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Modeling Data-Centric Routing in Wireless Sensor Networks

Modeling Data-Centric Routing in Wireless Sensor Networks. Bhaskar Krishnamachari, Deborah Estrin, Stephan Wicker. OUTLINE. Introduction Routing Models Data Aggregation Models Theoretical Results Experimental Results Shortcomings Related Work and Conclusions. INTRODUCTION.

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Modeling Data-Centric Routing in Wireless Sensor Networks

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  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 • Data Redundancy • Sensors Not Mobile • Data Aggregation • Eliminate Redundancy • Minimize Transmissions • Save Energy

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

  5. Routing Models • Senarios • All sources have different information • All sources have same data • 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 • Max, min etc…. • Node transmits 1 packet for multiple inputs • Optimal Aggregation • Minimum Steiner tree problem (multicast tree) • Optimum no . Of transmission = no. of edges in the minimum Steiner tree. • 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 5 2 2 b d g b d g 3 1 3 1 1 4 1 5 2 1 e h e h 1 2 2 1 a c f a 3 2 3 *Definition taken from the NIST site. http://www.nist.gov/dads/HTML/steinertree.html

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

  9. Source Placement Models • Nodes distributed randomly per unit sq. • Communication radius • Event Radius Model • Single point origin of event • Data sources in Sensing Range, S • no. of data sources = π * S 2 * n • Random Sources model • 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 • NA = d1 + d2 + …… + dk = sum(di) ------ ( 1 ) • Result 2: optimal transmissions for D.C • source nodes = S1, S2, …. Sk. • diameter X >= 1 • Max of the Pair-wise shortest path between nodes • No. of Transmissions = ND • Optimal ND <= (k – 1)X + min(di) -------- ( 2 ) ND >= min(di) + (k - 1) ----------- ( 3 )

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

  14. Theoretical Results • Result 4: if X <= min(di) then ND < NA • Proof of 4: • ND < ( k – 1) X + min(di) < (k)min(di)  ND < sum(di) = NA --------------------- ( 4 ) • Fractional Savings FS • FS = ( NA – ND ) / ( NA ) ------------------- ( 5 ) • 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-(min(di) + k – 1)/sum(di) --------- ( 7 ) • Result 6: • if min(di) = max(di) = d • 1 – ((k-1)X + d)/kd <= FS <= 1-(d + k – 1)/kd ----- ( 8 ) • If X and k are constant d  ∞ • FS = 1 – 1/k -------------------------------------- ( 9 ) • 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’ = (S1 ….. Sk) is connected  data aggregation in polynomial time • Proof of 7: Start GIT ( greedy incremental tree ) • Initialized with path from sink to nearest source. • New source added in each step. Since G’ is connected • No. of edges = dmin+ 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 • Proof of 8: • If R > 2S all sources are one hop of each other • GIT and CNS result in optimal tree

  17. Experimental Results • ER model • Sensing range S = 0.1 to 0.3 • Communication radius R = 0.15 to 0.45 incr 0.05 • RS model • No of sources k = 1 to 15 incr of 2 • 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 • Communication range low • Reasoning • More sources more transmissions • 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 • 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 • CNSDC is poor • Sources are random • No point aggregating near the sink

  25. No of sources varied

  26. No of sources varied • ER model • CNSDC poor • 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

  27. Delay due to D.C • With Aggregation • Delay proportional to the between sink and furthest source • Difference between these distances • Greatest distance when • Communication radius is low • 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 • A.C cost is path to sink • For given energy budget • More sources in D.C than A.C • More robustness if only fraction of sources accurate

  31. Robustness graph E-R model R-S model

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

  33. Related work • Smart dust motes • TinyOS • PicoRadio • Directed diffusion

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

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