Sensor Placement and Lifetime of Wireless Sensor Networks: Theory and Performance Analysis

1. Sensor Placement and Lifetime of Wireless Sensor Networks:Theory and Performance Analysis Ekta Jain and Qilian Liang, Department of Electrical Engineering, University of Texas at Arlington IEEE GLOBECOM 2005

2. Outline • Introduction • Preliminaries • Node Lifetime Evaluation • Network Lifetime Analysis Using Reliability Theory • Simulation • Conclusion

3. Introduction (1/3) • Sensor networks have limited network lifetime. • energy-constrained • Most applications have pre-specifiedlifetime requirement. • Example: [4] has a requirement of at least 9 months • Estimation of lifetime becomes a necessity. [4] A. Mainwaring, J. Polastre, R. Szewczyk, D. Culler, J. Anderson, ”Wireless Sensor Networks for Habitat Monitoring”

4. Introduction (2/3) • SensorPlacement vs. Lifetime Estimation • Two basic placement schemes: Square Grid, Hex-Grid. • Bottom-up approach lifetime evaluation. • Theoretical Result vs. Actual Result • by extensive simulations

5. Introduction (3/3) • Bottom-up approach to lifetime evaluation of a network. Lifetime Behavior Analysis (single sensor node) Lifetime Behavior Analysis (sensor networks using two basic placement schemes)

6. PreliminariesBasic Model • rs : the sensing range • rc : the communication range • neighbors • distance of separationr ≤ rc assume rs = rc rs r

7. PreliminariesBasic Model • The maximum distance between two neighboring nodes: • rmax = rc = rs • A network is said to be deployed with minimum density when: • the distance between its neighboring nodes is r =rmax

8. PreliminariesPlacement Schemes Placement Schemes 3-neighbor group 4-neighbor group 2-neighbor group Square Grid described in [1] Hex-Grid [1] K. Kar, S. Banerjee, ”Node Placement for Connected Coverage in Sensor Networks”

9. PreliminariesPlacement Scheme in Reference [1] 2-neighbor group and provides full coverage!! [1] K. Kar, S. Banerjee, ”Node Placement for Connected Coverage in Sensor Networks”

10. Square Grid Hex-Grid PreliminariesPlacement Schemes

11. PreliminariesCoverage and Connectivity • Various levels of coverage may be acceptable. • depends on the application requirement • In our analysis… • require the network to provide complete coverage • only 100% connectivity is acceptable • the network fails with loss of connectivity

12. PreliminariesLifetime • consider basic placement schemes Square- Grid Hex- Grid

13. PreliminariesLifetime • Tolerate the failure of a node all of whose neighbors are functioning. • Define minimum network lifetime as the time to failure of any two neighboring nodes. • i.e. the first loss of coverage

14. Node Lifetime Evaluation (1/5) • A sensor node is said to have: • m possiblemodesof operation • at any given time, the node is in one of these m nodes • wi: fraction of time that a node spends in i-th mode 1 2 …… m …… w1 w2 wm

15. Node Lifetime Evaluation (2/5) • Wiare modeled as random variables. • take values from 0 to 1 • probability density function (pdf) • Etotal: total energy • Pi: power spended in the i-th mode per unit time • Tnode: lifetime of the node • Eth: threshold energy value

16. Node Lifetime Evaluation (3/5) • The lifetime of a single node can be represented as a random variable. • takes different values by its probability density function (pdf), ft (t)

17. Node Lifetime Evaluation (4/5) • Assume that the node has two modes of operation. • Active: Pr (node is active) = p,w1 • Idle: Pr (node is idle) = 1-p,w2 = 1- w1 • Observe the node over T time units. • binomial distribution

18. Node Lifetime Evaluation (5/5) • As T becomes large: • binomial distribution ~ N(μ, σ) • μ(mean) = Tp, σ(variance) = Tp(1-p) • The fraction of time (w1 andw2)follows the normal distribution. • The reciprocal of the lifetime of a node is normally distributed.

19. Network Lifetime AnalysisReliability Theory • The network lifetime is also a random variable. • Using Reliability Theory to find the distribution of the network lifetime.

20. Reliability Theory • Concerned with the duration of the useful life of components and systems. • We model the lifetime as a continuous non-negative variable T. • pdf, cdf, Survivor Function, System Reliability, RBD.

21. Reliability Theorypdf and cdf • Probability Density Function • f(t): the probability of the random variable taking a certain value • Cumulative Distribution Function • F(t): the proportion of the entire population that fails by time t.

22. Reliability TheorySurvivor Function • Survivor Function: S(t) • the probability that a unit is functioning at any time t • survivor function vs. pdf S(0) = 1, S(t) is non-decreasing

23. Reliability TheorySystem Reliability • To consider the relationship between components in the system. • using RBD distribution of the components single node distribution of the system entire network

24. Reliability TheoryReliability Block Diagram (RBD) • Any complex system can be realized in the form of combination blocks, connected in series and parallel. • S1(t) and S2(t) are the survivor functions of two components. S1(t) S2(t) S1(t) S2(t)

25. Network Lifetime Analysis • minimum network lifetime: the time tofailure of two adjacent nodes • Assume that: • All sensor nodes have the same survivor function. • Each sensor node fails independent of one another.

26. Network Lifetime AnalysisSquare Grid • Square Grid Placement Analysis Region 1 Region 1 a b c d Region 2 x x y or y Region 2

27. Network Lifetime AnalysisSquare Grid Block 1 : RBD for Region 1 Region 1 b a a c d b c ∵ sensors are identical

28. Network Lifetime AnalysisSquare Grid Region 2 Block 2 : RBD for Region 2 x x y x or y y ∵ sensors are identical, have the same survivor function

29. Network Lifetime AnalysisNetwork Survivor Function for Square Grid • block 1’s • block 2’s • connect in series

30. Network Lifetime AnalysisHex-Grid • Hex-Grid Placement Analysis Block : RBD for Hex-Grid b a a c d b c d ∵ sensors are identical, have the same survivor function

31. Network Lifetime AnalysisNetwork Survivor Function for Hex-Grid • blocks connect in series. Why ?

32. SimulationFlow Chart Node Lifetime Analysis Network Lifetime Analysis Given Network Protocol p.d.f. (single node) Distribution of Wi Survivor Function (single node) Node Lifetime Calculation Survivor Function (network) p.d.f. (single node) p.d.f. (network) theoretical vs. actual theoretical vs. actual

33. SimulationNode Lifetime Distribution actual p.d.f. theoretical p.d.f.

34. SimulationNetwork Lifetime Distribution • Square Grid Placement Scheme actual p.d.f. theoretical p.d.f. closely match!

35. SimulationNetwork Lifetime Distribution • Hex-Grid Placement Scheme actual p.d.f. theoretical p.d.f. closely match!

36. Conclusion • The analytical results based on the application of Reliability Theory. • We came up not with any particular value, but a p.d.f. for minimum network lifetime. • The theoretical results and the methodology used will enable analysis of: • other sensor placement scheme • tradeoff between lifetime and cost • performance of energy efficiency algorithm