1. ECE 753: FAULT-TOLERANT COMPUTING Kewal K.Saluja Department of Electrical and Computer Engineering Byzantine faults and Agreement Problem (Sensor Networks)

2. ECE 753 Fault Tolerant Computing2 Overview Sensor fusion problem Agreement in the presence of faults –Precision and accuracy issuePrecision and accuracy issue –Byzantine faultsByzantine faults

3. ECE 753 Fault Tolerant Computing3 Introduction What is sensor network –Sensor networkSensor network –Its relation to agreement problemIts relation to agreement problem Motivation –Multiple sensors sensing same environment in different manner, but need to arrive at a common and same decision – some of the sensors may be faultyMultiple sensors sensing same environment in different manner, but need to arrive at a common and same decision – some of the sensors may be faulty

4. ECE 753 Fault Tolerant Computing4 Sensor Fusion Problem v2v7 v3 v6 v1 v4 v12 v10 v5 v11 v8 v13 11 1 1 1 1 1 1 1 1 1 1 v9 1

5. ECE 753 Fault Tolerant Computing5 Fault Tolerant Fusion Fusion as described earlier but some of the nodes/sensors may be faulty Agreement requirement: –Precision requirement: all non faulty nodes in region make same decision. –Accuracy requirement: the decision is representative of the environment. For example: decision is “detect” if there is an object in the region.

6. ECE 753 Fault Tolerant Computing6 Agreement Precision Accuracy

7. ECE 753 Fault Tolerant Computing7 Agreement (cont.) BC A 00 1 BC A 01 1 B can not differentiate between 2 scenarios. Agreement requires 3m+1 nodes to tolerate m Byzantine faults

8. ECE 753 Fault Tolerant Computing8 Fault Tolerant Fusion Precision: Exact agreement solves inconsistency problem –All non faulty nodes obtain the same set of values 0 ? 1 0 S? S S

9. ECE 753 Fault Tolerant Computing9 Fault Tolerant Fusion Precision: Exact agreement solves inconsistency problem –All non faulty nodes obtain the same set of values 0 ? 1 0 ? 1 1 1 1 1 1 1 1 1 1 1 1 0 {1}

10. ECE 753 Fault Tolerant Computing10 Fault Tolerant Fusion Precision: Exact agreement solves inconsistency problem –All non faulty nodes obtain the same set of values ?1 ? 0 0 0 1 0 1 0 0 {1,0} 0 ? 1 0 0 1 0

11. ECE 753 Fault Tolerant Computing11 Fault Tolerant Fusion Precision: Exact agreement solves inconsistency problem –All non faulty nodes obtain the same set of values ?0 ? 0 0 0 1 0 1 0 0 {1,0,0} 0 ? 1 0 0 0 0

12. ECE 753 Fault Tolerant Computing12 Fault Tolerant Fusion Precision: Exact agreement solves inconsistency problem –All non faulty nodes obtain the same set of values ?0 ? 0 0 0 1 0 10 0 {1,0,0,0} 0 ? 1 0 0 0 0

13. ECE 753 Fault Tolerant Computing13 Fault Tolerant Fusion (cont.) Accuracy: consistent outliers remain in the set of values –Dropping highest and lowest values S m m N-2m used for decision

14. ECE 753 Fault Tolerant Computing14 Some research issues: Two approaches for detection Value fusionDecision fusion v1v4?v2 SS?S 11?1 fusion decision v1v4?v2 10?1 11?1 fusion decision

15. ECE 753 Fault Tolerant Computing15 Two approaches for detection Value fusion 1. Perform exact agreement on values 2. Drop highest m and lowest m values 3. Compute average of remaining values 4. Compare to threshold Decision fusion 1. Compare to threshold 2. Perform exact agreement on decision 3. Drop highest m and lowest m decisions 4. Compute average of remaining decision and compare to threshold