Metrics_VTC10_Metrics for Performance Prediction of Wireless Sensor Networks

7/30/2019 Metrics_VTC10_Metrics for Performance Prediction of Wireless Sensor Networks

1/5

Metrics for Performance Prediction

of Wireless Sensor NetworksFrank Oldewurtel and Petri Mahonen

Institute for Networked Systems, RWTH Aachen University

Kackertstrasse 9, D-52072 Aachen, Germany

Email: [email protected]

AbstractWe present the derivation of a novel metric for theperformance prediction of Wireless Sensor Networks (WSNs). Inparticular, the metric can be applied in, for example, monitoringand surveillance applications where WSNs are used. Those

networks execute protocols or techniques that are often sensitiveto spatial correlation. The proposed metric is based on thecorrelation in the sensed phenomenon and the correlation in thelocation of the sensor nodes. The main application area of theperformance prediction metric lies in the design and optimisationof WSNs prior to the costly deployment phase. Since extensivesimulations can be completely avoided it serves as a rapid andlightweight evaluation tool for comparative analysis of WSNs.The concept is applicable and also extensible through mergingof selected performance criteria.

I. INTRODUCTION

Wireless Sensor Networks (WSNs) can greatly enhance

our capability to control and monitor physical phenomena.

Typically, they consist of a large number of nodes, whichare usually resource-constrained sensing devices. Sensor nodes

are battery-operated and have very low capabilities in terms

of computation and communication. A major criterion to

characterise the performance and the operational lifetime of

WSNs is their ability to save energy. Hence, energy con-

sumption is the paramount performance criterion considered.

Depending on the application other criteria can be included

in the overall performance evaluation. Many known phenom-

ena, for example, forest fire or rainfall areas, exhibit certain

subregions or a collection of interesting locations that are

more important than other regions to the application user.

Those interesting points may represent local deviations of thephenomena and can be seen as activities or events. Often most

of the information regarding phenomena can be obtained and

analysed by monitoring such sets of interesting points. In such

scenarios the effectiveness of WSNs is often determined to a

large extent by the sensing coverage provided by the actual

node deployment.

Performance prediction of WSNs is a difficult but highly

important task. Extensive simulations using environments with

increasing level of detail is the primary approach for tackling

this task. The major drawbacks are significant implementation

efforts and long simulation times. Hence, the goal of our

approach is to overcome this situation by deriving a metric

that enables rapid and lightweight prediction of the overall

performance under selected criteria. Similar to simulations,

this metric makes use of input data such as the phenomenon

under study and the chosen network topology. In contrast to

simulations, the proposed metric allows quick and lightweight

evaluation by exploiting two concepts borrowed from the field

of spatial statistics.Recently there has been work on the estimation of the

phenomenon itself facing the energy-distortion trade-off, see,

for example [1]. Furthermore, in the area of power profiling

sensor nodes have been investigated using predicted opera-

tion states and their associated state holding times, see, for

example [2]. Within our scope it has been shown that the

correlation in both the phenomenon data and the locations

of the nodes strongly affect energy consumption, operational

lifetime and sensing coverage [3][6]. However, to the best of

our knowledge there is no approach reported that addresses

the performance prediction of correlation-sensitive WSNs as

proposed in our work. In this paper, we derive the performance

prediction metric considering energy consumption as the majorperformance criterion. In addition, we extend this metric by

including sensing coverage as second criterion exemplarily.

Furthermore, we evaluate the proposed concept through exten-

sive simulations and apply the performance prediction metric

to our use cases.

The remainder of the paper is structured as follows. In

Section II the reference system model is briefly described.

Section III introduces two concepts borrowed from the field

of spatial statistics. In Section IV we derive the performance

prediction metric and evaluate the proposed metric considering

energy consumption as major criterion. Section V extends

the proposed metric by taking into account sensing coverageas second performance criterion. Finally, Section VI draws

conclusions.

II . REFERENCE SYSTEM MODEL

In this section we motivate the reference system model

which consists of five components.

A. Phenomenon model and Deployment model

The physical phenomena monitored by WSNs, e.g., temper-

ature and light intensity usually yields sensed data exhibiting

strong correlations in the spatial domain [7], [8]. In our studies

we make use of synthetically generated and spatially correlated

data fields h(x, y) [9]. The model used is independent on thenode density, the number of nodes or the topology. The gener-


2/5

ated data sampled from the model shows good correspondence

when statistically compared with experimental data.

The node deployment model consists of the specification of

the total number of nodes N, and the coordinates (xi, yi)Ni=1of the individual nodes. We assume a fixed region A witharea |A| and that the coordinates are defined by a random

point process (PP) [10]. PPs were successfully applied to

deployment modeling in, for example, [3], [6].

B. Communication model

In terms of communication we assume that each sensor

node has an omni-directional transmission range and utilizes

erroneous links. For modeling error characteristics a widely

used model is the Gilbert-Elliot bit error model [11]. This

model is fundamentally based on a two-state Markov model

that takes bit error bursts into account. In the case of packeterrors, generated by this model, retransmissions are initiated.

The maximum number of packet retransmissions is based

on the IEEE 802.15.4 specification and is thus set to three.

The physical parameters such as transmission ranges, packet

header size and payload size were determined by the Telos

platform running the embedded operating system TinyOS 2.x.

We apply Distributed Source Coding (DSC) achieving high

energy-efficiency through exploitation of spatial correlations

in the sensed phenomena [12], [13]. In terms of mobility the

sensor nodes are quasi-stationary at known positions and the

overall network density is constant in all cases. Regarding

cluster head selection we focus on the closest-to-center of

gravity scheme. Throughout the scenarios the shortest pathmultihop routing protocol is applied.

C. Observation model and Energy model

The observation model s(x, y) describes the observationsor measurements of the sensed phenomena at the node loca-

tions and can therewith directly and explicitly formulated as

s(x, y) =h(xi, yi) for i{1, . . . , N } and undefined otherwise.We apply the energy model e(xi, yi) introduced in our

previous work [3]. The model takes into account packet header

overhead and the additional energy consumption due to the

DSC-related signal processing such as encoding, joint decod-

ing and entropy tracking. The entropy tracking algorithm esti-mates the underlying joint probability density function (PDF)

of the sensor readings observed by the node pair. The energy

model is essentially based on measurements obtained from real

experiments using the Telos sensor node platform [12].

III . SPATIAL STATISTICS

We shall now outline the techniques used to characterise

correlations both in the spatial phenomena being sensed by

the WSN, and in the locations of the nodes themselves. We

denote the value of the phenomena under study at x R2 byh(x). In order to characterise h using statistics, we assume it tobe a realisation of a random field, that is, a stochastic process

defined on a region of the plane. For most physical phenomena

of interest, such as humidity, atmospheric pressure or the

strength of the magnetic field, nearby samples ofh are heavily

correlated. We can characterise these correlations by means of

the second-order semivariogram (also called semivariance) [9]

(s t) =1

2 Var{h(s) h(t)}. (1)

The reader should note that the value of the semivariogram as

a function of the distance |st| is sufficient for stationary andisotropic h. In our context the two-dimensional isotropic caseis assumed in which the semivariogram depends only upon the

Euclidean distance r between any two locations.To facilitate comparison to the correlations in node loca-

tions, we use instead of the semivariogram the correlogram

defined by

C(s, t) E {h(s)h(t)} (s)(t), (2)

where (s) denotes the mean value of h at s. The be-haviour of the correlogram is opposite to that of the semi-

variogram. Indeed, the semivariogram and the correlogram

are related for sufficiently well-behaved h by the relation(h) = C(0) C(h).

The correlations between measurements of h depend notonly on correlations in h (characterised by the correlogram)but also on correlations in the locations of the sensor nodes

carrying out the measurements. Suppose the nodes have overall

area density A. Intuitively, sensor nodes grouped together(high location correlations) measure more highly correlated

values of the phenomena than nodes deployed on, say, a grid.

Such correlations in node locations can be measured by the

pair correlation function g(r), defined in terms of the jointprobability density

dP = 2Ag(r) dA1 dA2 (3)

of finding one point in each of the two area elements dA1and dA2 separated by the distance r. In the case of totallyrandom locations we obviously have g(r) = 1. High values ofg(r) indicate clustering at the relevant length scale, whereasvalues below one indicate regularity (as is the case for grid,

for example). Integrating the pair correlation function from

zero to a distance r directly yields the expected number ofneighbors at distance r for an arbitrary node in the network.It is thus clearly related to the level of correlation exhibited by

the measurements of the nodes in the network. Pair correlation

functions have been also successfully used to characterise

wireless networks in [14].

IV. PERFORMANCE PREDICTION METRIC

Simulation work in the context of correlation-sensitive

WSNs takes into account the phenomena under study and

the chosen network topology as major input data. While

the correlogram characterises the correlation structure in the

phenomena data the pair correlation function describes the

correlation in the node locations. Considering average energy

consumption Eas the performance criterion we thus argue thatthe performance of WSNs can be expressed as a linear function

of the form e = k f(C(r), g(r)), where k is a constant.


3/5

0 10 20 30 400

5

10

15

20

25

30

distance r

correlation

dph

= 10

dph

= 9

dph = 7d

ph= 5

dph

= 3

Fig. 1. Correlograms of phenomena exhibiting different correlation distances.

Figure 1 depicts the (empirical) correlograms of the consid-

ered phenomena exhibiting varying correlation distance dph.If the distance between data elements of the phenomena is

more than dph, then they cannot be directly derived from eachother. Hence, we expect that by decreasing dph the correlogramwill converge earlier. In fact, we observe that the shape (in

particular the slope and the convergence behaviour) of the

curve changes as expected dependent on dph. We see that thecorrelogram decreases overall in value as distance is increased,

corresponding to the intuition that far away values are less

correlated than nearby ones.

The pair correlation functions of various topologies are

depicted in Figure 2. The topologies are sampled from two

types of cluster point processes [10]. The Thomas PP is based

on a Poisson PP (uniform random distribution) of intensity Twhich is used to generate cluster centers. Then each parent or

cluster center point is replaced by a cluster of points. The num-

ber of points in each cluster is a Poisson distributed random

variable with mean value T. The locations of nodes in eachcluster are sampled from a normal distribution with variance

2T and the mean located at the cluster center. Another clusterprocess is the Matern PP. As for the Thomas PP, the number

of parent points are distributed according to a Poisson PP with

intensity M. The number of cluster members in each clusteris also sampled from a Poisson distribution with mean M.The only difference lies in how the cluster points themselves

are distributed. While for the Thomas PP a normal distribution

is used, the cluster points of a Matern PP are uniformly

distributed over a disc of radius RM with the respective parentpoint as center. Again, the parent points do not occur in the

resulting realisation of the PP. In our simulations we used the

parameters (T, T) = (M, M) = ( 8.4104, 12) while thethird parameter, T in the Thomas case and RM in the Materncase, controls the cluster spread.

From our analysis we derive the inner product as candi-

date solution for the linear function leading to the proposed

performance prediction metric defined as

=C(r), g(r)

. (4)

0 5 10 15 20 250

2

4

6

8

10

12

distance r

paircorrelation

Matern, RM

= 11

Matern, RM

= 14

Thomas, T = 3

Thomas, T

= 4

Thomas, T

= 5

Fig. 2. Pair correlation functions of the considered topologies; sampled fromdifferent types of random point processes with varying cluster spread.

Maximising leads to large metric values indicating minimalenergy consumption. For evaluation we conducted extensive

simulations (2000 runs each) obtaining average energy con-

sumption values E and computed the respective -metricvalues using equation 4. Figure 3 shows the energy consumed

vs. the prediction metric. Interconnected data points belong

to phenomena with identical dph. Markers indicate specifictopologies. From Figure 3 we observe that the energy con-

sumption is directly related to the performance prediction

metric, i.e. E . This interesting relation holds across allconsidered topologies with arbitrary but fixed dph. Further-more, Figure 4 is similar to Figure 3 but in contrast shows

interconnected data points which belong to arbitrary but fixed

topologies deployed on phenomena with varying dph. We havefound that E is again directly related to for any particulartopology across phenomena exhibiting different dph.

As a result, the inner product can be used as a lightweight

and powerful metric for the performance prediction of WSNs.

It is based on C(r) and g(r) solely. While only the correla-tion structure of the phenomenon needs to be estimated the

pair correlation functions of candidate topologies need to be

stored using a minimal amount of memory. Using prior

to the costly WSN deployment is a lightweight approach tosignificantly improve the cost-efficiency of the system. Since

extensive simulations can be completely avoided during the

system design phase this metric enables rapid comparative

performance evaluation of various deployment strategies.

V. EXTENDED METRIC AND ITS APPLICATION

Depending on the application other performance criteria can

play an important role. Since the effectiveness of WSNs is

often dependent on the sensing coverage we extend the per-

formance prediction metric by considering sensing coverage as

second criterion. Full sensing coverage (100 %) is achieved if

the deployed nodes cover at least the collection of interesting

locations of the phenomenon. We denote all those locations

as the set of points of interest (POI). POI is essentially

a point cloud which is selected based on significant local


4/5

0 200 400 600 800 1000550

600

650

700

750

800

850

900

performance prediction metric

averageenergyconsumed

[J]

Matern, RM

= 11

Matern, RM

= 14

Thomas, T

= 3

Thomas, T

= 4

Thomas, T

= 5

dph

= 3

dph

= 7

dph

= 5

dph

= 10

dph

= 9

Fig. 3. Direct relationship between performance prediction metric and

energy consumption according to varying correlation distance dph; markersindicate specific topologies.

deviations of the actual neighbouring phenomenon values.

Those deviations represent the highest information content and

are assumed to be most important to the application user. It

is noteworthy that nodes deployed in the area that do not

cover the POI still provide less but useful information. In

order to identify the POI we particularly apply the Laplace

operator and low-pass filtering to the entire phenomenon.

The Laplace operator on the function f is in the two-

dimensional cartesian case a second order differential operatorof the form f = 2f =

2fx2

+ 2f

y2. From the POI we can

derive a priori information which can be incorporated into the

random deployment models in order to improve the sensing

coverage of WSNs. The analysis of enhanced deployment

models exploiting a priori information has been presented in

our previous works [6], [15] and is not the focus of this paper.

However, in Table I we include a fraction of our results

adopted from [6] to be self-contained. Focusing on phenomena

with dph = 10 exemplarily, Table I lists simulation results (2000runs) such as average energy consumption E and averagesensing coverage v in respect to various deployment models.

The parameters of the models where estimated from the POIusing the minimum contrast method [16]. The term parent-

modified refers to the case where the parent point locations

(cluster centers) are restricted to lie on the first principal

component of the POI. In addition, the term non-symmetric

refers to case where the shape of the node distribution in each

cluster is dependent on the shape factor . Both options areexamples of how phenomena-related a priori information can

be exploited in order to improve the sensing coverage of the

deployment.

From our analysis, we find that the degree of similarity

between the PDFs of the POI and the chosen deployment

model is directly related to sensing coverage. As similarity

measures to estimate the distance between distributions we

take into account the Kullback-Leibler divergence [17] and

the Hellinger metric [18]. The symmetric Kullback-Leibler

0 200 400 600 800 1000550

600

650

700

750

800

850

900

performance prediction metric

averageenergyconsumed

[J]

Matern, RM

= 11

Matern, RM

= 14

Thomas, T

= 3

Thomas, T

= 4

Thomas, T

= 5

Fig. 4. Direct relationship between performance prediciton metric and

energy consumption according to various topologies.

divergence of two PDFs p and q is defined as

KL(p, q) = D(p||q) + D(q||p), with (5)

D(p||q) =

p(x)logp(x)/q(x)

.

Furthermore, the Hellinger metric is defined as

HM =

j

p(xj)

q(xj)

2 12. (6)

It is preferred to not rely on similarity measures that operate

on PDFs solely since those may be misleading. Hence, we

use in addition the Kolmogorov-Smirnov statistic [19] and the

Area metric which operate on cumulative distribution functions

(CDFs). The weighted Kolmogorov-Smirnov metric is defined

as

KS= maxx

|I(x) M(x)|/

M(x)

1 M(x)

, (7)

where I is the CDF of the POI and M is the CDF of thechosen deployment model. Furthermore, the Area metric Q asapplied in, for example, [20] is defined as

Q(I,M) =

1

J

J

j=1

log(I

1

(j/J)) log(M1

(j/J))

log(I1(1/J)) log(M1(1/J))2J

log(I1(1)) log(M1(1))2J

,

(8)

where J denotes the size of the observation window. Sincean increasing degree of similarity of two distribution func-

tions implies decreasing values in the distance between those

functions we denote the similarity measure in the case ofPDF-based measures = 1/KL and = 1/HM, respectively.Similarly in the case of CDF-based measures it follows

= 1/KS and = 1/Q, respectively. The extended predictionmetric can then be defined as

= , (9)


5/5

TABLE IAVERAGE ENERGY CONSUMPTION EAND SENSING COVERAGE v

No. Model description E[J] v[%]

1 Poisson (P = 0.0313) 1066.20 2.99

2 Thomas (T, T, T)(1.12103, 27.9, 5.0) 797.4 3 3 .29

5 Parent-mod. non-sym. Thomas (= 2) 802.37 9.106 Parent-mod. non-sym. Thomas (= 3) 804.03 9.237 Matern (M, M, RM)(1.1510

3, 27.1, 9.4) 678.4 0 3 .5010 Parent-mod. non-sym. Matern (= 2) 626.27 9.5411 Parent-mod. non-sym. Matern (= 3) 628.55 10.53

where denotes the introduced performance prediction metricaccording to energy consumption. For the evaluation of the

deployment strategies we develop the -metric

= v/E, (10)

which takes into account simulation results such as energyconsumption E and sensing coverage v.

Figure 5 shows the direct relationship between the extended

prediction metric and the -metric considering the deploy-ment strategies achieving largest v-values. Markers indicatethe topology type 5, 6, 10 and 11 from Table I. We can see

the behaviour of all considered similarity measures in respect

to the best performing deployment strategies. While all curves

behave similarly we observe that the CDF-based curves allow

a more clear distinction. Figure 5 shows that the extended

prediction metric can be used instead of the -metric whichcaptures the overall performance of WSNs from simulations

viewpoint. Thus, the concept of the performance prediction

metric is applicable and can also be extended through merging

of selected performance criteria.

V I. CONCLUSIONS

In this paper we presented the derivation of a novel metric

for the performance prediction of Wireless Sensor Networks

(WSNs). The proposed metric is based on the correlation in

the sensed phenomenon and the correlation in the location of

the sensor nodes. The main application area of the perfor-

mance prediction metric lies in the design and optimization of

WSNs prior to the costly deployment phase. Since extensive

simulations can be completely avoided it serves as a rapid

and lightweight evaluation tool for comparative analysis ofWSNs. We have shown that this concept is applicable and also

extensible through merging of selected performance criteria.

ACKNOWLEDGMENT

This work was financially supported by the German Re-

search Foundation (DFG) through the UMIC-research centre

at the RWTH Aachen University. We would like to thank Janne

Riihijarvi for stimulating discussions on spatial statistics.

REFERENCES

[1] W. Bajwa, J. Haupt, A. Sayeed, and R. Nowak, Joint Source-ChannelCommunication for Distributed Estimation in Sensor Networks, IEEETrans. on Information Theory, vol. 53, no. 10, pp. 36293653, 2007.

[2] V. Shnayder, M. Hempstead, B. Chen, G. W. Allen, and M. Welsh,Simulating the power consumption of large-scale sensor network ap-plications, in Proceedings of the SENSYS, Baltimore, USA, 2004, pp.188200.

11 12 13 14 15 16 1710

3.2

103.4

103.6

103.8

metric 1000

metric

KL

HM

KS

Q

type 5

type 6type 10

type 11

Fig. 5. Relation between and -metric in respect to the consideredsimilarity measures; markers indicate the topology type.

[3] F. Oldewurtel and P. Mahonen, Efficiency Analysis and Derivation ofEnhanced Deployment Models for Sensor Networks, Int. Journal of Ad

Hoc and Ubiquitous Computing (IJAHUC), 2010, accepted.

[4] Y. Zou and K. Chakrabarty, Sensor Deployment and Target Localizationin Distributed Sensor Networks, ACM Trans. on Embedded ComputingSystems (TECS), vol. 3, no. 1, pp. 6191, 2004.

[5] G. Wang, G. Cao, and T. L. Porta, Movement-Assisted Sensor Deploy-ment, IEEE Trans. on Mobile Computing, vol. 5, no. 6, pp. 640652,2006.

[6] F. Oldewurtel and P. Mahonen, Analysis of Enhanced DeploymentModels for Sensor Networks, in Proceedings of the VTC spring, Taipei,Taiwan, 2010, accepted.

[7] S. Pattem, B. Krishnamachari, and R. Govindan, The Impact of SpatialCorrelation on Routing with Compression in Wireless Sensor Networks,

ACM Trans. on Sensor Networks (TOSN), vol. 4, no. 4, pp. 133, 2008.[8] F. Oldewurtel, J. Ansari, and P. Mahonen, Cross-Layer Design for Dis-

tributed Source Coding in Wireless Sensor Networks, in Proceedingsof the SENSORCOMM, Cap Esterel, France, 2008, pp. 435443.

[9] A. Jindal and K. Psounis, Modeling Spatially Correlated Data in SensorNetworks, ACM Trans. on Sensor Networks (TOSN), vol. 2, no. 4, pp.466499, 2006.

[10] D. Stoyan, W. S. Kendall, and J. Mecke, Stochastic Geometry and itsApplications. Wiley, 1995.

[11] J.-P. Ebert, A. Willig, and A. Wolisz, A Gilbert-Elliot Bit Error Modeland the Efficient Use in Packet Level Simulation, in TKN technicalreport TKN-99-002, 1999.

[12] F. Oldewurtel, M. Foks, and P. Mahonen, On a Practical DistributedSource Coding Scheme for Wireless Sensor Networks, in Proceedingsof the VTC spring, Marina Bay, Singapore, March 2008, pp. 228232.

[13] F. Oldewurtel, J. Riihijarvi, and P. Mahonen, Efficiency of Distributed

Compression and its Dependence on Sensor Node Deployments, inProceedings of the VTC spring, Taipei, Taiwan, 2010, accepted.

[14] J. Riihijarvi, P. Mahonen, and M. Rubsamen, Characterizing Wire-less Networks by Spatial Correlations, IEEE Communications Letters,vol. 11, no. 1, pp. 3739, 2007.

[15] F. Oldewurtel and P. Mahonen, Estimation and Evaluation of Deploy-ment Models for Sensor Networks, in Proceedings of the VTC fall,Anchorage, USA, 2009, pp. 15.

[16] P. J. Diggle and R. J. Gratton, Monte Carlo Methods of Inference forImplicit Statistical Models, Journal of the Royal Statistical Society,vol. 46, no. 2, pp. 193227, 1984.

[17] T. M. Cover and J. A. Thomas, Elements of Information Theory. Wiley,2006.

[18] A. Ferrante, M. Pavon, and F. Ramponi, Hellinger versus Kullback-Leibler Multivariable Spectrum Approximation, IEEE Trans. on Auto-matic Control, vol. 53, no. 4, pp. 954967, 2008.

[19] F. Massey, The Kolmogorov-Smirnov test for Goodness of Fit, Journal

of the American Statistical Assoc., vol. 46, no. 253, pp. 6878, 1951.[20] M. Wellens, J. Riihijarvi, and P. Mahonen, Empirical Time and Fre-

quency Domain Models of Spectrum Use, Elsevier Physical Commu-nication, vol. 2, no. 1-2, pp. 1032, 2009.

Metrics_VTC10_Metrics for Performance Prediction of Wireless Sensor Networks

Documents

Transcript of Metrics_VTC10_Metrics for Performance Prediction of Wireless Sensor Networks