Modeling DataCentric Routing in Wireless Sensor Networks Bhaskar

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

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

Routing Models Senarios n n n 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

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

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 b 4 5 d 3 1 1 e 1 a g b 1 2 e 2 c g 3 1 h 1 f 2 d 1 h 2 3 2 a 3 *Definition taken from the NIST site. http: //www. nist. gov/dads/HTML/steinertree. html

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

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

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

Source Placement (random) Figure from the original paper.

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

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

Theoretical Results Result 4: if X <= min(di) then ND < NA Proof of 4: n ND < ( k – 1) X + min(di) < (k)min(di) ND < sum(di) = NA ----------- ( 4 ) Fractional Savings FS n n FS = ( NA – ND ) / ( NA ) ---------- ( 5 ) Range from 0 to 1

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

Theoretical Results Result 7: if Sub-graph G’ = (S 1 …. . Sk) is connected data aggregation in polynomial time Proof of 7: Start GIT ( greedy incremental tree ) n n n 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 > 2 S optimal D. C runs in polynomial time n R = communication radius, S = event Radius Proof of 8: n n If R > 2 S all sources are one hop of each other GIT and CNS result in optimal tree

Experimental Results ER model n n Sensing range S = 0. 1 to 0. 3 Communication radius R = 0. 15 to 0. 45 incr 0. 05 RS model n n 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

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

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

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

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

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

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

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

No of sources varied

No of sources varied ER model n CNSDC poor e. g s = 0. 3 nearly 1/3 of all nodes are sources Route directly to sink is faster R-S model n GITDC performance significantly better

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

Communication radius varied

No. of sources varied

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

Robustness graph E-R model R-S model

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

Related work Smart dust motes Tiny. OS Pico. Radio Directed diffusion

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