Effect of Redundancy on Mean Time to Failure of Wireless Sensor Networks

Anh Phan Speer, Ing-Ray ChenPaper Presented by: Misha , Neha & VidhyaCS 5214 Paper Presentation04/05/2006

OutlineIntroduction to WSNMajor System FaultsScope of the paperSystem ModelParameters of the System ModelProbability ModelNumeric ResultsComparison Chart (Effect of Redundancy on MTTF)Analysis of Graphical ResultsConclusion

Introduction to WSN

Comprises of a large # of application-specific wireless sensor nodes spread over varying topographies

Applications:Security and surveillance monitoringBattlefield command and controlWildlife or medical monitoring

Used in critical applications and inaccessible locations

Primary concern :Energy conservationCorrect 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

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:

2 Major System Faults In WSN

Energy depletion of sensor nodes, so WSN exhausts its energy to answer queries

Sensor faults including measurement faults

Failure: WSN fails to deliver sensor data correctly in response to application-level query due to 2 major system 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 nodesperforms 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 RedundancyTime RedundancyInformation 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 this paper

Scope of this paper

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: 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 WSNUsing Bayesian Algorithm for Sensor Faults

System ModelThe 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 nodes 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 ModelAll 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

n total number of nodes in the WSNns no of sensors in the clusterNc 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 ModelMTTF of Sensor Data System: Avg. # of queries the system can answer before it failsFailure caused by energy depletion or sensor faults

Expected value of Eq(k):

Eq = npk=1 Eq(k) Pq(k)

Avg. # of queries system is able to respond to before energy depletion:Nq = Einitial E threshold

EqReliability of a query:

Rq = npk=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 centerDeliver requested sensor data if any of m redundant paths aliveFailure 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

Cluster heads and non-cluster head sensors also distributed with rates p and (1-p)

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(p)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 = 1Ech = 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 msMaximize MTTF, given a set of system parameters characterizing the application and network conditions

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]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)

1.Optimal level: m = 2, ms = 3 & MTTF ~ 35000002.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 = 34. 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.

Analysis Of Graphical Results

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 increasesPhysical 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 decreasesPhysical meaning: More clusters and all of them respond to query.More energy consumed per query,due to more cluster heads

ConclusionAnalysis 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.

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