CS 5214 Paper Presentation
Effect of Redundancy on Mean Time to
Failure of Wireless Sensor Networks
Anh Phan Speer, Ing-Ray Chen
Paper Presented by: Misha , Neha & Vidhya
04/05/2006
Outline
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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
Introduction to WSN
• Comprises of a large # of application-specific wireless sensor
nodes spread over varying topographies
• Applications:
– Security and surveillance monitoring
– Battlefield command and control
– Wildlife or medical monitoring
• Used in critical applications and inaccessible locations
• Primary concern :
– Energy conservation
– Correct operation of underlying WSN
• In query based WSN, sensors perform data sensing,retrieval
and data aggregation as response to a query at runtime
2 Major System Faults In WSN
WSN
Failure:
WSN
to deliver
sensor
data
Failure: WSN
failsfails
to deliver
sensor data
correctly
in correctly
response to
application-level
due to energy depletion
sensor
in
response toquery
application-level
queryordue
to faults:
2
major system faults.
• Due to energy depletion
of sensor nodes, so WSN
• Energy depletion of
exhausts its energy to
sensor nodes, so WSN
answer queries
exhausts its energy to
answer queries
• Due to Sensor faults
including
measurement
.
• Sensor
faults
including
faults
measurement
faults
• To reduce energy depletion of sensor nodes:
– WSN self organizes into clusters to conserve energy
– Within each cluster ,cluster head elected,
• performs more in-network data aggregation and relay duties
than normal sensor nodes
• performs compression to reduce energy consumption
– Cluster head rotated among sensor nodes in cluster for
balancing energy consumption by sensors
– Cluster reconfigured globally or in a distributed
manner on a per sensor-node basis
• To reduce sensor faults-Introduce fault tolerance
mechanism in WSN by:
– Hardware Redundancy
– Time Redundancy
– Information Redundancy
– HARDWARE REDUNDANCY:(Scope of this paper)
• Use Extra hardware for fault detection or masking.
• Types:
– Source redundancy
– Path redundancy
– TIME REDUNDANCY:
• Same hardware but execute query different times (Infinitesimally
small intervals) to cope with temporary failures of sensors.
• Fault detection by acceptance testing.
– INFORMATION REDUNDANCY:
• Same hardware but redundancy in fundamental law relations used
– Excess redundancy reduces sensor faults but increases
energy depletion of sensor nodes (detrimental effect on
MTTF)
Scope of
of this
this paper
paper
Scope
• MTTF used as a metric to measure effectiveness of
underlying WSN to answer queries
– # of queries answered correctly before failing due to sensor
faults or energy depletion
• Analyze effect of hardware redundancy on MTTF of cluster
structured ,query based WSN
• Find an optimal redundancy level to maximize MTTF of
cluster structured WSN
Using Bayesian Algorithm for Sensor
Faults
• 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
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
Cluster based WSN architecture
• 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
HEED
HYBRID ENERGY EFFICIENT
DISTRIBUTED CLUSTERING APPROACH
• For electing cluster heads
Primary parameter: residual energy (Er)
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.
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.
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.
• 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
Parameters of the System Model
• All sensors deployed in a square sensor area of size A2 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
• ns – no of sensors in the cluster
• Nc – no of clusters in the system
• Nc = n/ns
• E0 = 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 Nc
• ms = no of sensors to return sensor results to the cluster
• ms > 1 to provide fault tolerance through source redundancy
• 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/ns
Nc = n/ns = np
• The initial energy level of each sensor is E0 Joules
• The initial energy level of the system E initial = nE0
• When the energy level of the system falls below a
threshold E threshold the WSN is considered to have
depleted its energy
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
• Pq(k) = Prob {query requires k clusters to respond}
• Eq(k) = Energy Consumption of system to answer a query that
requires k clusters to respond
• Rq(k) = Reliability of a query that requires k clusters to respond
requires k clusters to respond
• Eq = Avg. amt. of energy consumed per query
• Expected value of Eq(k):
Eq = np∑k=1 Eq(k) Pq(k)
• Avg. # of queries system is able to respond to before energy
depletion:
Nq = Einitial – E threshold
Eq
• Reliability of a query:
Rq = np∑k=1 Rq(k) Pq(k)
• 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
• 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:
Nhinter = ┌ E (h) ┐
• 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}
• Source Redundancy: use ms 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
– 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 :
dnc
= 1 / 2(pλ)1/2
– If dnc > per-hop distance r, then a sensor will take a
multi-hop route to transmit sensor data to cluster head
– Avg # of intermediate sensors = dnc / r
• 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} = pfs =
• Failure prob{all ms 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}:
• 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) : Rq(k)
= 1- Pf
• As per energy ratio model, energy used for communication: Eelec per bit
• Energy spent by a sensor node to sense (or to receive) and transmit a
data packet of length nb bits:
Epacket = 2 nb Eelec
• Avg # of hops b/w a sensor and its cluster head = Nhintra
• Avg energy for system to transmit sensor data from a sensor to
its cluster head: Epacket * Nhintra
• If k clusters required, each with ms 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: Es = Epacket * Nhintra * k * ms
•
Ech = total energy consumed by the WSN to transmit sensor
data from k source cluster heads to the processing center for
m=1
Ech = Epacket * Nhinter * k * 1
• 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:
Eq(k) = mEch + Es
• Objective:
– Find best redundancy level represented by m and ms
– Maximize MTTF, given a set of system parameters
characterizing the application and network conditions
Numeric Results
WSN with model parameters:
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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]
nb = 50bytes [Data packet length]
Eelec = 50 nJ/bit [Energy used for communication]
Eo = 2J [Initial energy of each sensor node]
Ethreshold = 0 [If energy falls below this ,system fails]
ns = 10 to 100 nodes[No of sensors in a cluster]
• 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
• ms = 1 to7 [Redundant sensor nodes answering query within
source cluster]
• Assume Pq(k) = 1 [For fixed values of k] {Probability that
query requires k clusters to respond}
• Pq(k = np) = 1 [Query requires all clusters to respond]
• Calculate:
MTTF vs. (m, ms)
MTTF (z coordinate), ms (x coordinate) & m (y coordinate)
Analysis Of Graphical Results
1.Optimal level: m = 2, ms = 3 & MTTF ~ 3500000
2.When q = 10-8
• System favors m=1(No path redundancy) and ms =1(No source
redundancy) since chance of path or source failure is low.
3. When q = 10-3
• System favors m = 3 and ms = 3
4. As q increases:
• System favors higher(m,ms) combination.
Physical meaning: Redundancy prolongs system lifetime in terms of
answering query correctly when per-node failure probability is high.
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
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
• 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!