1. 1-1 CMPE 259 Sensor Networks Katia Obraczka Winter 2005 Topology Control II

2. 1-2 Announcements r Homework due on 02.14. r Projects? r Gabriel Elkaim’s talk on GPS: 02.09. r Venkatesh Rajendra’s talk on MAC: 02.16.

3. 1-3 PEAS

4. 1-4 PEAS r Probing Environment, Adaptive Sleeping. r “Extra” nodes are turned off. r Nodes keep minimum state. m No need for neighborhood-related state. r PEAS consiers very high node density and failures are likely to happen.

5. 1-5 Bi-modal operation r Probing environment. r Adaptive sleeping.

6. 1-6 PEAS state diagram Working Sleeping Probing No reply for probe Wakes up Hears probe reply.

7. 1-7 Probing r When node wakes up, enters probing mode. r Is there working node in range? m Broadcasts PROBE to range Rp. m Working nodes send REPLY (randomly scheduled). m Upon receiving REPLY, node goes back to sleep. Adjusts sleeping interval accordingly. m Else, switches to working state.

8. 1-8 Considerations r Probing range is application-specific. m Robustness (sensing and communication) versus energy-efficiency. r Location-based probing as a way to achieve balance between redundancy and energy efficiency. r Randomized sleeping time. m Better resilience to failure. m Less contention. m Adaptive based on “desired probing rate”.

9. 1-9 More considerations… r Multiple PROBEs (and multiple REPLIES) to compensate for losses. m Multiple PROBEs randomly spread over time. r Multiple working nodes in the neighborhood. m Favor “oldest” one. r Nodes with fixed transmit power. r Deployment density.

10. 1-10 Evaluation r Simulations. r Simulated failures: failure rate and failure percentage. r Metrics: m Coverage lifetime. m Delivery lifetime.

11. 1-11 Results r With and without failures. r From the paper…

12. 1-12 “Exposure In Wireless Ad- Hoc Sensor Networks”

13. 1-13 Sensor Coverage r Given: m Field A m N sensors How well can the field be observed ? r Closest Sensor (minimum distance) only m Worst Case Coverage: Maximal Breach Path m Best Case Coverage: Maximal Support Path r Multiple Sensors: speed and path considered Minimal Exposure Path

14. 1-14 Exposure - Semantics r Likelihood of detection by sensors function of time interval and distance from sensors. r Minimal exposure paths indicate the worst case scenarios in a field: m Can be used as a metric for coverage Sensor detection coverage Wireless (RF) transmission coverage r For RF transmission, exposure is a potential measure of quality of service along a specific path.

15. 1-15 Preliminaries: Sensing Model Sensing model S at an arbitrary point p for a sensor s : where d(s,p) is the Euclidean distance between the sensor s and the point p, and positive constants and K are technology- and environment-dependent parameters.

16. 1-16 Preliminaries: Intensity Model(s) Effective sensing intensity at point p in field F : All Sensors Closest Sensor K Closest Sensors K=3 for Trilateration

17. 1-17 Definition: Exposure The Exposure for an object O in the sensor field during the interval [t 1,t 2 ] along the path p(t) is:

18. 1-18 Exposure – Coverage Problem Formulation Given: m Field A m N sensors m Initial and final points I and F Problem: Find the Minimal Exposure Path P minE in A, starting in I and ending in F. P minE is the path in A, along which the exposure is the smallest among all paths from I to F.

19. 1-19 Special case – one sensor Minimal exposure path for one sensor in a square field:

20. 1-20 General Exposure Computations r Analytically intractable. r Need efficient and scalable methods to approximate exposure integrals and search for Minimal Exposure Paths. Use a grid-based approach and numerical methods to approximate Exposure integrals. Use a grid-based approach and numerical methods to approximate Exposure integrals. Use existing efficient graph search algorithms to find Minimal Exposure Paths. Use existing efficient graph search algorithms to find Minimal Exposure Paths.

21. 1-21 Minimal Exposure Path Algorithm r Use a grid to approximate path exposures. r The exposure (weight) along each edge of the grid approximated using numerical techniques. r Use Dijkstra’s Single-Source Shortest Path Algorithm on the weighted graph (grid) to find the Minimal Exposure Path. r Can also use Floyd-Warshall All-Pairs Shortest Paths Algorithm to find P minE between arbitrary start and end points.

22. 1-22 Generalized Grid Generalized Grid – 1 st order, 2 nd order, 3 rd order … More movement freedom  more accurate results Approximation quality improves by increasing grid divisions with higher costs of storage and run-time.

23. 1-23 Minimal Exposure Path Algorithm Complexity r Single Source Shortest Path (Dijkstra) m Each point is visited once in the worst case. m For an nxn grid with m divisions per edge: n 2 (2m-1)+2nm+1 total grid points. m Worst case search: O(n 2 m) m Dominated by grid construction. m 1GHz workstation with 256MB RAM requires less than 1 minute for n=32, m=8 grids. r All-Pairs Shortest Paths (Floyd-Warshall) m Has a average case complexity of O(p 3 ). m Dominated by the search: O((n 2 m) 3 ) m Requires large data structures to store paths.

24. 1-24 Uniform Random Deployment Minimal exposure path for 50 randomly deployed sensors using the All-Sensor intensity model (I A ). 8x8 m=1 Exposure:0.7079 Length:1633.9 16x16 m=2 Exposure:0.6976 Length:1607.7 32x32 m=8 Exposure:0.6945 Length:1581.0

25. 1-25 Exposure – Statistical Behavior Diminishing relative standard deviation in exposure for 1/d 2 and 1/d 4 sensor models.

26. 1-26 Deterministic Deployments Minimal exposure path under the All-Sensor intensity model (I A ) and deterministic sensor deployment schemes. CrossSquareTriangleHexagon Exposure Level (compared to Square) 1.5x 30x~120 1.5x3x 6x~20 HexagonTriangleCrossSensors

27. 1-27 Exposure – Research Directions r Localized implementations r Performance and cost studies subject to m Wireless Protocols (MAC, routing, etc) m Errors in measurements Locationing Sensing Numerical errors m Computation based on incomplete information Not every node will know the exact position and information about all other nodes

28. 1-28 Parametric probabilistic routing

29. 1-29 Approaches to routing r Ad hoc network “on-demand” routing: m Compute path then send data. m If data is small, overkill? r Flooding is expensive. r Wanderer approach: pick neighbor with some probability to forward data to. m Problems? r Pure gossip: flooding+wanderer. m At each node, picks one or the other with some probability. m Either almost all nodes receive packet or almost no nodes receive it.

30. 1-30 Proposed approach r Parametric probability routing: m Controlled flooding. m Every node decides to forward packet to neighbors using a probability function. m Probability function based on: distance to destination, distance from original source to destination, number of copies already received, etc. m 2 variants: Destination attractor. –S-D distance and CS-D distance. Directed transmission. –Also uses number of hops already traversed by packet.

31. 1-31 Destination attractor r P Ri, or retransmission probability, given by: m (1+k) P Ri-1 if packet is getting closer to D. m (1-k) P Ri-1 if packet is getting farther from D. m P Ri-1 if same or undefined. r k can be adjusted to compensate for “noise” due to losses, mobility, etc.

32. 1-32 Directed transmission r Nodes on shortest path from S-D should forward with high probability. r P Ri = exp{k[d(S,D) – d(Ri,D) – I]}, where m d(S,D) is distance between source and destination. m d(Ri,D) is distance between current node and destination, and m i is number of hops traveled so far.

33. 1-33 Estimating global information r Number of hops traveled so far, i, is easy. r Estimating distance to D: m Each sensor includes its current estimate of distance to D. m When receiving that information from neighbor, sensor updates its information by adding 1. m Sensor chooses its d(S,D) to be the minimum of the currently received information from neighbors.

34. 1-34 Evaluation r Simulations. r Noise is used to simulate inaccuracies. r Metrics: m Load m Lag. m Fraction delivered. m Overhead?

35. 1-35 Results r From paper…