceleration Noise Dwell Period Dwell Time Tx Time Tx Power Tracking Alg.

11. Setpoint Explosion Problem 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 m k setpoints. –Even a linear algorithm may take a long time. One Dimension Two Dimensions Three Dimensions Four Dimensions

12. Optimization goal: Maximize total system utility while meeting resource constraints. Algorithm: –Generate concave majorant of utility/resource curve for each target. –Assign minimum resource allocation to all targets. –Increase allocation for target with the highest marginal utility. –Repeat until all resources have been allocated. Solution Properties –Optimal in continuous case –Within a fixed distance of optimal in discrete case. Q-RAM Overview Resources Utility Resources Utility Track 1 Track 2 Dwell Period: 100ms Dwell Time: 1ms Power: 1.3 kW Tracking Alg.: Kalman

13. Slope Based Traversal Algorithm –Determine minimum and maximum QoS points. –Eliminate points under the line connecting them. –Apply concave majorant to remaining points. Initial scan is linear –Reduces number of points to which we must apply the concave majorant algorithm. –Some reduction in execution time. –But, still must examine every setpoint. Compound Resource Utility

14. Fast Convex Hull Algorithms 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. We call dimensions with the above property “monotonic” dimensions. All other dimensions are called “non- monotonic” dimensions. Dwell Period Transmit Power R U R U R U

15. Fast Traversal Methods 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 “non- monotonic” dimensions separately. Compound Resource Utility

16. Fast Traversal Algorithms FOFT: First Order Fast Traversal Algorithm: –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. Dwell Period Transmit Power Compound Resource Utility R* U U U U U U U U U U

17. Higher Order Traversal Algorithms 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. Experimental results show that –SOFT* requires more execution time than FOFT and SOFT. –Resulting concave majorant is slightly better than FOFT. Dwell Period Transmit Power 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. Dwell Period Transmit Power

18. Optimization with Non-Monotonic Dimensions Compound Resource Utility Dwell Period Transmit Power Dwell Period Transmit Power Algorithm Kalman αβγ Concave Majorant Generation with Non-Monotonic Dimensions For each combination of non- monotonic parameters, apply the traversal algorithm. Generate the concave majorant from the combined set of setpoints.

19. Concave Majorant Compound Resource Utility

20. Slope-Based Concave Majorant

21. FOFT Concave Majorant Approximation

22. 2-FOFT Concave Majorant Approximation

23. Global Utility

24. Number of Setpoint per Task

25. Total Optimization Time

26. 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.