1. AISP Workshop, May 2, 20071 Querying in Wireless Sensor Networks Bhaskar Krishnamachari Ming Hsieh Department of Electrical Engineering USC Viterbi School of Engineering

2. 2 Example: Interference-Free Channel Allocation Prior Work: Phase Transitions and Complexity in Wireless Networks Work with Ramon Bejar, Stephen Wicker, Cesar Fernandez, Bart Selman, Ashish Goel, Sanatan Rai

3. 3 Wireless Sensor Networks Large scale networks of small embedded devices, each with sensing, computation and communication capabilities. Use of wireless networks of embedded computers “could well dwarf previous milestones in the information revolution” – National Research Council Report: Embedded, Everywhere, 2001.

4. 4 Structural monitoringBio-habitat monitoring Military surveillanceDisaster management Industrial monitoring Note: images used may be copyrighted. Used here for limited educational purposes only. Not intended for commercial or public use. Home/building security Wide Ranging Applications

5. 5 Two Paradigms Continuous collection Distributed storage and querying

6. 6 Focus of this Talk Analysis and Design of Mechanisms for Storage and Querying: –Fundamental Scaling Laws –Comparison of Push-Pull Query Mechanisms –Enhancing Random Walk-based Queries

7. 7 Fundamental Scaling Laws for Store and Query Sensor Networks Joon Ahn and Bhaskar Krishnamachari, "Fundamental Scaling Laws for Energy- Efficient Storage and Querying in Wireless Sensor Networks", ACM MobiHoc, May 2006.

8. 8 Race between increasing supply and demand: - Energy and storage - Application-specific event and query traffic The winner of this race determines scalability. In a Nutshell

9. 9 N nodes deployed in a 2D area with constant density for some time duration T m atomic events and q i queries for the i th event, all uniformly distributed Can create r i replicas for event i to reduce search cost (at the expense of increased replication cost) Each transmission incurs a unit energy cost Preliminaries

10. 10 Data-Centric Querying Approaches Unstructured: expanding ring searches, random walks. Structured: Geographic Hash Table, DIFS, DIM

11. 11 Energy Cost Scaling C replication = c 1 r : # of copies of an event N : # of nodes C search ( unstructured ) = c 2 C search ( structured ) = c 3 EVENTEVENT REPLICATIONUNSTRUCTURED QUERYSTRUCTURED QUERY

12. 12 Energy Optimization Formulation S : total storage size m : the total number of events q i : the query rate for i th event r i : the number of copies of i th event C s (r i ) : the expected minimum search cost of i th event C r (r i ) : the expected replication cost of i th event C r (r) = c 1 C s (r) = c 2

13. 13 Optimization Solution Minimizer The Optimized Total Cost (inactive constraint) (active constraint) q i : # of queries for event i N : # of nodes S : total storage size m : # of events

14. 14 Optimal Total Cost Simplified, assuming : q : # of queries per event N : # of nodes S : total storage size m : # of events if

15. 15 Illustration of Energy Scaling m : # of events q : # of queries per event

16. 16 I - Storage and Energy Scalability Results Energy Condition The energy requirement per node is bounded if and only if mq 1/2 = O(N 1/4 )  Energy constraint is stricter than storage constraint m : # of events q : # of queries per event N : # of nodes Storage Condition A network scales efficiently with bounded storage per node if mq 1/2 = o(N 3/4 )

17. 17 II - Fixed Energy Budget Results S – successful operation region N : # of nodes e: per-node energy budget

18. 18 III - Network Lifetime Scaling Results Network Lifetime as a function of Network Size

19. 19 Summary Only certain classes of applications can be sustained in arbitrarily large sensor networks. Specifically, if mq 1/2 = O(N 1/4 ) for unstructured networks, and mq 2/3 = O(N 1/2 ) for structured networks: a.The network can operate with bounded energy and storage per node. b.The network lifetime does not decrease with network size for a given energy budget. These results generalize in a straightforward manner to 1D and 3D deployments. 3D deployments are inherently more scalable. The results can be reinterpreted to understand how to tier sensor networks into zones with localized queries

20. 20 Comparison of Push-Pull Schemes for Querying Shyam Kapadia and Bhaskar Krishnamachari, "Comparative Analysis of Push-Pull Query Strategies for Wireless Sensor Networks," DCOSS, 2006.

21. 21 Overview Two Hybrid Push-Pull Schemes: –Geographic Hash Tables/Data Centric Storage [1] –Comb-Needles [2] [1] S. Shenker et al., Data-centric storage in sensornets, ACM CCR, Jan 2003. [2] X. Liu et al., Combs, needles, haystacks: balancing push and pull for discovery in large-scale sensor networks, ACM SenSys '04.

22. 22 - sink/querier - source/event node -Hashed location where events are stored Data Centric Storage (DCS)

23. 23 - sink/querier - source/event node Needles Query path (comb) s Comb Needles (CN)

24. 24 Model Assumptions Square Grid of N nodes Sink located at left-bottom corner Events (say E) valid for an epoch –Single attribute (event type) –Uniform distribution of events across nodes Energy measured in number of unicast transmissions Query probability Q Aggregation –One packet summary of all events No modeling of collisions and contention

25. 25 ALL-Type Query: DCS vs CN (Without Summaries)

26. 26 ALL-Type Query: DCS vs CN (With Summaries) Θ ~ 39.78

27. 27 ANY-Type Query: DCS vs SCN Θ lower ~ 1.56 Θ upper ~ 3.16

28. 28 Random Walk Queries For Heterogeneous Networks Marco Zuniga, Chen Avin, and Bhaskar Krishnamachari, "Using Heterogeneity to Enhance Random Walk-based Queries," USC Computer Engineering Technical Report CENG-2006- 8, August 2006.

29. 29 Random Walk Queries For Heterogeneous Networks Marco Zuniga, Chen Avin, and Bhaskar Krishnamachari, "Using Heterogeneity to Enhance Random Walk-based Queries," USC Computer Engineering Technical Report CENG-2006- 8, August 2006.

30. 30 Simple Enhancement for Heterogeneous Networks Push event greedily to high degree nodes (local maximum) Querier issues simple random walk

31. 31 Simulation Results A small fraction of high-degree cluster-heads (<10%) can provide a query cost improvement between 30% and 90%.

32. 32 Analysis on Linear Topology d kk

33. 33 Resistance Method Hitting time (h uv ) : expected time taken by a random walk starting at u to reach. Commute time (C uv ) : expected time taken by a random walk starting at u to reach v and come back to u. C uv = h uv + h vu, in general h uv ≠ h vu but in case of symmetry h uv = h vu 1 ohm resistors C uv = 2 m R uv m : number of edges R uv : effective resistance between u and v Chandra et al., 1989, The electrical resistance of a graph captures its commute and cover times, ACM STOC

34. 34 d k Region 1 Region 2 Region 3 r(k) k k d k d 3 Regions 2k <= d k < d <2k d <= k

35. 35 Region 1 [ 2k <= d] d k k

36. 36 d-k r(d-k) 1/2 << = α = 2k-d d-k r(d-k) 1/2 Region 2 [ k < d < 2k ] α r(d-k)

37. 37 = Region 3 [ d =k ] d

38. 38 Expected Hitting Time

39. 39 Result The first local minima for the query cost is obtained when the fraction of high-degree nodes is 4/5k, where cost is reduced by a factor of Θ(k 2 )

40. 40 Enhancing Random Walks Using Power of Choice Chen Avin and Bhaskar Krishnamachari, "The Power of Choice in Random Walks: An Empirical Study," 9th ACM/IEEE International Symposium on Modeling, Analysis and Simulation of Wireless and Mobile Systems, (MSWiM), Malaga, Spain, October 2006. (Best Paper Award)

41. 41 Cover TimeVisit Load

42. 42 Thanks