Robust k-Coverage Algorithms for Sensor Networks

1. Robust k-Coverage Algorithms for Sensor Networks 노상훈@pllab.kut 2009. 04. 27 PLLAB@KUT

2. Contents PLLAB@KUT • Introduction • CGS Algorithm • Background • Assumption • QoS Metrics • Algorithm • Fault Tolerance of The CGS Algorithm • Result • Summary

3. Introduction PLLAB@KUT • Purpose • Energy conservation -> Prolong network lifetime • Random approach • Assign probability • Awake/sleep randomly on probability • Cannot ensure k-coverage • Coordinated approach • Use “drowsiness factor” for scheduling • Centralized approach • Distributed approach • Ensure k-coverage if physically possible • Cost: network overhead and energy consumption

4. CGS Algorithm: background #1 PLLAB@KUT • CGS:Controlled greedy sleep • Graph: G(R∪S,E) • R:Range • S:Sensors • E:Edges • k-Coverage problem • subgraph problem • G’(R∪S’,E’)where S’ ⊆ S • Minimal k-Coverage problem • Nonredundant withG’’(R∪S’’,E’’)where S’’ ⊆ S

5. CGS Algorithm: background #2 PLLAB@KUT • Centralized solution • A Coordinated node knows whole graph G • Distributed solution • Each node q knows itself and it’s neighborsand covers Rq • Gq(Rq∪Sq,Eq)

6. CGS Algorithm: assumption #1 PLLAB@KUT • Assumption 1 • communication radius ≥2*sensing radius • Assumption 2 • Coverage of each sensor modeled by a sensing disk and the radius is B • Approximation of the sensing disk by a set of squares

7. CGS Algorithm: assumption #2 PLLAB@KUT • Assumption 3 • The sensors know their own coordinates and the observed area Σ • Reflect Maximum location error Δl

8. CGS Algorithm: QoS Metrics PLLAB@KUT • k-coverage ratio • Ak: area of the k-coverage regions • A: Area of the target space Σ • Approximation of • Nk: number of the k-covered regions • N: total number of regions in the target space • k-lifetime of a network • Maximum operation time of the network with

9. CGS Alogirthm #1 PLLAB@KUT • Drowsiness factor • Energy status • importance in the network • Coverage ratio of region r • cr: degree of region r in Gs • positive if overcovered

10. CGS Alogirthm #2 Whole sensors awaken Drowsiness Factor Decision Time Delay Awake Message List of awake neighbors Delay List PLLAB@KUT

11. Fault Tolerance of the CGS Algorithm:Fault Model PLLAB@KUT • Kind of Messages • Hello messages • DTD messages • AMs • Messages can be lost • Collision • Fading • External disturbances • Assume • Any messages can be lost (worst case whole message) • but received message is correct (error detecting coding)

12. Fault Tolerance of the CGS Algorithm:Guaranteed Coverage, Effect of Lost Messages PLLAB@KUT • Theorem: If physically possible, the algorithm will provide • Lost Hello Messages • Prevent inclusion of neighbors to in the alive neighbor set Ss → drowsiness factor will be unnecessarily high • Lost DTD messages • The DTD is higher → harmful • Sender is not considered as a potential participant in the coverage • Lost AMs • Potential overcoverage • Cannot rely on the presence of the senders of them • Lost messages cause overcoverage • Unnecessarily high number of sensors staying awake • Shortening of the network lifetime

13. Fault Tolerance of the CGS Algorithm:Effect of Node Failures PLLAB@KUT • Effect of node failure can be divide by steps • During an awake period • Some regions will undercovered until the end of the period • Next election will provide sufficient coverage • During a sleep period: No effect • During the Hello phase • CGS behavior is equivalent to the loss of Hello messages • During the DTD phase (problem!) • Node with higher drowsiness factor may incorrectly rely on the presence of the failed node • Node failure generally cause • Shortening of the lifetime of the network • Possible coverage in certain regions and total amount of energy in the network decrease

14. Fault Tolerance of the CGS Algorithm:Effect of Time synchoronization Errors PLLAB@KUT • A out of synchronized node • Wakes up while the synchronization phase is running • Synchronize again • Cannot synchronize • Provide extra coverage in its neighborhood • To ensure proper operation, • The synchronization period must be long enough • To enable all nodes to wake up and join the synchronization • Small timing errors have no effect • On Hello/DTD messages • But AM’s timing error might change priority • In general, • Large timing errors cause large message delays(ultimately loss) • But the algorithm is very tolerant in this respect • Do not affect the provided k-coverage, still shorten the network lifetime

15. Result PLLAB@KUT

16. Summary PLLAB@KUT • Distributed algorithm proposed • Solve k-coverage problems • Provide prolong network time • Proposed algorithm broadcast few messages • CGS algorithm is robust and fault tolerant • CGS algorithm is better than random k-coverage algorithm • Guarantees required coverage if possible • Degrading curve is much gentler

17. Reference PLLAB@KUT G. Simon, M. Molnar, L. Gonczy, B. Cousin, Robust k-Coverage Algorithms for Sensor Networks, IEEE Transactions on Instrumentation and Measurement, Vol. 57, No. 8, pp. 1741-1748, Aug. 2008.

18. Supplement #1 PLLAB@KUT See Theorem 1

19. Supplement #2 Back PLLAB@KUT

20. Supplement #3 Back PLLAB@KUT