Spatial Distribution of Wireless Sensor Nodes in the Urban

Environment

Vendula Hejlová

Department of Geoinformatics, Palacký University Olomouc, 17. listopadu 50, Olomouc, Czech Republic

Keywords: Wireless Sensor Node, Distribution of Nodes, Graph Theory.

Abstract: Wireless sensor nodes are an important part of every wireless sensor network. If wireless sensor nodes have

implemented or connected sensors, then they can be used for different types of measurements. These

measurements can be carried out either in internal or external environment. Spatial distribution of sensor

nodes in the urban environment is a crucial decision because on its basis the selected elements will be

measured in the suggested places. It is necessary to choose localities where these measurements have the

long term significance. Distribution of sensor nodes in the urban environment is determined by a lot of

factors. These factors are related to technical parameters of nodes, terrain characteristics and parameters of

measured elements. Distribution of sensor nodes is made on the basis of distribution algorithms or the

sensor nodes are randomly spread to the area of interest. The graph theory is usually the background of

distribution algorithms. This theory primarily does not take into account the characteristics of terrain and

measured elements. This paper describes factors that influence the distribution of sensor nodes. The graphs

that are used in the wireless sensor networks are described and the most suitable solution for

implementing terrain characteristics is selected.

1 INTRODUCTION

Spatial distribution of wireless sensor nodes in the

urban environment is a crucial decision because on

its basis the selected elements will be measured in

the suggested places. Measurements of chosen

elements will be realized in the long term so that it is

necessary to choose the localities where the

measurements of selected elements will have long-

term significance. Distribution methods are used to

solve this task but these methods can be effectively

used only in the indoor conditions because it takes

into account only technical parameters and

possibilities of the sensor nodes. The background of

these algorithms is in the most cases based on the

graph theory. A lot of factors influence the

distribution of wireless sensor nodes in the urban

environment so that the effective distribution of

nodes is more complicated. Till now nobody paid

the attention to the terrain characteristics which play

an important role in the distribution process. These

characteristics are very important in the case that the

sensor nodes are situated in the urban environment

so that they should be included in the distribution

methods.

The author solves the problem of distribution of

wireless sensor nodes in the urban environment on

the basis of suggested factors. These factors contain

not only technical requirements for nodes but they

also include terrain factors and parameters of

measured elements. The main objective of this paper

is to analyze graphs which are used in the wireless

sensor networks and select the most suitable one.

The spatial distribution of sensor nodes in the urban

environment could be carried out on the basis of the

selected graph. The crucial requirement for the

graph is to involve technical and terrain factors to its

construction. If terrain factors were included in the

distribution problem then the deployment of wireless

sensor nodes in the outdoor environment could be

effectively solved.

2 STAGE OF RESEARCH

This research has been ending its theoretical part.

The literature, the articles and the distribution

algorithms were studied in this part. The reasearch is

now starting its practical part. The parameters which

influence the distribution of sensor nodes in the

Hejlová V..

Spatial Distribution of Wireless Sensor Nodes in the Urban Environment.

 2014 SCITEPRESS (Science and Technology Publications, Lda.)

urban environment were defined. The graph which is

the most suitable for implementing of terrain

parameters was scouted out. The method which will

take into account not only technical parameters but it

will solve the problem of distribution of sensor

nodes more complex will be proposed in the future

work.

3 OUTLINE OF OBJECTIVES

The objectives of this paper are to:

 define factors that influence the distribution of

sensor nodes in the urban environment,

 scouted out graphs that can be used in the

wireless sensor networks,

 select the most suitable graph for implementing

terrain factors,

 suggest the way how the terrain factors can be

implemented to the graph.

Till now no attention has been paid to the

implementation of terrain factors into the

distribution methods. These factors are very

important in the case that the sensor nodes are

distributed in the urban environment so that their

inclusion in the distribution methods is necessary.

4 RESEARCH PROBLEM

The first problem of this research is to situate sensor

nodes in the urban environment. Nodes placed in

external conditions have to be protected against

external influences. Their localization is influenced

by other factors like technical characteristics of the

node, terrain characteristics of the area of interest

and parameters of measured elements. It is important

to suggest method which will involve all factors that

influence the distribution of sensor nodes in the

external environment.

4.1 Factors that Influence the

Distribution of Sensor Nodes

Basic factors influencing distribution of sensor

nodes that have to be determined at the beginning

are:

 area covered by nodes (size, type),

 count of nodes that will be situated in this area,

 density - factor which deals with the number of

nodes and the size of selected area (there have to

be situated enough nodes but not to many of

them because the redundant data could be

obtained).

Other factors influencing the distribution of nodes

can be divided into two groups – technical and

terrain. Terrain factors include demands on

characteristics of measured elements (Table 1).

Table. 1: Factors that influence the distribution of nodes.

Number of

group

Technical factors Terrain factors

1 Battery life Landcover (type)

2 Communication range

Obstacles (visibility,

quality of signal)

Balanced number of node

neighbours

Characteristics of

measured elements

(recording interval)

Back up communication

paths

Security

5 Property conditions

4.1.1 Technical Factors

Technical factors influencing spatial distribution of

sensor nodes in the area of interest are related to the

technical equipment and technical possibilities of

sensor nodes.

Battery life is the most important technical

parameter. Battery is not used equally in all nodes

because some nodes are used more for

communication than the others so that their battery

is more depleted. It is important to ensure that the

battery consumption in all nodes is as equal as

possible. There could be a power cut in overloaded

nodes and measured data could be lost. Routers are

usually more loaded with the communication so that

they should be charged up with better type of

batteries or equipped by the solar panel. Battery is

discharged with the second power of communication

distance. The better solution is if the nodes

communicate for shorter distances than the longer

ones.

Communication distance shows the maximal

distance that enables the communication among

nodes. Communication distance depends on the used

protocol and terrain characteristics.

Every node should have balanced number of

neighbours. One sensor node should not be

overloaded with communication and the other sensor

nodes should not be used only rarely. Balanced

communication deals with energy consumption of

nodes which are participating in the wireless sensor

network.

Back up communication paths in the graph are

necessary in the case of the power cut of one sensor

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node. Data that are sent through this node can not be

directed to the gateway so that they can be lost.

4.1.2 Terrain Factors

Terrain factors include the demands on measured

elements. The major terrain factors that influence

spatial distribution of sensor nodes are composited

of landcover, characteristics of measured elements

and property conditions.

Landcover shows the different types of the land

surface. A lot of types of landcover that influence

values of measured elements are situated in the

urban environment. Nodes have to cover all types of

landcover in the area of interest. Every type of

landcover has different characteristics which depend

on heat absorption and reflection. It is necessary to

involve these facts to obtain comparable data from

different types of landcover. All types of landcover

have to be covered by at least one node. Another aim

of spatial distribution of sensor nodes in the urban

environment is to locate nodes to more and less

polluted parts of the area of interest (depend on the

distance from the source of air pollutants). The

comparison of data obtained in the different parts of

area with different level of air pollutants is useful for

predicting and modelling of different types of

pollutants dispersion scenarios.

Terrain obstacle is an object in the

communication path which can affect

communication among two nodes. Obstacles can be

natural or human made. Different kinds of obstacles

can influence signal transmission in the various

ways. It depends on their structure and angle of

arrival of the transmitting wave. It is suggested to

avoid any obstacles that are situated between two

nodes which are communicating with each other.

Demand on direct visibility between two

communicating nodes comes from terrain obstacles.

Quality of signal depends on the degree of visibility

between nodes which communicate with each other.

If these nodes are located in the area without

obstacles, signal is only slightly influenced by

dispersion and noise. Quality of signal can be

influenced by another device which transmits in the

same range as the sensor nodes.

Every measured element has defined the

standardized height above surface, degree of shading

and time of recording of measurement. Interval of

recording is a parameter which points out the time

step of data recording and it depends on the

measured elements. Basic meteorological elements

are recorded in the climatologic determined times.

Three basic climatologic terms are defined (7 am, 2

pm, 9 pm). Detailed measurements can be recorded

in more detailed climatologic terms. Own intervals

for measurement can be determined but they have to

be the same for all nodes to obtain comparable data.

It is appropriate to select an interval which does not

yield redundant data. The interval does not have to

be too large because some differences in values of

selected elements can appear in short time periods.

Security is a demand which is very complicated

to fulfil. It is necessary to situate nodes into “safe”

area to protect them against vandals. It can be used

some tricks which can increase the probability that

the nodes will not be stolen. These arrangements can

involve the placement of nodes in:

 higher positions

 less visible places

 places with low human movement

 hardly accessible places

 fenced places

Property conditions are important factor if the nodes

are situated in the private properties because the

owner has to agree with their placement on his

property.

5 STATE OF ART

A lot of studies deal with the application of graph

theory in wireless sensor networks because the

communication among nodes can be easily

described by this theory. Wireless sensor nodes are

represented by nodes in the graph and

communication paths are depicted with edges. The

aim of lower number of studies is to search the most

suitable localization for wireless sensor nodes. These

studies do not involve terrain characteristics and

parameters of measured elements in the proposed

algorithms. The obstacles which influence signal

transmitting are included only in the elementary

basis because graph theory does not primarily count

with the usage of nodes in the external conditions.

The most frequently solved factors which influence

distribution of wireless sensor nodes are battery life

and communication distance.

Mizera (2011) dealt with the proposition of

wireless sensor network which was applied to the

monitoring of potential forest fires in the selected

area which was situated in the eastern part of the

Czech Republic. Mesh topology was used for this

kind of monitoring. This type of topology allows to

use more communication paths among nodes. The

nodes were situated in squares. The distance

SpatialDistributionofWirelessSensorNodesintheUrbanEnvironment

between two neighbour nodes was 200 meters.

Terrain obstacles were only mentioned and they

were not involved in the calculation but they could

be expressed as weights in the graph. Sarioz (2012)

aimed his dissertation thesis at data transmitting in

wireless sensor networks. The communication

among nodes was described by graph theory. His

attention was concentrated on obstacles and their

distribution in the communication paths. He tested

which deployment of obstacles influences more the

transmitting wave and which modifies the wave only

subtly. Kawagashi (2005) presented a model which

uses percolation, a kind of random graph where the

edges are formed and the communication is

performed only among the nearest nodes. He has

commented that the jump effect of the phase

transition appears sharply by synergistic effect with

radio wave attenuation as the distance between the

transmitter and the receiver increases. The distance

between the nodes should be in effective range. Yan

(2008) has dealt with multilevel clustering as a

mechanism for prolonging the lifetime of wireless

sensor network node. Root tree with the

performances of the minimal relay set and the

maximal weight according to graph theory was

declared. Energy-aware multilevel algorithm was

proposed. This algorithm is able to reduce the

number of relays used for data transmission and it

enables to load energy evenly among all sensors in

the network. Jorio (2013) proposed a new algorithm

which concentrates on the energy issue in the

wireless sensor nodes. K-Way Special Clustering

Algorithm in wireless sensor network was proposed.

This algorithm is based on spectral classification.

The aim of this algorithm is to find the ideal

distribution of wireless sensor nodes and their

cluster heads in the area of interests. Classification

method determines similar nodes before identifying

cluster heads. Residual energy is taken into account

when the cluster head is scouted out. Nodes and

communication links are represented by the graph

theory. Results show that this method ensures lower

energy consumption in nodes. Ding (2008) aimed

the attention at limited energy source in wireless

sensor nodes. He proposed a new two dimensional

model with percolations using random graph which

connects only neighbour nodes. Connectivity and

energy consumption was investigated. The energy

consumption was analyzed by Markov process and

all the results were investigated in the simulation

process. The energy consumption in nodes is solved

in the other studies like the one from Lu (2005). This

study deals with the question of providing periodic

energy-efficient radio sleep cycles while minimize

the end to end communication delays. He aimed his

attention at communication latency because every

sensor node has a duty to be awake for given time

slots and data do not have to be obtained in this

given time. He formulated a graph theoretical

abstraction of the problem. The data transmitting

which is displayed with graph theory is described in

the study from Baranidharan (2012). This study

deals with a design of energy efficient protocol for

clustered wireless sensor networks. First of all the

cluster head is selected. Data are collected in all

clusters and they are sent to the head of their cluster.

The algorithm which is based on the graph theory is

proposed. The shortest path from the selected node

to the cluster head is searched. Silva (2009)

proposed a model that protects against the overflow

of communication channel. This overflow can cause

the lost of transmitted packets. Two types of

congestion can appear in the wireless sensor

networks – node level (caused by buffer overflow)

or link level (caused by sharing wireless channels).

Link overflows are studied in this paper. The

measurement of congestion is the inverse value of

the greatest eigenvalue of the adjacency matrix in

the random graph. This measure gives an

approximation of the average quantity of wireless

links of a certain length in the network. The

congestion number is linked to the number of

connected paths of given length. Haghpanahi (2012)

solved the problem of connectivity in large scale

wireless sensor networks. The desired path of traffic

flow is displayed with the flow vector. The known

count of flows from one node leads to the known

number of edges which originate in every sensor

node. The existence of enough paths connecting the

source and the destination node is guaranteed. The

density of wireless sensor network is known. Kar

(2008) aimed his work at design of wireless sensor

network topology. This paper studies the problem of

designing the topology assigning the probabilities of

communication among nodes to maximalize the rate

of convergence of average consensus. The failtures

that can appear in wireless communication among

nodes are taken into account. The network is

modelled as a Bernoulli random topology. It is

shown that the topology design with random link

failtures, link communications costs and

communication constraint is a convex optimization

problem that can be solved by semidefinite

programming techniques.

The articles about distribution algorithms,

implementation of graphs in the wireless sensor

networks or application of wireless sensor networks

can be found. Only a few studies implement

SENSORNETS2014-DoctoralConsortium

distribution algorithms to the distribution process.

The sensor nodes are in the most cases distributed

randomly in the selected area. Nobody tried to

include terrain characteristics in the distribution

process.

6 METHODOLOGY

The suggested methodology for the distribution of

wireless sensor nodes in the area of interest is graph

theory because the wireless sensor network

communication can be easily described by graph.

Nodes of wireless sensor network are represented by

nodes in graph and communication paths are

depicted with edges.

6.1 Graph Theory in Wireless Sensor

Networks

Graph theory is very commonly used in wireless

sensor networks for solving problems with

communication paths among nodes. The usage of

graph theory in wireless sensor networks can

decrease energy consumption and increase the

effectiveness of the system. Following graphs are

considered to be localized structures for topology

construction and they are used in wireless sensor

networks:

 Unit Disk Graph,

 Minimum Spanning Tree, Localized Spanning

Tree

 Gabriel Graph,

 Yao Graph,

 Relative Neighbourhood Graph,

 Delaunay Triangulation (this triangulation is a

basis for Thiesson Polygons) (Stojmenović,

2005).

6.1.1 Unit Disk Graph

The wireless sensor network is consisted of known

number of sensors and known communication

distance which is the same for all nodes. It is

possible to determine the broadcast area for all the

nodes and to determine the nodes which

communicate with each other. If the position of

nodes is unknown it is necessary to select possible

localities of their occurrence. Nodes which

communicate with each other are neighbours

(Stojmenović, 2005). This graph enables to suppress

the communication range and reduce the energy

consumption. If the position of nodes is known it is

necessary to choose the unit which will be the same

for all nodes. This unit is either communication

range or average count of nodes for one node. Figure

1 shows the spatial distribution of nodes in the Unit

Disk Graph without the basemap and with the

basemap which gives the spatial base to the sensor

nodes distribution. The unit is the communication

range.

Figure 1: Unit graph for 8 nodes.

This type of graph can be used only with limits

in the distribution process of sensor nodes in the

urban environment. The highest attention is paid to

the communication range. This graph solves from

the above mentioned factors all technical ones.

Terrain factors can be expressed indirectly by using

weight values but the weights can be primarily used

only for one factor and not for all of them. The

average weight for all factors could be determined.

The property conditions, type of landcover and

security can be easily expressed manually.

6.1.2 Minimum Spanning Tree and

Localized Tree

Minimum spanning tree is a subgraph of Unit Disk

Graph which is continuous, contains all nodes and

the sum of all lengths in graph is minimal. This

graph is edge-weight depend (Stojmenović, 2005).

Minimum spanning tree can be localized – it means

that every node collects positions of its single-hop

neighbours.

This type of graph can be used for observing the

length of edges and their weight evaluations which

determine edge preferences. Obstacles can be

displayed by edge preferences. This type of graph

can not primarily include types of landcover,

security and property conditions. The localized type

of this graph is more appropriate for analyzes of

spatial distribution because the positions of nodes in

the graph are known as well as the count of node

neighbours.

6.1.3 Gabriel Graph

Edge e is in the Gabriel Graph if and only if the

SpatialDistributionofWirelessSensorNodesintheUrbanEnvironment

circle with edge e as the diameter contains no other

node inside it. The Gabriel graph partitions the graph

into faces that are bound by polygons and make up

the edges of the graph (Matula, 2010, Stojmenović,

2003).

The fulfilment (green, smaller one) and non-

fulfilment (red, bigger one) of the Gabriel condition

is shown on the left side of Figure 2. The example of

distribution of nodes which fulfils the Gabriel

condition is shown on the right side of Figure 2.

Figure 2: Communication possibilities in Gabriel Graph.

This type of graph is used for detection of

distances where the nodes will be situated. No third

node can be situated between them and disturb their

communication. This communication is carried out

among neighbours so that the communication range

is as short as possible. All above-mentioned

technical factors can be described by this type of

graph. Terrain factors like obstacles can be

expressed by weight values but the Gabriel condition

has to be fulfilled. Different types of landcover,

property conditions and security can be situated in

the communication range but these factors are not

directly expressed in this type of graph.

6.1.4 Yao Graph

The basic thought of Yao graph is the segmentation

of the space into the sectors which have the same

angle size. Every node communicates with the

nearest node in every sector (Scheideler, 2004).

Figure 3 shows the communication among nodes in

quadrates.

This graph is used in oriented applications such

as in the case when the azimuths are known. All

technical factors can be solved in this type of graph.

Communication range is determined by the distance

of nodes in the sectors. This distance is not the same

for all sectors. Battery life can be increased because

the node communicates only with the nearest node

in every sector. The number of neighbours of one

node is influenced by the number of quadrants.

Terrain factors like obstacles could be described by

weights but in some cases the basic principal of this

type of graph could be broken. Factors like security,

property conditions and landcover can not be

involved in the calculations in this type of graph.

Figure 3: Communication in Yao Graph.

6.1.5 Relative Neighbourhood Graph

Edge is involved in the graph only in case that it is

not the longest edge in the uvw triangle. If the suture

of two nodes is situated in the middle of two nodes,

then no other node must be situated in the

intersection of circles (Stojmenović, 2005). Graph

which can be called Relative Neighbourhood Graph

is shown in Figure 4. It fulfils the demand on the

nearest nodes connection in all its nodes.

Figure 4: Relative Neighbourhood Graph for 8 nodes.

This type of graph deals with the problem of

communication distance - the nearest node is

scouted out. All technical factors can be complied in

this type of graph. It will be complicated to include

terrain factors to this graph because assigning

weights to edges could lead to the contravention of

the rules.

6.1.6 Delaunay Triangulation

Delaunay Triangulation is commonly used method

for the representation of surface characteristics. The

aim of this method is to create triangles which are as

SENSORNETS2014-DoctoralConsortium

equilateral as possible. The circumscribing circle to

every triangle must not contain any other node

except for the vertices of the triangle (Stojmenović,

2005). Figure 5 shows the communication among 5

selected nodes. This communication is displayed in

orange colour. All requirements for Delaunay

Triangulation are fulfilled in this case.

Figure 5: Delaunay Triangulation for 8 nodes.

Delaunay Triangulation can be used for

distribution of sensor nodes in wireless sensor

networks but in the case of its usage it is important

to take into account that the energy consumption is

higher because the communication has to be

performed in triangles so that every node

communicates with at least three other nodes. All

technical factors can be expressed with this method.

Terrain factors may be marginally included in the

calculation.

Delaunay Triangulation is connected to the

Thiesson Polygons Method. This method determines

the catchment area of the node. Figure 6 shows the

catchment area of every node in the wireless sensor

network.

7 EXPECTED OUTCOME

The expected outcome of this paper is only one

objective of dissertation thesis which is aimed at the

distribution and following monitoring of air

pollution in the city of Olomouc.

The outcome of this particular objective is aimed

at the suggestion of technical and terrain factors that

influence the distribution of sensor nodes in the

urban environment. The selection of the most

suitable graph for including terrain characteristics in

the distribution process is necessary. These

characteristics should be added to the existing

methods and suggest one compact method or

algorithm that will have universal usage for

distribution of sensor nodes in the urban

environment.

8 CONCLUSIONS

Factors that influence the spatial distribution of

wireless sensor nodes in the urban environment were

suggested in this paper. These factors were divided

into two groups – technical and terrain. Terrain

factors included parameters of measured elements.

Graphs are usually used as a basis of distribution

algorithms. Seven types of graphs are commonly

used in the wireless sensor networks. The technical

factors are included in the majority of graphs but the

terrain factors have to be implemented to them. It is

not possible to implement terrain factors in all types

of graphs because of the basic rule for graph

construction would be broken. The most suitable

graph for the implementing of terrain factors was

analyzed as the Unit Disk Graph.

The future work is aimed at the usage of the

selected graph in the practical part of work. Firstly,

the way how to implement the terrain factors to the

selected graph will be practically certified. The

suggested method will be verified in the real task

which deals with the distribution of sensor nodes for

monitoring of air pollutants in the urban

environment.

Figure 6: Catchment area of 8 nodes.

9 DISCUSSION

There are a lot of factors that influence the

distribution of sensor nodes. The major factors that

influence the distribution sensor nodes depend on

the technical and software equipment of sensor

nodes. This paper suggests technical and terrain

SpatialDistributionofWirelessSensorNodesintheUrbanEnvironment

factors that should be included in the distribution of

sensor nodes in the urban environment. Are these

factors enough for the effective distribution of

sensor nodes in the urban environment or are there

other significant influences? Some factors can be

more important than the others in the different types

of application. Should the suggested factors be

evaluated by weights? The graph theory is a way

how to express the communication in the wireless

sensor network. Seven types of graphs are usually

used in the wireless sensor networks. Would it be

possible to use some other type of graph that is not

primarily used in the wireless sensor networks or

suggest the new one? The graph theory is not the

only method that can solve the problem of

distribution of wireless sensor nodes in the urban

environment. There are other methods like chaos

theory that can be used for the distribution of sensor

nodes. Would this theory be more appropriate for

implementing terrain characteristics in the

calculation? The problem of implementing terrain

factors into the distribution methods is crucial in the

case that the sensor nodes are situated in the urban

environment. The solution of this problem would

make the distribution of sensor nodes more efficient.

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