Modelling Data-Centric Routing in Wireless Sensor Networks IEEE INFOCOM 2002. Author:

1. Modelling Data-Centric Routing in Wireless Sensor Networks IEEE INFOCOM 2002. Author: Bhaskar Krishnamachari Deborah Estrin Stephen Wicker Presented by: 高柏鈞(R91725061)

2. Outline • Introduction • Routing Models • Data Aggregation • Energy Savings due to Data Aggregation • Delay due to Data Aggregation • Robustness due to Data Aggregation • Shortcomings of the Modelling • Conclusions

3. Introduction • The Wireless Sensor Networks features: • Consist many inexpensive wireless nodes. • Each node with some computational power and sensing capability. • Operating in an unattended mode. • Because of miniature sensing and radio capability, there are many research with further improvements in cost and capabilities.

4. Introduction (Cont’d) • Similar to mobile ad-hoc networks (MANETs) • Both involve multi-hop communications. • Significantly different for sensor networks • From multiple data sources to a data sink (like reverse-multicast) rather than pairs. • Base on common phenomena, there is likely to be some redundancy data. • In most scenarios the sensors are not mobile.

5. Introduction (Cont’d) • The single major resource constraint in sensor network is that of Energy. • The energy problem is much worse than MANETs, because of unattended operation environment. • Manage Energy Resources more carefully- • Precludes high data rate communication. • End-to-end routing protocols that have been proposed for MANETs are not suitable.

6. Introduction (Cont’d) • Data Aggregation has been put forward as a useful paradigm for sensor networks routing. • Eliminating Redundancy • Minimizing the number of transmissions • Saving Energy • In this paper, we compare the gains and tradeoffs by using two routing models.

7. Routing Models • Two Routing Models: • Address-centric Protocol (AC): Not use data aggregation, each source independently sends data along the shortest path. • Data-centric Protocol (DC): Use data aggregation, regards as data content and perform aggregation function on intermediate.

8. Routing Models (Cont’d)

9. Routing Models (Cont’d) • Differentiating Scenarios • All sources send completely different information (no redundancy). • All sources send identical information (complete redundancy). • The sources send information with some intermediate level of redundancy.

10. Routing Models (Cont’d) • In case 1, both AC and DC protocols will incur the same number of transmissions. • In case 2, the AC protocol can be modified better than the DC protocol. • Let sink monitor the incoming information, if duplication happen then ask others to stop transmitting. • In case 3, the AC protocol cannot be modified much better than the DC, so in this paper we assume this scenario holds.

11. Data Aggregation • Optimal Aggregation • k sources, labelled S1 through Sk. • A sink, labelled D. • Network Graph G=(V,E) consist of all nodes V, with E consisting of edges between nodes that can communicate with each other directly. With the Assumption of the number of transmissions from any node in the data aggregation tree is exactly one, the tree can be thought of as the reverse of a multicast tree: all the sources are sending a single packet to the same receiver.

12. Data Aggregation (Cont’d) Result 1: it is well-known the multicast tree with a minimum number of edges is a minimum Steiner tree, so the optimum number of transmissions required per datum for the DC protocol is equal to the number of edges in the minimum Steiner tree which contains the node set (S1,…Sk, D). Corollary: Assuming an arbitrary placement of sources, the task of doing DC routing with optimal data aggregation is NP-hard.

13. Data Aggregation (Cont’d) Minimum Steiner tree

14. Data Aggregation (Cont’d) • Suboptimal Aggregation • Center at Nearest Source (CNS): the source nearest the sink acts as aggregation point. • Shortest Paths Tree (SPT): Combine all shortest paths from all sources to the sink. • Greedy incremental Tree (GIT): Each step connect the source closest to the current tree. These heuristics of the data aggregation are NP-complete, prove by reference [11] M.R. Garey and D.S. Johnson, Computers and Intractability: A Guide to the Theory of NP-completeness, 1979.

15. Data Aggregation (Cont’d) • Performance measures • Energy Savings:due to aggregation the information, the number of transmissions is reduced, translating to a savings in energy. • Delay: data from nearer sources may have to be held back in order to wait for farther information to combine. • Robustness: with data aggregation there is a decrease in the marginal energy cost of connecting additional sources to the sink.

16. Data Aggregation (Cont’d) • Source Placement Models • Event-Radius Model (ER) • S is sensing range for event • The average number of sources is about π* S2 * n , where nis total nodes of this square.

17. Data Aggregation (Cont’d) • Source Placement Models (Cont’d) • Random-Sources Model (RS) • k of the nodes that are not sinks are randomly selected to be sources. • The sources are not necessarily clustered near each other.

18. Energy Savings • Theoretical Results • Give some analytical bounds on the energy costs and savings based on: • The distances between the sources and the sink. • The inter-distances among the sources. • Upshot: greatest gains when • The sources are all close together. • The sources are far away from the sink.

19. Energy Savings (Cont’d) • Let di be the distance of the shortest path from source Sito the sink in the graph. • Per datum, the total number of transmissions required for the optimal AC protocol (NA) is: Result 2: Let the number of transmissions required for the optimal DC protocol be ND. Then ND≤ NA. NA = d1 + d2 + … + dk = sum(di) (1)

20. Energy Savings (Cont’d) Def: The diameter X = maxi,j∈SourcesSP(i, j) , where SP(i, j) is the shortest number of hops needed to go from node i to j in graph. Result 3: if source S1to Skhave a diameterX ≥ 1, then the following bounds hold: ND≤ (k-1)X + min(di) (2) ND ≥ (k-1)*1 + min(di) (3)

21. Energy Savings (Cont’d) Result 4: if X < min(di), then ND < NA. Base on the (2)  ND < (k-1)X + min(di) < k * min(di)  ND < sum(di) = NA(4) Def: the fractional savings (FS), FS = (NA - ND) / (NA) = 1 – ND / NA (5) • FS can range from 0 (no savings) to 1 (100% savings)

22. Energy Savings (Cont’d) Result 5:directly from (2) and (3), FS satisfies the following bounds: FS ≥ 1-((k-1)X + min(di)) / sum(di) (6) FS ≤ 1-(min(di) + k -1 ) / sum(di) (7) ND≤ (k-1)X + min(di) (2) ND ≥ (k-1)*1 + min(di) (3)

23. Energy Savings (Cont’d) Assume that all sources are at the same shortest-path distance from the sink, i.e. min(di) = max(di) = d. Then we have that Result 6: AssumeX and k are fixed, then

24. Energy Savings (Cont’d) Proof,

25. Energy Savings (Cont’d) Result 7: if the subgraph G’ of the communication graph G induced by the set of source nodes (S1,…Sk) is connected, the optimal data aggregation tree can be formed in polynomial time. Result 8: in the ER model, when R>2S, the optimal data aggregation tree can be formed in polynomial time.

26. Energy Savings (Cont’d) • Experimental Results • For the ER model, sensing range S from 0.10,0.15, 0.20, 0.25, 0.30 are tested. • For the RS model, the number of sourcesk is varied 1 to 15 in increments of 2. • For both, the communication radius R is varied from 0.15 to 0.45 in increments of 0.05. • For each combination of S or k and R100 experiments were run.

27. Energy Savings (Cont’d)

28. Energy Savings (Cont’d)

29. Energy Savings (Cont’d)

30. Delay

31. Delay (Cont’d)

32. Robustness

33. Shortcomings • Make a stark contrast between routing protocols, AC versus DC, is overly simplistic. • Lack of considering overhead costs involved in setting up or maintaining the routing paths. • The analysis of the delay focused only on the latency due to aggregation. • The analysis has focused on the case where there is a single sink.

34. Conclusions • Whether the sources are clustered near each other (ER) or located randomly (RS), significant energy gains are possible with data aggregation. • These gains are greatest when • The number of sources (k) is large . • The sources are located relatively close to each other. • The sources are far from the sink.

35. Conclusions (Cont’d) • The modelling suggest that aggregation latency could be non-negligible and should be taken into consideration during the design process.