1. Modeling Data-Centric Routing in Wireless Sensor Networks Bhaskar Krishnamachari, Deborah Estrin, Stephan Wicker

2. OUTLINE Introduction Routing Models Data Aggregation Models Theoretical Results Experimental Results Shortcomings Related Work and Conclusions

3. INTRODUCTION Sensor Nets Properties Reverse Multicast Reverse Multicast Data Redundancy Data Redundancy Sensors Not Mobile Sensors Not Mobile Data Aggregation Eliminate Redundancy Eliminate Redundancy Minimize Transmissions Minimize Transmissions Save Energy Save Energy

4. Routing Models Address Centric Each source independently send data to sink Each source independently send data to sink Data Centric Routing nodes en-route look at data sent Routing nodes en-route look at data sent Source 2 Source 1 Sink BA Source 2 Source 1 Sink BA

5. Routing Models Senarios All sources have different information All sources have different information All sources have same data All sources have same data Sources send Info with not deterministic redundancy. Sources send Info with not deterministic redundancy. 1 A.C and D.C equivalent 2.A.C can be better 3 D.C is better

6. DATA AGGREGATION Aggregation function is simple Duplicate suppression Duplicate suppression Max, min etc…. Max, min etc…. Node transmits 1 packet for multiple inputs Node transmits 1 packet for multiple inputs Optimal Aggregation Minimum Steiner tree problem (multicast tree) Minimum Steiner tree problem (multicast tree) Optimum no. Of transmission = no. of edges in the minimum Steiner tree. Optimum no. Of transmission = no. of edges in the minimum Steiner tree. NP Hard problem NP Hard problem

7. Steiner Trees *A minimum-weight tree connecting a designated set of vertices, called terminals, in a weighted graph or points in a space. The tree may include non- terminals, which are called Steiner vertices or Steiner points bdg a e c h f 5 2 5 41 12 32 3 2 31 2 1 bdg a eh 1 2 1 31 *Definition taken from the NIST site. http://www.nist.gov/dads/HTML/steinertree.html

8. Data Aggregation Suboptimal Aggregation Center at Nearest Source (CNS) Center at Nearest Source (CNS) Shortest Paths Tree (SPT) Shortest Paths Tree (SPT) Greedy Incremental tree (GIT) Greedy Incremental tree (GIT) Performance measures Energy savings Energy savings Delay Delay Robustness Robustness

9. Source Placement Models Nodes distributed randomly per unit sq. Communication radius Communication radius Event Radius Model Single point origin of event Single point origin of event Data sources in Sensing Range, S Data sources in Sensing Range, S no. of data sources = π * S 2 * n no. of data sources = π * S 2 * n Random Sources model K nodes randomly distributed act as sources K nodes randomly distributed act as sources

10. Source Placement (Event Radius) Figure from the original paper.

11. Source Placement (random) Figure from the original paper.

12. Theoretical Results Max gains sources close together, sink far Result 1: Total no. of transmissions for A.C N A = d 1 + d 2 + …… + d k = sum(d i ) ------ ( 1 ) N A = d 1 + d 2 + …… + d k = sum(d i ) ------ ( 1 ) Result 2: optimal transmissions for D.C source nodes = S 1, S 2, …. S k. source nodes = S 1, S 2, …. S k. diameter X >= 1 diameter X >= 1 Max of the Pair-wise shortest path between nodes No. of Transmissions = N D No. of Transmissions = N D Optimal N D <= (k – 1)X + min(d i ) -------- ( 2 ) Optimal N D <= (k – 1)X + min(d i ) -------- ( 2 ) N D >= min(d i ) + (k - 1) ----------- ( 3 ) N D >= min(d i ) + (k - 1) ----------- ( 3 )

13. Theoretical results Proof of 2. Data aggregation tree Data aggregation tree K – 1 sources  source nearest sink K – 1 sources  source nearest sink No. of edges <= ( k – 1 )X + min(di) No. of edges <= ( k – 1 )X + min(di) Optimum <= No of edges Optimum <= No of edges Proof of 3 Smallest possible steiner tree if X = 1 Smallest possible steiner tree if X = 1

14. Theoretical Results Result 4: if X <= min(d i ) then N D < N A Proof of 4: N D < ( k – 1) X + min(d i ) < (k)min(d i ) N D < ( k – 1) X + min(d i ) < (k)min(d i )  N D < sum(d i ) = N A --------------------- ( 4 ) Fractional Savings FS FS = ( N A – N D ) / ( N A ) ------------------- ( 5 ) FS = ( N A – N D ) / ( N A ) ------------------- ( 5 ) Range from 0 to 1 Range from 0 to 1

15. Theoretical Results Result 5: bounds for FS FS >= 1 – ((k-1)X + min(di))/sum(di) ----- ( 6 ) FS >= 1 – ((k-1)X + min(di))/sum(di) ----- ( 6 ) FS <= 1-(min(di) + k – 1)/sum(di) --------- ( 7 ) FS <= 1-(min(di) + k – 1)/sum(di) --------- ( 7 ) Result 6: if min(di) = max(di) = d if min(di) = max(di) = d 1 – ((k-1)X + d)/kd <= FS <= 1-(d + k – 1)/kd ----- ( 8 ) 1 – ((k-1)X + d)/kd <= FS <= 1-(d + k – 1)/kd ----- ( 8 ) If X and k are constant d  ∞ If X and k are constant d  ∞ FS = 1 – 1/k -------------------------------------- ( 9 ) If sink is far and sources close FS is k fold If sink is far and sources close FS is k fold 4 sources FS = 1-1/4 = 75% fewer transmissions 10 sources = 90 %

16. Theoretical Results Result 7: if Sub-graph G’ = (S 1 ….. S k ) is connected  data aggregation in polynomial time Proof of 7: Start GIT ( greedy incremental tree ) Initialized with path from sink to nearest source. Initialized with path from sink to nearest source. New source added in each step. Since G’ is connected New source added in each step. Since G’ is connected No. of edges = d min + k – 1 = lower bound in ( 3 ) No. of edges = d min + k – 1 = lower bound in ( 3 ) Result 8: in ER model when R > 2S optimal D.C runs in polynomial time R = communication radius, S = event Radius R = communication radius, S = event Radius Proof of 8: If R > 2S all sources are one hop of each other If R > 2S all sources are one hop of each other GIT and CNS result in optimal tree GIT and CNS result in optimal tree

17. Experimental Results ER model Sensing range S = 0.1 to 0.3 Sensing range S = 0.1 to 0.3 Communication radius R = 0.15 to 0.45 incr 0.05 Communication radius R = 0.15 to 0.45 incr 0.05 RS model No of sources k = 1 to 15 incr of 2 No of sources k = 1 to 15 incr of 2 Communication radius same as above. Communication radius same as above. N = 100 nodes randomly placed / unit area NEXT EXPERIMENTAL RESULTS

18. Ideal A.C for E-R model Figure from the original paper.

19. Ideal A.C for R-S model Figure from the original paper.

20. A.C Model Cost highest when More sources More sources Communication range low Communication range lowReasoning More sources more transmissions More sources more transmissions More hops between sink and sources More hops between sink and sources

21. Energy Costs E-R model Figure from the original paper.

22. Energy Costs E-R model GITDC coincides with optimal Even Moderate S  connected subgraph Even Moderate S  connected subgraph Result 7 holds As R increases  CNSDC optimal Result 8 holds

23. Energy Costs R-S model Figure from the original paper.

24. Energy Costs R-S model As R increases GITDS is best SPTDS, CNSDS and AC SPTDS, CNSDS and AC CNSDC is poor Sources are random Sources are random No point aggregating near the sink No point aggregating near the sink

25. No of sources varied

26. ER model CNSDC poor CNSDC poor e.g s = 0.3 nearly 1/3 of all nodes are sources e.g s = 0.3 nearly 1/3 of all nodes are sources Route directly to sink is faster R-S model GITDC performance significantly better GITDC performance significantly better

27. Delay due to D.C With Aggregation Delay proportional to the between sink and furthest source Delay proportional to the between sink and furthest source Difference between these distances Difference between these distances Greatest distance when Communication radius is low Communication radius is low No. of sources is high No. of sources is high

28. Communication radius varied

29. No. of sources varied

30. Robustness Lower cost of adding nodes E.g. GITDC cost is shortest path of new node from tree E.g. GITDC cost is shortest path of new node from tree A.C cost is path to sink A.C cost is path to sink For given energy budget More sources in D.C than A.C More sources in D.C than A.C More robustness if only fraction of sources accurate More robustness if only fraction of sources accurate

31. Robustness graph E-R modelR-S model

32. Shortcomings Overly simplistic A.C vs D.C Not considered overhead costs of routing Routing specific Routing specific Delay considered only specific to aggregation Processing delay, congestion Processing delay, congestion Single sink

33. Related work Smart dust motes TinyOSPicoRadio Directed diffusion

34. Conclusion Gains from D.C most when sources clustered together and far from sink Robustness increase Latency can be no negligible