Monitoring and control systems that are based on networked wireless sensors have been recognized as an indivisible component for current and future smart systems in many applications such as healthcare, home security, disaster response, and environmental monitoring. From the viewpoint of researchers, developers and even consumers, reliability analysis is an indispensable step before wireless sensor network systems can be widely deployed for mission-critical applications. In this talk, reliability modeling and analysis for wireless sensor networks will be discussed under two different communication paradigms: infrastructure communication and application communication. Five data delivery models (sink unicast, sink anycast, sink multicast, sink manycast, and sink broadcast) will be presented for the infrastructure communication reliability analysis. Impact of different routing algorithms and network topology characteristics like connectivity, average path length, average degree, diameter, and clustering coefficient on the network reliability will also be discussed.

1. Reliability Analysis for Wireless
Sensor Networks
(无线传感器网络可靠性分析)
Dr. Liudong Xing
(邢留冬博士)
©2012 ASQ & Presentation Xing
©2012 ASQ & Presentation Xing
Presented live on Nov 17th, 2012
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3. Reliability Analysis for Wireless
Sensor Networks
(无线传感器网络可靠性分析)
Presented by
Dr. Liudong Xing (邢留冬)
E-mail: lxing@umassd.edu
University of Massachusetts, Dartmouth
www.massachusetts.edu
ASQ Reliability Division Webinar Series 2012
US National Science Foundation No. 1112947 & 1112935

4. Wireless Sensor Networks (WSN)
 A network consisting of many spatially-distributed sensor
devices for monitoring physical or environmental
conditions and cooperatively passing their data through
the network to a main location
http://en.wikipedia.org/wiki/Wireless_sensor_network
2

5. WSN Communication
 Infrastructure communication
 Relates to delivery of configuration and maintenance
messages
 From base station (sink node) to sensor nodes
 Application communication
 Relates to transfer of sensed data collected from physical
environment
 From sensor nodes to base station
http://monet.postech.ac.kr/research.html 3

6. WSN Graph Model: G(V, E)
 V: sensor nodes
 E: wireless links (i, j) ϵ E iff d(i,j) ≤ tr
 d(i,j): Euclidean distance between nodes i and j
 tr: transmitting range; a node can communicate with other
sensor nodes within a Euclidean distance of tr
 sr: sensing range; a node can monitor any point that is
within a radius of sr from that sensor
4

7. Agenda
 WSN Topologies
 Infrastructure Communication Reliability
 Application Communication Reliability
5

8. WSN Topologies (1)
 Star
 Organizes peripheral nodes around central hub
 Hierarchical/Tree
 Natural and logical extension of star
 Sink at the root and nodes at different layers
connected via direct links
 Mesh
 Each node also functions as router
 Multi-hop communication
 Multiple paths through the network
6

9. WSN Topologies (2)
 Hierarchical clustering
 Sensor nodes form
clusters
 Cluster heads in a lower
layer are arranged into
clusters in higher layer
 A cluster head is assigned
for each layer cluster
7

10. Which topology is the most reliable one?
b a b a
c c
d d
Base Station Base Station
Node deployment Mesh
b a Level-1 Cluster Head
Level-0 Cluster Head
c Gateway Node
Ordinary Sensor Node
d
Base Station
Hierarchical cluster Tree
8

11. Intuitively Speaking...
 Star/Tree (least reliable)
 when a link is obstructed, there are no alternate paths from affected
node to base station
 Mesh (most reliable)
 highly fault tolerant: offers multiple redundant paths through
network
 Hierarchical cluster (intermediate)
 maintain multiple redundant paths through network
 cluster heads: single-point of failures
A. Shrestha and L. Xing, “Quantifying Application Communication Reliability of Wireless Sensor Networks,”
International Journal of Performability Engineering, Special Issue on Reliability & Quality in Design, 2008; 4(1): 43-56 9

12. Example Verification c
b a
d
Failure rate (hr-1) for nodes and links
Links Base station Cluster head Nodes Base Station
2e-6 1e-7 1e-6 1e-6
b a Level-1 Cluster Head
Level-0 Cluster Head
c Gateway Node
Reliability values for mission time of 10,000 hours Ordinary Sensor Node
d
Base Clustered
Mesh Tree
Station  Hierarchical
Base Station
a 0.96407761 0.93120456 0.91301771
b 0.96404580 0.95712310 0.91301771
c 0.99340368 0.93124373 0.91301771
d 0.96495799 0.95960433 0.91301771
a, b, c, d 0.92097894 0.83314192 0.80977407
10

13. Agenda
 WSN topologies
 Infrastructure communication reliability
 Data delivery models
 Network characteristics
 Application communication reliability
11

14. Data Delivery Models
 Unicast
 To a single sensor Infrastructure communication
 Multicast reliability (ICR): probability
 To a group of sensors that there exists operational
 Broadcast path from sink node to ......
 To all sensors
 Anycast
 To any one sensor out of a group of qualified sensors
 Manycast
 To a subset of sensors out of a group of qualified sensors
12

15. ICR under Unicast
 Probability that there exists an operational path from
sink node (sink) to destination sensor node (a).
 Example: tree topology
  
E 2 sink to PN t ht  E 2 PN t ht to PN t 1ht 1   

 Pr
 
   

ICRunicast
1h to PN 0 h  E PN 0 h to a
E 2 PN 1 
 0 2 0 
hk: PN that is hierarchically above a at level-k, 0 ≤ k ≤ t
E2: event - there exists an operational path between a given pair of nodes
Pr(E2): two-terminal reliability (BDD-based method)
L. Xing, “An Efficient Binary Decision Diagrams Based Approach for Network Reliability and Sensitivity Analysis,”
IEEE Trans. Systems, Man, and Cybernetics, Part A: Systems and Humans 2008; 38 (1): 105-115. 13

16. ICR under Anycast
 Probability that there exists an operational path from
sink to any one sensor node out of a qualified group (Q)
Q = {n1, n2}

    
E 2 sink to PN t ht  E 2 PN t ht to PN t 1ht 1    

ICR anycast  Pr  
 1 0  
aQ E 2 PN h1 to PN h0  E 2 PN h0 to a 0  


  
14

17. Example Results (unicast, anycast)
 Failure rates: link (2e-6/hr), sink (5e-7/hr), sensor
node (1e-6/hr)
n2 1
n1
n5
PN1 Q1
PN2 n3 0.8
Sink Q2
n4
Reliability
0.6 Q3
Level-1 PN
Level-0 PN Q4
Sensor Node 0.4
Q1 = {n1} (unicast) 0.2
Q2 = {n1, n2}
Q3 = {n1, n2, n3} 0
0 1 2 3 4
Q4 = {n1, n2, n3, n4} Mission time: hours 5
x 10
15

18. ICR under Multicast
 Probability that there exists an operational path from
sink to all the sensor nodes in a qualified group (Q)
Q = {n1, n2}


 iH   


   
E 2 sink to PN t i    iH t E 2 PN t i to PN t 1 j  
 t   jH t 1  
ICR multicast  Pr 
 
  1  
0   
 0 
    ijH1 E 2 PN i to PN j    iaH 0 E 2 PN i to a   

   H 0    Q 
16

19. ICR under Manycast
 Probability that there exists an operational path from
sink to at least one subset of nodes (Rx) out of a
qualified group (Q)
Q = {n1, n2, n3, n4}
n = 4, m = 2
 

 Cnm  iH t ,x
 
  
 jH t 1,x
   
E 2 sink to PN t i  iH t ,x E 2 PN t i to PN t 1 j  
 
ICRmanycast  Pr   
   
 x 1     iH1,x E PN 1i to PN 0  j    iH 0 ,x E PN 0 i to a  
  jH 0 ,x 2  aRx 2  
      
17

20. Example Results (multicast, manycast)
1
n2
n1 Q1
n5 0.8
PN1
PN2 n3 Q2
Sink
Reliability
n4 0.6 Q3
Level-1 PN
Level-0 PN 0.4
Sensor Node
0.2
Q1 = {n1, n2} (multicast)
0
Q2 = {n1, n2, n3} 0 1 2 3 4
Q3 = {n1, n2, n3, n4} Mission time: hours 5
x 10
18

21. ICR under Broadcast
 Probability that there exists an operational path from
sink to all sensor nodes in WSN

 
 i

E 2 sink to PN t i   
 i ,j

 
E 2 PN t i to PN t 1 j 





ICRbroadcast  Pr 
  



  E PN
 i ,j 2
  
1i to PN 0  j   
  i ,a 2
 
E PN  
0 i to a  


19

22. Example Results (all models for tree
topology)
1
Unicast
0.8
Anycast
Multicast
Reliability
0.6
Manycast
0.4 Broadcast
0.2
0
0 1 2 3 4
Mission time: hours 5
x 10
C. Wang, L. Xing, V. M. Vokkarane, and Y. Sun, "Reliability of Wireless Sensor Networks with Tree Topology,"
20
International Journal of Performability Engineering 2012; 8 (2): 213-216

23. Example & Results for Clustering
Topology n1
n5
n2 Level-1 CH
Level-0 CH
1 Level-1 Gateway
n3
CH2 Level-0 Gateway
CH1 1 Sink
n4 Sensor Node
1 1 1
Q1 Broadcast Multicast
Q2 Multicast:Q1 Manycast
0.8 0.8 0.8
Manycast:Q2 Anycast
Q3
Unicast
Q4
Reliability
0.6
Reliability
Reliability
0.6 0.6
0.4 0.4 0.4
0.2 0.2 0.2
0 0 0
0 1 2 3 4 0 1 2 3 4 0 1 2 3 4
Mission time: hours 5 Mission time: hours 5 Mission time: hours 5
x 10 x 10 x 10
Q1 = {n1} (unicast) Q2 = {n1, n2} Q1 = {n1, n2} Q = {n1, n2, n3}
Q3 = {n1, n2, n3} Q4 = {n1, n2, n3, n4} Q2 = {n1, n2, n3}
C. Wang, L. Xing, V. M. Vokkarane, and Y. Sun, "Manycast and Anycast-Based Infrastructure Communication Reliability
for Wireless Sensor Networks," The 18th ISSAT Intl Conf. on Reliability and Quality in Design, Boston, MA, July 2012 21

24. Summary
 WSN with anycast is the most reliable
 WSN with broadcast is the least reliable
 WSN with manycast is more reliable than WSN with
multicast for a given qualified group
 WSN reliability increases as number of sensor nodes in
the qualified group increases for anycast and manycast
models
22

25. Agenda
 WSN topologies
 Infrastructure communication reliability
 Data delivery models
 Network characteristics
Connectivity, average path length, average nodal degree,
network diameter, clustering coefficient
 Application communication reliability
23

26. Connectivity
 A graph is connected if every pair of vertices is
connected via a path
 A graph is k-connected if the graph remains connected
when fewer than k vertices are deleted from the graph
Average Path Length
 Average number of hops along the shortest path for all
possible pairs of network nodes
 Indicates the efficiency of information transfer over
the network
24

27. Average Nodal Degree
 Nodal degree: number of edges connected to the node
 Average nodal degree for entire network is the average
number of edges connected per node
 Indicates the density of a network
Network Diameter
 The longest path length of all the shortest paths for all
possible pairs of network nodes
 Indicates the linear size of a network
25

28. Clustering Coefficient
 For a node
 ratio of existing links connecting a node’s neighbors to
each other to the maximum possible number of such
links
 average fraction of pairs of neighbors of a node which
are also neighbors of each other
 For the entire network
 average of clustering coefficient of all the nodes of the
network
26

29. Five-Node Connected Graphs
01 02 03 04 05 06 07
08 09 10 11 12 13 14
15 16 17 18 19 20 21
failure rates: links (2e-6/hr), nodes (1e-6/hr)
27

30. Number k-connected Average Path Length Average Nodal Degree Network Diameter Average Clustering Coefficient
01 1 1.6 1.6 2 0
02 1 1.8 1.6 3 0
03 1 1.5 2 2 0.43
04 1 1.6 2 3 0.33
05 1 1.6 2 3 0
06 1 1.4 2.4 2 0.6
07 2 1.4 2.4 2 0
08 2 1.3 2.8 2 0.8
09 1 2 1.6 4 0
10 1 1.7 2 3 0.47
11 1 1.4 2.4 2 0.87
12 1 1.5 2.4 3 0.53
13 1 1.3 2.8 2 0.7
14 2 1.5 2 2 0
15 2 1.4 2.4 2 0.33
16 2 1.3 2.8 2 0.77
17 2 1.2 3.2 2 0.87
18 2 1.3 2.8 2 0.4
19 3 1.2 3.2 2 0.67
20 3 1.1 3.6 2 0.9 28

31. Connectivity
1
0.9
1-connected 2-connected
0.8
3-connected Fully-connected
0.7
0.6
Reliability
0.5
0.4
0.3
0.2
0.1
0
Time: Hours
29

32. Average Path Length
0.7
t=100000hours t=200000hours t=300000hours
0.6
0.5
0.4
Reliability
0.3
0.2
0.1
0
Average Path Length (Graph Number)
30

33. Average Degrees
0.7
t=100000hours t=200000hours t=300000hours
0.6
0.5
Reliability
0.4
0.3
0.2
0.1
0
Average Degree (Graph Number)
31

34. Network Diameter
0.7
t=100000hours t=200000hours t=300000hours
0.6
0.5
Reliability
0.4
0.3
0.2
0.1
0
Diameter (Graph Number)
32

35. Average Clustering Coefficients
0.7
t=100000hours t=200000hours t=300000hours
0.6
0.5
Reliability
0.4
0.3
0.2
0.1
0
Average Clustering Coefficient (Graph Number)
33

36. Summary
 In general, higher connectivity, shorter average path
length, larger average nodal degree, and shorter
network diameter lead to higher network reliability
 Clustering coefficient property is not a good indicator
of the network reliability
C. Wang, L. Xing, V. M. Vokkarane, and Y. Sun, "Reliability Analysis of Wireless Sensor Networks using Different Network
Topology Characteristics," Proc. of Intl Conf. on Quality, Reliability, Risk, Maintenance, and Safety Engineering (QR2MSE2012), 34
Chengdu, China, June 2012.

37. Agenda
 WSN Topologies
 Infrastructure Communication Reliability
 Application Communication Reliability
35

38. Application Communication
 Acquisition of sensed data from a specific area by
senor nodes
 Related to sensing coverage: ability to monitor every
point in the region by at least one node
 More generally, K-coverage requires every point to be
covered by at least K sensors
 Having a reliable communication from sensor nodes
which observe data to the sink node.
 Related to network connectivity and routing procotols
WSN ACR = Pr {(every point in the sensed field is observed by at least K
nodes) AND (there exists an operational path from each of these nodes
to sink node)}
36

39. K-Coverage
 Every point in the area that is covered by at least K sensors
1-covered
2-covered
3-covered
 K Unit-disk Coverage (K-UC)
 each sensor has the same sensing range
 K Non-unit-disk Coverage (K-NC)
 each sensor may have a different sensing range
37

40. K-Coverage Analysis
 The distance between each point in the monitored area and
each sensor is calculated to check which points are in the
sensing range of which senor.
 Each sensor is associated with a matrix modeling all points
within the monitored area; an element in matrix is 1 if the
corresponding point is within sr of sensor.
 Adding all sensors matrixes to obtain an overall coverage
matrix: ratio between # of elements not less than K and
total # of elements in the matrix  K-coverage analysis.
38

41. Example
 98.29% of the whole area is
covered by at least one sensor
node corresponding to 1-
coverage
 65.08%: 2-coverage
 44.6%: 3-coverage
30 sensors (sr=1) randomly
distributed a 5 by 5 area
(density of 1.2 sensors /sq.)
39

42. Effect of Density on Coverage
Percentage of the whole area that is K-covered
(K=1, 2 and 3) increases as density increases.
40

43. K-coverage Set
 A minimal set of sensors such that each point in the
specific area is covered by at least K different sensors.
 Identify all sensors that cover the whole or part of the
specific area
 For all possible combinations of those sensors.
 Check summation of the corresponding matrixes for
all sensors in the combination
 If each element of the summation matrix is greater
than or equal to K, then that combination supports K-
coverage.
 Remove combinations that have redundancy.
41

44. K-coverage Reliability
 Probability that all points in the specific area are covered
by at least K different sensors
RK  Pr{ SN1,1  SN1,2 ... SN1, M1  SN 2,1 SN 2,2 ... SN 2, M1  ...
 NK  Mi
  
SN N K ,1 SN N K ,2 ... SN N K , M N   i 1  j 1

}  Pr   SNi, j  ,

  
K
 NK : number of K-coverage sets
 Mj : number of sensors in ith K-coverage set
 SNi,j : jth sensor node in ith K-coverage set
 Evaluation methods
 Inclusion/exclusion (I/E), Sum of Disjoint Products (SDP), or
BDD
A. E. Zonouz, L. Xing, V. M.Vokkarane, and Y. Sun, “K-coverage Reliability Evaluation for Wireless Sensor Networks,” The
18th ISSAT International Conference on Reliability and Quality in Design, Boston, MA, July 2012 42

45. Example: Randomly Deployed WSN
 50 sensors (sr=1.5m, tr=2m, λ=5e-5/hr ) are randomly
distributed in an 8m by 8m area.
{1}, {10}: 1-coverage {1, 10}:2-coverage
43

46. Example: Predefined Deployed WSN
λ=5e-5
K K-coverage sets for area (0.5 ~ 1, 0 ~ 0.5),
1 {{2}, {3}, {6}, {8}, {5, 10}}
2 {{2, 3},{2, 6},{2, 8},{3, 6},{3, 8},{6, 8},{2,
5, 10}, {3, 5, 10},{5, 6, 10},{5, 8, 10}}
3 {{2, 3, 6},{2, 3, 8},{2, 6, 8},{3, 6, 8},{2, 3, 5, K-coverage reliability decreases as
10},{2, 5, 6, 10},{2, 5, 8, 10},{3, 5, 6, 10},{3,
5, 8, 10},{5, 6, 8, 10}}
K value increases for the same
4 {{2, 3, 6, 8},{2, 3, 5, 6, 10},{2, 3, 5, 8, 10}, deployment
{2, 5, 6, 8, 10}, {3, 5, 6, 8, 10}}
5 {{2, 3, 5, 6, 8, 10}} 44

47. Effect of Density on K-coverage Reliability
K-UC reliability (sr=1, λ=5e-5) for K-NC reliability (avg sr=0.6, λ=5e-5) for
A) 2.5 sensors/sq. A) 2 sensors/sq. B) 3 sensors/sq.
B) 5 sensors/sq. C) 4 sensors/sq.
Larger K-coverage can be supported as density becomes higher
For specific K, WSN with higher density provides higher K-coverage reliability 45

48. Application Communication
Reliability (ACR)
 Communication reliability of delivering the observed data
from sensor nodes within the identified K-coverage sets
to sink node
 N K th 

ACR  Pr  i K - coverage set  sink  
 i 1 
 Two single-path routing algorithms:
 Shortest-path distance algorithm (D): Dijkstra’s algorithm
 Shortest-path hop algorithm (H): Breadth-first search (BFS)
A. E. Zonouz, L. Xing, V. M.Vokkarane, and Y. Sun, “Application Communication Reliability of Wireless Sensor Networks
Supporting K-coverage in the Presence of Shadowing,” IEEE International Conference on Communications, 2013 (under review) 46

49. Link Unreliability
 Lognormal shadowing radio propagation model
   r  
10 log    
1 
 tr    ,   ; iff r  1,
PLink (r )  1  erf 
2  2 log(10)    tr
  
  
 tr: transmitting range
of sensor node
 ψ: ratio between standard
deviation of shadowing (σ)
and pathloss exponent (η)
47

50. Example: Predefined Deployed WSN
 20 sensors (sr=1.5m, tr=2m, λ=5e-5/hr) in a 5m by 5m area
 Monitored area: (0.5 ~ 1, 0.5 ~ 1)
{2}, {9}: 1-coverage
{2, 9}: 2-coverage
48

51. ACR Results
 D algorithm is more reliable than H algorithm.
 Both algorithms generate paths with 3 hops, but links on
paths generated by D are shorter and thus more reliable.
Single-paths from sensor
#2, # 9 to sink
D algorithm:
{212821}
{911621}
H algorithm:
{21521}
{911621}.
49

52. Example: Randomly Deployed WSN
Parameter Value
# of Sensors 20 (density of 0.8)
Sensing range (sr) 1.5m
Transmitting range (tr) 2m
Failure rate (λ) 5e-5
Deployment area 5m by 5m
Specific area (0.5~1,0.5~1)m
Channel condition (Ψ) 2
Sensor node failure rate 5.0 e-5 (fph)
D algorithm is more reliable than H algorithm at the beginning (sensor node
has high reliability, effect of link reliability on ACR is relatively more
significant)
H algorithm can be more reliable than D algorithm as time passes (reliability of
sensor node decreases greatly, its effect on ACR would become more
significant; D algorithm may involves more hops/nodes) 50

53. Different Channel Conditions
ψ=2 ψ=5
 Similar trend can be observed
 ACR results with larger ψ are smaller because link failure probabilities
increase with increasing value of ψ (worse channel condition)
51

54. Different Network Densities
density=0.8 density=1
Density 0.8 1 Increasing density leads to shorter paths
Diameter 6.435447 5.926134 and fewer hops involved in sending the
Avg. node degree 6.34919 8.667 sensed data to the sink node  better ACR
Clustering coefficient 0.70534 0.72497 results
Avg. distance using D 3.1885 2.9408
Avg. no. of hops using H 3.556 3.337
52

55. Conclusion
 WSN reliability under infrastructure communication and
application communication were discussed
 Different network topologies: start, tree, mesh, hierarchical
clustering
 Different data delivery models: unicast, anycast, multicast,
manycast, and broadcast
 Different network characteristics: connectivity, average path
length, average nodal degree, network diameter, clustering
coefficient
 Different routing algorithms: shortest-path distance (D) and
shortest-path hop (H)
 Different K-coverage requirements and densities
53

56. Thank You!
谢谢!
Dr. Liudong Xing (邢留冬)
E-mail: lxing@umassd.edu
Phone: +1-508-9998883
http://www.ece.umassd.edu/faculty/lxing/home.html
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