1. Effect of Redundancy on Mean Time to Failure of Wireless Sensor Networks Anh Phan Speer, Ing-Ray Chen Paper Presented by: Misha, Neha & Vidhya CS 5214 Paper Presentation 04/05/2006

2. Outline Introduction to WSN Major System Faults Scope of the paper System Model Parameters of the System Model Probability Model Numeric Results Comparison Chart (Effect of Redundancy on MTTF) Analysis of Graphical Results Conclusion

5. 2 Major System Faults In WSN Due to energy depletion of sensor nodes, so WSN exhausts its energy to answer queries Due to Sensor faults including measurement faults. Failure: WSN fails to deliver sensor data correctly in response to application-level query due to energy depletion or sensor faults:

9. Scope of this paper

10. Using Bayesian algorithm: System disambiguates sensor faults from true measurement when redundancy is involved Majority reading from the different sensors via multiple paths is passed by processing center as legitimate reading to the application Bayesian algorithm:Measurement errors due to faulty equipment are likely to be uncorrelated, while environmental conditions are spatially correlated. Contribution of Paper: Mathematical analysis of tradeoff between fault tolerance and energy consumption of WSN Using Bayesian Algorithm for Sensor Faults

11. System Model The WSN consists of low power sensor nodes deployed through air drop in the geographical area All the sensors have same initial energy level Sensors group themselves into clusters (for energy conservation) Each cluster elects a cluster head

12. Cluster based WSN architecture

13. The cluster head is rotated fairly among sensors in the cluster based on cluster head rotation algorithms such as HEED and LEACH The transmission power of the sensor is reduced to minimum level to enable it to communicate with its neighbor within one hop radio range Users can issue query through any cluster head

14. HEED HYBRID ENERGY EFFICIENT DISTRIBUTED CLUSTERING APPROACH For electing cluster heads Primary parameter: residual energy (E r ) Secondary parameter: communication cost (used to break ties) For joining a cluster - Discover neighbors within cluster range - Compute the initial cluster head probability If node received some cluster head messages, choose one head with minimum cost If node does not have a cluster head, elect to become a cluster head with the cluster head probability computed earlier.

15. LEACH (Low Energy Adaptive Clustering Hierarchy) Randomized rotation of the high-energy cluster head position among the sensors to avoid draining the battery of any one sensor in the network. Cluster heads broadcast an advertisement message using a CSMA MAC protocol Non-cluster head node determines its cluster for this round by choosing cluster head that requires the minimum communication energy Each node reports to its cluster head using a CSMA protocol.

16. LEACH (contd….) Based on all the messages received within the cluster, the cluster head creates a TDMA schedule for intra-node transmission. During data transmission, non-cluster-nodes can be turned off until the node ’ s allocated transmission time.

17. A query may involve –all clusters or –a subset k of total clusters to respond to the query for data sensing and retrieval The involved clusters are termed as source clusters Due to cluster head rotation, the notion of high energy consumption by critical nodes does not exist Energy consumed by the source cluster depends on the length of the path connecting the source cluster and the processing center A failure probability parameter q characterizes the failure behavior of a sensor due to hardware failure

18. Parameters of the System Model All sensors deployed in a square sensor area of size A 2 with each side of length A Sensors in the network distributed according to a homogeneous spatial Poisson process with intensity λ n – total number of nodes in the WSN n s – no of sensors in the cluster N c – no of clusters in the system

19. N c = n/n s E 0 = initial energy of each sensor node in Joule The size of the cluster depends on the clustering algorithm employed and it affects the MTTF of the system A user query may require up to k clusters to respond to a query where k can range from 1 to N c m s = no of sensors to return sensor results to the cluster m s > 1 to provide fault tolerance through source redundancy

20. r – one hop radio range of the sensors The cluster size determines whether a single hop or a multiple hop route is required for a sensor to communicate with the cluster head A cluster head rotation algorithm such as HEED used to achieve a perfect rotation of the cluster head among all sensors in the cluster. Therefore each sensor node would consume energy at the same rate. p – probability that a node will become a cluster head p = 1/n s N c = n/n s = np

21. The initial energy level of each sensor is E 0 Joules The initial energy level of the system E initial = nE 0 When the energy level of the system falls below a threshold E threshold the WSN is considered to have depleted its energy

22. Probability Model MTTF of Sensor Data System: –Avg. # of queries the system can answer before it fails –Failure caused by energy depletion or sensor faults P q (k) = Prob {query requires k clusters to respond} E q (k) = Energy Consumption of system to answer a query that requires k clusters to respond R q (k) = Reliability of a query that requires k clusters to respond requires k clusters to respond E q = Avg. amt. of energy consumed per query

23. Expected value of E q (k): E q = np ∑ k=1 E q (k) P q (k) Avg. # of queries system is able to respond to before energy depletion: N q = E initial – E threshold E q Reliability of a query: R q = np ∑ k=1 R q (k) P q (k)

24. MTTF of the system : Expected # of queries the system can answer without failure ( with upper bound of Nq) Tradeoff between Eq and Rq depending on redundancy level used d (a random variable): distance between a source cluster head and the processing center # of intermediate hops between the processing center and the source cluster head : h = (d/r) - 1

25. Source cluster head randomly located at (Xi, Yi) in a square sensor area with –A/2 ≤ Xi ≤ A/2 and –A/2 ≤ Yi ≤ A/2 and the processing center be located in the center of the sensor area with the coordinate at (0, 0) Avg. # of hops to forward sensor data from a source cluster head to processing center: N h inter = ┌ E (h) ┐

26. Failure prob. of that source cluster failing to send data to processing center, when there is single path from cluster head to processing center: For fault tolerance: –Path Redundancy: use m disjoint paths b/w a source cluster head and the processing center Deliver requested sensor data if any of m redundant paths alive Failure prob { a source cluster fails to deliver data to the processing center } = prob {all m paths have failed}

27. Source Redundancy: use m s sensors in each cluster –Return sensor readings to their cluster head to cope with incorrect readings and sensor faults –Sensor becomes a cluster head with prob. p –all sensors distributed in the area with intensity λ –Cluster heads and non-cluster head sensors also distributed with rates pλ and (1-p)λ –Non-cluster-head sensors join the cluster of the closest cluster head to form a Voronoi Cell corresponding to a cluster in the WSN

28. –Avg # of non-cluster-head sensors in each Voronoi cell: (1-p)/p –Avg distance from a non-cluster-head sensor to the cluster head : d nc = 1 / 2(pλ) 1/2 –If d nc > per-hop distance r, then a sensor will take a multi-hop route to transmit sensor data to cluster head –Avg # of intermediate sensors = d nc / r

29. Avg # of hops to forward sensor data from a sensor to its cluster head: If any hop fails, then prob {sensor fails to forward its data to its cluster head} = p fs = Failure prob{all m s sensors within a cluster fail to forward their sensor readings to the cluster head}: Failure prob {a cluster not able to return a correct response, due to path or source failure or both}:

30. If –k source clusters required to return sensor data to answer a query –query fails when any of the k clusters fails to deliver data then, overall query failure prob = Reliability (query requiring k clusters to respond) : R q (k) = 1- P f As per energy ratio model, energy used for communication: E elec per bit Energy spent by a sensor node to sense (or to receive) and transmit a data packet of length n b bits: E packet = 2 n b E elec

31. Avg # of hops b/w a sensor and its cluster head = N h intra Avg energy for system to transmit sensor data from a sensor to its cluster head: E packet * N h intra If k clusters required, each with m s sensors for source redundancy, to respond to a query, then total energy reqd for these sensors within k clusters to gather and forward data to their cluster heads: E s = E packet * N h intra * k * m s E ch = total energy consumed by the WSN to transmit sensor data from k source cluster heads to the processing center for m = 1 E ch = E packet * N h inter * k * 1

32. Amount of energy spent by the system to answer a query requiring k clusters to respond, each with m disjoint paths connecting the cluster head to the processing center for path redundancy: E q (k) = mE ch + E s Objective: –Find best redundancy level represented by m and m s –Maximize MTTF, given a set of system parameters characterizing the application and network conditions

33. Numeric Results WSN with model parameters: n = 1000 [Total no of nodes] r = 1 [One hop radio range of sensor] = 10 nodes/sq. unit [Sensors distributed with intensity ] A=10units [A is side of square of sensor deployment] n b = 50bytes [Data packet length] E elec = 50 nJ/bit [Energy used for communication] E o = 2J [Initial energy of each sensor node] E threshold = 0 [If energy falls below this,system fails] n s = 10 to 100 nodes[No of sensors in a cluster]

34. q = 10 -8 to 10 -3 [Failure prob. of a sensor due to environmental conditions] m = 1 to 4 [Redundant disjoint paths from source cluster head to processing center m s = 1 to7 [Redundant sensor nodes answering query within source cluster] Assume P q (k) = 1 [For fixed values of k] {Probability that query requires k clusters to respond} P q (k = np) = 1 [Query requires all clusters to respond] Calculate:

35. MTTF vs. (m, m s ) MTTF (z coordinate), m s (x coordinate) & m (y coordinate)

36. 1.Optimal level: m = 2, m s = 3 & MTTF ~ 3500000 2.When q = 10 -8 System favors m=1(No path redundancy) and m s =1(No source redundancy) since chance of path or source failure is low. 3. When q = 10 -3 System favors m = 3 and m s = 3 4. As q increases: System favors higher(m,m s ) combination. Physical meaning: Redundancy prolongs system lifetime in terms of answering query correctly when per-node failure probability is high. Analysis Of Graphical Results

37. 5.When k = 1 (only one cluster needs to respond to query) As p (probability of sensor becoming cluster head) increases (or) 1/p (cluster size) decreases, MTTF increases Physical meaning: Few sensors are involved in answering query in a cluster,so less energy is consumed per query 6. When k = np (All clusters need to respond to query) As p increases (or) 1/p decreases, MTTF decreases Physical meaning: More clusters and all of them respond to query.More energy consumed per query,due to more cluster heads

38. Conclusion Analysis of the intrinsic tradeoff between fault tolerance and energy conservation for prolonging the lifetime of WSNs designed to answer user queries System failure defined as the inability of the system to answer queries due to either sensor faults or energy depletion Using probability model, shown that though path and source redundancy increase the probability that data are delivered reliably, a tradeoff exists b/w reliable data delivery and energy consumption

39. Optimal level of redundancy should be used by the system to maximize MTTF, when given a set of parameters characterizing the WSN and workload environment. Optimal path and source redundancy levels determined by the system designer at static time, can be deployed in the WSN to prolong the lifetime of the system. THANK YOU!