Bing Wang, Wei Wei, Hieu Dinh, Wei Zeng, Krishna R. Pattipati (Fellow IEEE) IEEE Transactions on Mobile Computing, March 2012

 Introduction  Problem Setting and Goal  Optimal Sequential Testing  Heuristic Sequential Testing Schemes ◦ Ordering Algorithm ◦ Greedy Algorithm  Performance Evaluation  Conclusions

 Wireless sensor networks have been deployed in a wide range of applications.  A deployed sensor network may suffer from many network-related faults, e.g., malfunctioning or lossy nodes or links.  These faults affect the normal operation of the network, and hence should be detected localized and corrected/repairs.

 Two categories exist in literature ◦ Active Measurement ◦ Passive Measurement

 Active Measurement ◦ A node needs to monitor itself or its neighbors, and transmit the monitoring results locally or to a centralized server. ◦ Advantages  Exactly pinpoint the faults. ◦ Drawback  Consume precious resources of sensor nodes  Reduce the lifetime of the network.

 Passive Measurement ◦ Uses existing end-to-end data inside networks: if end-to-end data indicate faulty end-to-end behaviors, then some components in the network must be faulty. ◦ Advantage  No additional traffic into the network ◦ Drawback  It poses the challenge of fault inference-accurate inference from end-to-end data.

 Motivated by the complementary strengths of active and passive measurements, the authors propose an approach ◦ Using active measurement to resolve ambiguity in passive measurements ◦ Using passive measurement to guide active measurements to reduce expected testing cost

 Consider a sensor network where sensed data are sent from sources to a sink.  The amount of end-to-end data can be used to detect faults in the network.  The goal of this paper is to localize persistently lossy links that are used in routing.

 The status of a component can be tested through active measurements.  The test incurs a testing cost ◦ The personnel wages when human is involved ◦ The resources used at a sensor node to monitor itself and neighboring nodes/links ◦ The energy and network bandwidths used to transfer the monitoring results to the sink

 A link is lossy or not based on its average loss rate or reception rate.  The threshold, t l, can clearly separate good and bad links.

 Complete path information ◦ Know the path used by a source at any point of time  Probabilistic path information ◦ Only know the set of paths that are used by a source and the probability using each path

 The authors define path reception rate as the probability that a packet traverses a path successfully. ◦ When n data packets are transmitted along a path and m packets are received successfully, the path reception rate is estimated as m/n.

 Using end-to-end data, we have narrowed down the potential lossy links to the set of links that are used by bad paths/pairs, excluding those used by good paths/pairs. Testing cost

 An optimal solution to the sequential testing problem is one that leads to the minimum expected total test cost  The goal of this paper ◦ To minimize expected testing cost  The authors also proved the sequential testing problem is NP-hard problem.

 For a given instance of the optimal sequential testing problem, I  The recursive equation: the minimum expected testing cost the testing cost of link l k the prior probability that link l k is lossy I kb is the resultant instance when l k is found to be lossy I kg is the resultant instance when l k is found to be good

P1P1 P2P2 Expected testing cost: c 1

P1P1 P2P2 Expected testing cost: c 3 + (1-p 3 )*(c 1 + c 2 )

 Two heuristic schemes are proposed in this paper. ◦ Ordering Algorithm ◦ Greedy Algorithm

 In each step, this algorithm picks the link with the highest n k p k /c k to test, ◦ where n k is the number of paths that use link l k

4 paths: P 1 =(l 2, l 1 ) P 2 =(l 3, l 1 ) P 3 =(l 4, l 1 ) P 4 =(l 5 ) If we know complete path information l 1, l 2, l 3, l 4 l1l1 l 2, l 3, l 4 l1l1 G B nkpk/cknkpk/ck

If we know probabilistic path information 3 bad pairs: P 1 =(l 2, l 1 ) P 2 =(l 3, l 1 ) P 3 =(l 4, l 1, l 5 )

 In each step, this algorithm picks the link that provides the highest gain.  The gain from knowing the status of a link is defined as the cost savings subtracted by the testing cost of this link.

 If we know the complete path information 4 paths: P 1 =(l 2, l 1 ) P 2 =(l 3, l 1 ) P 3 =(l 4, l 1 ) P 4 =(l 5 )

 If we know the probabilistic path information 3 bad pairs: P 1 =(l 2, l 1 ) P 2 =(l 3, l 1 ) P 3 =(l 4, l 1, l 5 )

 The complexity of the ordering algorithm is O(| L | 2 | P |)  The complexity of the greedy algorithm is O(| L | 3 | P |)  In some special topology cases, the greedy scheme leads to optimal solutions while the greedy scheme may not.

 The network is deployed in a 10unit X 10unit square.  A single sink is deployed at the center.  500 nodes are deployed in the square.  The transmission range of each node is 3 units.  At a given point of time, the paths from the sources to the sink form a reversed tree.

 The exhaustive inspection approach infers in parallel a set of potential faulty components from end-to-end measurements, tests each identified component, and repairs the faulty ones at the end of the iteration.

 The authors formulated an optimal sequential testing problem that carefully combines active and passive measurements for fault localization in WSN.  The authors proposed a recursive approach and two heuristic algorithms to solve it.