Router Nodes Positioning for Wireless Networks Using Artificial

Immune Systems

P. H. G. Coelho, J. L. M. do Amaral, J. F. M. do Amaral, L. F. de A. Barreira and A. V. de Barros

State Univ. of Rio de Janeiro, FEN/DETEL, R. S. Francisco Xavier, 524/Sala 5001E, Maracanã, RJ, 20550-900, Brazil

Keywords: Artificial Immune Systems, Artificial Intelligence Applications, Node Positioning, Wireless networks.

Abstract: This paper proposes the positioning of intermediate router nodes using artificial immune systems for use in

industrial wireless sensor networks. These nodes are responsible for the transmission of data from sensors to

the gateway in order to meet criteria especially those that lead to a low degree of failure and reducing the

number of retransmissions by routers. These criteria can be enabled individually or in groups, combined

with weights. Positioning is performed in two stages, the first uses elements of two types of immune

networks, SSAIS (Self-Stabilising Artificial Immune System) and AINET (Artificial Immune Network),

and the second uses potential fields for positioning the routers such that the critical sensors attract them

while obstacles and other routers repel them. Case studies are presented to illustrate the procedure.

1 INTRODUCTION

Data transmission through the use of wireless

technology has grown dramatically in society. The

wireless technology has taken over the world and the

field of industrial automation is no exception. Main

advantages are reduced installation time of devices,

no need of cabling structure, cost saving projects,

infrastructure savings, device configuration

flexibility, cost savings in installation, flexibility in

changing the existing architectures, possibility of

installing sensors in hard-to-access locations and

others. Safety, reliability, availability, robustness

and performance are of paramount importance in the

area of industrial automation. The network cannot be

sensitive to interference nor stop operation because

of an equipment failure, nor can have high latency in

data transmission and ensure that information is not

misplaced (Zheng and Lee, 2006). In industrial

automation environment, data transmission in a

wireless network faces the problem of interference

generated by other electrical equipment, such as

walkie-talkies, other wireless communication

networks and electrical equipment, moving

obstacles (trucks, cranes, etc.) and fixed ones(

buildings , pipelines , tanks , etc.). In an attempt to

minimize these effects, frequency scattering

techniques and mesh or tree topologies are used, in

which a message can be transmitted from one node

to another with the aid of other nodes, which act as

intermediate routers, directing messages to other

nodes until it reaches its final destination. This

allows the network to get a longer range and to be

nearly fault tolerant, because if an intermediate node

fails or cannot receive a message, that message

could be routed to another node. However, a mesh

network also requires careful placement of these

intermediate nodes, since they are responsible for

doing the forwarding of the data generated by the

sensor nodes in the network to the gateway directly

or indirectly, through hops. Those intermediate

nodes are responsible for meeting the criteria of

safety, reliability and robustness of the network and

are also of paramount importance in the forwarding

of data transmission. They could leave part or all the

network dead, if they display any fault (Hoffert et

al., 2007). Most solutions to the routers placement

solve this problem with optimization algorithms that

minimize the number of intermediate router nodes to

meet the criteria for coverage, network connectivity

and longevity of the network and data fidelity.

(Youssef and Younis , 2007), (Molina et al., 2008).

This paper proposes to solve this problem using

Artificial Immune Networks, based on the human

immune system. The algorithms based on immune

networks have very desirable characteristics in the

solution of this problem, among which we can

mention: scalability, self-organization, learning

ability and continuous treatment of noisy data

(Coelho et al., 2012). This paper is divided into four

415

H. G. Coelho P., L. M. do Amaral J., F. M. do Amaral J., F. de A. Barreira L. and V. de Barros A..

Router Nodes Positioning for Wireless Networks Using Artiﬁcial Immune Systems.

DOI: 10.5220/0004898904150421

In Proceedings of the 16th International Conference on Enterprise Information Systems (ICEIS-2014), pages 415-421

ISBN: 978-989-758-027-7

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

sections. Section 2 does a brief discussion of

artificial immune systems. Section 3 presents the

application of artificial immune systems to the

problem of node positioning and section 4 concludes

the paper by presenting results and conclusions.

2 IMMUNE SYSTEMS

Artificial immune systems (AISs) are models based

on natural immune systems which protect the human

body from a large number of pathogens or antigens

(Amaral, 2006). Due to these characteristics the

AISs are potentially suitable for solving problems

related to computer security and they inherit from

natural immune systems the properties of

uniqueness, distributed sensing, learning and

memory efficiency. In fact, the immune system is

unique to each individual. The detectors used by the

immune system are small, efficient and highly

distributed and are not subject to centralized control.

Moreover, it is not necessary that every pathogen is

fully detected, because the immune system is more

flexible, there is a compromise between the

resources used in the protection and breadth in

coverage. Anomaly detection is another important

feature, since it allows the immune system to detect

and respond to pathogens (agents that cause

diseases) for which they have not previously been

found. The immune system is able to learn the

structures of pathogens and remember these

structures so that future responses to these agents are

faster. In summary, these features make the immune

system scalable, robust and flexible. The immune

system uses distributed detection to distinguish the

elements of the organism itself, the self, and foreign

to the body, the non-self. The detection of the non-

self is a difficult task because its number, of the

order of 10

, is much superior to the number of self

patterns, around 10

, taking place in a highly

distributed environment. It should be also noted that

all these actions occur while the living organism

must continue in operation and the available

resources are scarce. Cells that perform the detection

or recognition of pathogens in the acquired or

adaptive immune system are called lymphocytes that

recognize pathogens joining them. The antigens are

detected when a molecular bond is established

between the pathogens and the receptors present on

the surface of lymphocytes. A given receiver will

not be able to join all antigens. A lymphocyte has

approximately 100,000 receptors on its surface

which however have the same structure, and

therefore can only join with structurally related

epitopes (the site on an antigen at which a specific

antibody becomes attached). Such epitopes define a

similarity subset of epitopes which lymphocytes can

detect. The number of receivers that can join the

pathogens defines the affinity of a lymphocyte to a

certain antigen. Lymphocytes can only be activated

by an antigen if their affinities exceed a certain

threshold. As this threshold increases, the number of

epitopes types capable of activating a lymphocyte

decreases, i.e., the similarity subset becomes

smaller. A receiver may be obtained by randomly

recombining possible elements (from the memory of

the immune system), producing a large number of

possible combinations indicating a wide range in the

structure of the receptors. Although it is possible to

generate approximately 10

receptor types, the

number present at a given instant of time is much

smaller, in the range of 10

to 10

(Silva, 2001).

The detection is approximate, since it is a difficult

task to evolve structures that are complementary to

receptor epitopes for which the organism has never

encountered before. If an exact complementarity was

needed, the chance of a random lymphocyte epitope

join a random would be very small. An important

consequence of that approximate detection is that

one single lymphocyte is capable of detecting a

subset of epitopes, which implies that a smaller

number of lymphocytes is required for protection

against a wide variety of possible antigens. The main

algorithms that implement the artificial immune

systems were developed from metaphors of the

immune system: the mechanism of negative

selection, the theory of immune network and the

clonal selection principle. The function of the

negative selection mechanism is to provide tolerance

to the self cells, namely those belonging to the

organism. Thus, the immune system gains the ability

to detect unknown antigens and not react to the

body's own cells. During the generation of T-cells,

which are cells produced in the bone marrow,

receptors are generated by a pseudo-random process

of genetic arrangement. Later on, they undergo a

maturation mechanism in the thymus, called

negative selection, in which T cells that react to

body proteins are destroyed. Thus, only cells that do

not connect to the body proteins can leave the

thymus. The T cells, known as mature cells,

circulate in the body for immune functions and to

protect it against antigens. The theory of immune

system network considers several important aspects

like the combination of antibodies with the antigens

for the early elimination of the antigens. Each

antibody has its own antigenic determinant, called

ICEIS2014-16thInternationalConferenceonEnterpriseInformationSystems

416

idiotope. In this context, (Jerne, 1974) proposed the

Immune Network Theory to describe the activity of

lymphocytes in an alternative way. According to

(Jerne, 1974) the antibodies and lymphocytes do not

act alone, but the immune system keeps a network of

B cells for antigen recognition. These cells can

stimulate and inhibit each other in various ways,

leading to stabilization of the network. Two B cells

are connected if they share an affinity above a

certain threshold and the strength of this connection

is directly proportional to the affinity they share. The

clonal selection principle describes the basic features

of an immune response to an antigenic stimulus, and

ensures that only cells that recognize the antigen are

selected to proliferate. The daughter cells are copies

or clones of their parents and are subject to a process

of mutation with high rates, called somatic

hypermutation. In the clonal selection the removal of

daughter cells are performed, and these cells have

receptors that respond to the body's own proteins as

well as the most suitable mature cell proliferation,

i.e., those with a greater affinity to the antigens

(Coelho et al., 2013).

3 AIS NODE POSITIONING

Router Nodes positioning has been addressed in the

literature by several researchers. (Cannons et al,

2008) propose an algorithm for positioning router

nodes and determine which router will relay the

information from each sensor. (Gersho and Gray,

1992), proposed one to promote the reliability of

wireless sensors communication network,

minimizing the average probability of sensor

transmission error. (Shi et al., 2009) propose a

positioning algorithm of multi-router nodes to

minimize energy consumption for data transmission

in mobile ad hoc network (MANET - Mobile Ad

Hoc Network). The problem was modeled as an

optimization clustering problem. The suggested

algorithm to solve the problem uses heuristic

methods based on the k-means algorithm. (Costa and

Amaral, 2010) describe an approach for router nodes

placement based on genetic algorithm which

minimizes the number of nodes required for network

routers, decreasing the amount critical nodes for all

involved devices and the number of hops of the

transmitted messages. The use of wireless sensor

network in industrial automation is still a matter of

concern with respect to the data reliability and

security by users. Thus, an appropriate node

positioning is of paramount importance for the

wireless network to meet safety, reliability and

efficiency criteria. Positioning of nodes is a difficult

task, because one should take into account all the

obstacles and interference present in an industrial

environment. The gateway as well as the sensors

generally have a fixed position near the control

room. But the placement of router nodes, which are

responsible for routing the data, generated by the

sensors network to the gateway directly or

indirectly, is determined by the characteristics of the

network. The main characteristics of wireless sensor

networks for industrial automation differ from

traditional ones by the following aspects: The

maximum number of sensors in a traditional wireless

network is on the order of millions while

automation wireless networks is on the order of tens

to hundreds; The network reliability and latency are

essential and fundamental factors for network

wireless automation. To determine the number of

router nodes and define t position in the network,

some important aspects in industrial automation

should be considered. It should be guaranteed: (1)

redundant paths so that the system be node fault-

tolerant; (2) full connectivity between nodes, both

sensors and routers, so that each node of the network

can be connected to all the others exploring the

collaborative role of routers; (3) node energy

efficiency such that no node is overwhelmed with

many relaying information from the sensors; (4)

low-latency system for better efficiency in response

time; (5) combined attributes for industrial processes

to avoid accidents due to, for example, high

monitored process temperature. (6) self-organization

ability, i.e. the ability of the network to reorganize

the retransmission of data paths when a new sensor

is added to the network or when a sensor stops

working due to lack of power or a problem in

wireless communication channel. All these factors

must be met, always taking into consideration the

prime factor security: the fault tolerance. In the end

of the router nodes placement, the network of

wireless sensors applied to industrial automation

should be robust, reliable, scalable and self-

organizing.

The positioning of router nodes in industrial

wireless sensor networks is a complex and critical

task to the network operation. It is through the final

position of routers that one can determine how

reliable, safe, affordable and robust the network is.

In the application of immune systems to router

nodes positioning reported in this paper, B cells that

make up the immune network will be composed by a

set of sensor nodes and a set of router nodes. The

sensor nodes are located in places where the plant

RouterNodesPositioningforWirelessNetworksUsingArtificialImmuneSystems

417

instrumentation is required. These nodes have fixed

coordinates, i.e. they cannot be moved. For security

to be guaranteed it is necessary to have redundant

paths between these nodes and the gateway. The set

of router nodes will be added to allow redundant

paths. The position of these nodes will be changed

during the process of obtaining the final network.

The stimulation of the B cells, corresponding to the

set of routers, is defined by the affinity degree

among B cells in the training of the network. In this

paper, the role of the antigen is viewed more broadly

as the entity that stimulates B cells. Thus, the

function of the antigen takes into consideration

possible missing paths to critical sensors, the

number of times that a router is used and its

proximity to sensors. The modeling of B cells

affinity is the weighted sum of the three criteria that

the positioning of each router will answer. The

criteria are: fault degree of each router, number of

times each router is used depending on the path and

number of sensor nodes neighboring to each router.

Process dynamics can be divided into two processes:

network pruning and cloning, and node mutation of

the network routers. In the pruning process, n

router

nodes that during a certain time failed to become

useful to the network will be removed from it. The

latter process is responsible for generating n

clones

of router nodes that were over stimulated. The

clones may suffer mutations of two kinds:

(i) hypermutation – for positioning new elements

in the network which are inversely proportional

to the degree of stimulation of the router node

selected and

(ii) net Mutation – for positioning the new

information into the network in order to assure

the new clones are neighbors of the selected

clone (Poduri et al , 2006).

After the inclusion of the new router nodes, a stop

condition is performed. If the condition is not met,

all routers undergo an action of repulsive forces,

generated by obstacles and routers for other nodes,

followed by attractive forces created by critical

sensor nodes. Those critical nodes are the ones that

do not meet the minimum number of paths necessary

to reach the gateway. The actions of repelling

potential fields have the function of driving them

away from obstacles, to allow direct line of sight for

the router network nodes to increase the reliability of

transmission and also increase the distance among

the routers to increase network coverage. On the

other hand, the attractive potential fields attract

routers to critical sensors, easing the formation of

redundant paths among sensors and the gateway.

After the action of potential fields, from the new

positioning of routers, a new network is established

and the procedure continues until the stopping

criterion is met.

Figure 1: The proposed algorithm.

The algorithm proposed in this paper deals with a

procedure based on artificial immune networks,

which solves the problem of positioning the router

nodes so that every sensor device is able to

communicate with the gateway directly and or

indirectly by redundant paths. Figure 1 shows the

main modules of the algorithm. The first module is

called immune network, and the second, positioning

module is called potential fields containing elements

used in positioning sensor networks using potential

fields (Howard, 2002). The immune network module

performs an algorithm that can be described by the

following steps:

Creation: Creation of an initial set of B cells to

form a network.

Evaluation: Determination of the B cells affinity

to calculate their stimulation.

Pruning: Performs the resource management and

remove cells that are without resources from the

network.

Selection: Selects the more stimulated B cells to

be cloned.

Cloning: Generates a set of clones from the most

stimulated B cells.

Mutation: Does the mutation of cloned cells.

In the stage of creation, an initial set of routers is

randomly generated to initiate the process of

obtaining the network, and the user can specify how

many routers to place it initially. In the evaluation

ICEIS2014-16thInternationalConferenceonEnterpriseInformationSystems

418

phase, a network which is represented by a graph is

formed with sensor nodes and router nodes. From

this graph, values of several variables are obtained

that will be used to calculate the affinity. Examples

of such variables are the number of paths that exist

between each sensor and the gateway, the number of

times that a router is used on the formed paths, etc.

It should be stressed that the affinity value is

calculated for each router and comprises three parts.

The first part provides the degree of fault of each

network router - this affinity is the most important of

all. It defines the value or importance each router

has in the network configuration. This is done as

follows: a router is removed from the network, and

the number of paths that remain active for the

sensors send information for the gateway is

evaluated. If the number of active paths remaining

after the node removal is small, the router node

needs another nearby router to reduce their degree of

fault. Furthermore, if the node suffers battery

discharge or hardware problems, other paths to relay

information should be guaranteed until the problem

is solved. The second part relates to the number of

times that each router is used in paths that relay the

information from the sensors to the gateway. The

greater the number of times it is used, more

important is that router. The third part relates the

number of sensor nodes neighboring to each router –

one can say that the more sensor nodes neighbors,

the greater the likelihood that it will become part of

the way that the sensor needs to transmit your

message to the gateway.

4 RESULTS AND CONCLUSIONS

Case studies were simulated in a 1 x 1 square

scenario. The cloning procedure considered that only

the router with higher affinity would be selected to

produce three clones in each generation. For each

case study 10 experiments were conducted that

demonstrate the algorithm’s ability to create at least

two redundant paths to get the information from any

sensor to the gateway. Two configurations were

considered to demonstrate the functionality of the

developed algorithm. The configurations used in the

simulation were motivated by oil & gas refinery

automation applications. The first one called POSA

consists of five network nodes, where node 1 is the

gateway and nodes 2, 3, 4 and 5 are fixed sensors.

The gateway has direct line of sight with all the

network nodes as shown in Figure 2. The second

scenario (POSB) considers a network with nine

nodes, where node one is the gateway and the others

are fixed sensors. As in scenario POSA, POSB has

direct line of sight with all the network nodes as

shown in Figure 3. For both configurations it will be

considered that there is no connectivity among them,

i.e. the distance between them will be greater than

their operating range.

Figure 2: Sensors and gateway POSA configuration.

(Legend: node 1:gateway; nodes 2 to 5: sensors).

Figure 3: Sensors and gateway POSB configuration.

(Legend: node 1:gateway; nodes 2 to 9 :sensors).

For the case study simulations considered, the goal

is to get any two paths for each sensor to transmit

the monitored sensor data to the gateway node. The

operating range for both cases is 0.2, i.e. for both

configurations there is no connectivity between any

sensor and the gateway. Table 1 describes the

parameters used in the case study 1. After

completion of ten experiments, the best network

configuration can be seen in figure 4, and the

consolidations of the tests are shown in table 2.

Figure 4 also shows that one of the paths from

sensor node 3 to the gateway shows three jumps (3-

7-8-1) i.e. the information had to be relayed by two

routers to reach the gateway node. Regarding the

degree of fault, all eight routers have 20 % degree of

fault tolerance. This means that 80 % of the paths

RouterNodesPositioningforWirelessNetworksUsingArtificialImmuneSystems

419

from the sensors to the gateway continue to exist

even after the removal of a node. With respect to the

maximum number of routers used in terms of paths,

the router node 8 is used twice in the paths 3-8-1 and

3-7-8-1. Consequently, this router will have a greater

battery consumption than the others, which could

make it stop working and be disconnected from the

network. But even if that happens, there will still be

a path (3-7-10-1) for node 3 to communicate to the

gateway.

Table 1: Case study 1 – POSA configuration parameters.

Simulation Parameters Values Method

Number of generations 50 -

Initial number of Routers 10 -

Affinity - Fault Degree

Table 2: Network performance for case study 1.

Network

Min. Av. Max. St. Dev.

No. of nodes 13 13,7 15 0,67

No. of routers 8 8,7 10 0,67

No. of critical sensors 0 0 0 -

No. a router is used 1 2,1 3 0,57

Case study 2 considers configuration POSB for the

sensors and gateway. Table 3 shows the parameters

used in the case study 2 simulation. The goal is still

obtain at least two paths for each sensor and gateway

but now the affinity criteria consider fault degree,

number of times a router is used and number of

neighbor sensors. After ten experiments the best

network configuration is shown in figure 5 and the

network performance is seen in table 4. Table 4

indicates that even using a low number of initial

routers the algorithm was able to reach a positioning

result meeting the goals and avoided again critical

nodes. Figure 5 also shows that node 3 in the path 3-

15-17-13-1 features four hops to the gateway. That

means that the information sent by these devices will

be delayed when received by the gateway node,

since it will need to be relayed through three

intermediate nodes. Regarding to the degree of fault,

the intermediate node 22 has 22 % degree of fault,

and all the other routers we have an index less than

22 %. Thus if node 22 is lost for device failure or

end of battery results that information sent by sensor

5 will not reach the gateway. Regarding to the

maximum number of routers used in terms of paths ,

router nodes 10 and 13 are used three times in the

paths 3-15-17-13-1 , 3-26-13-1 , 4-13-1 , 9 -18-12-

10-1, 9-24-10-1 and 2-11-10-1 .That means that

these devices will have their lifetime reduced

Figure 4: Node positioning for case study 1 in POSA

configuration.

Table 3: Case study 2 – POSA configuration parameters.

Simulation

Parameters

Values Method

Number of

generations

Initial number of

Routers

Affinity -

Failure Degree, No. of

times a router is used and

No. of neighbor sensors

Table 4: Network performance for case study 2.

Network

Min. Av. Max. St. Dev.

No. of nodes 23 25,3 28 1,49

No. of routers 14 16,3 19 1,49

No. of critical sensors 0 0 0 -

No. a router is used 3 3,7 5 0,67

Figure 5: Node positioning for case study 1 in POSB

configuration.

because their high levels of retransmission. As far as

the number of sensors to neighboring routers is

ICEIS2014-16thInternationalConferenceonEnterpriseInformationSystems

420

concerned, routers 15, 19, 22 and 26 can relay the

data sent by two sensors, and the sensors are also

used with relays. This makes these sensors and

routers consume more power, and as a result, battery

runs out sooner.

This paper proposed a positioning algorithm for

router nodes in wireless network using immune

systems techniques. The algorithm creates redundant

paths to the data collected by the sensors to be sent

to the gateway by any two or more paths, meeting

the criteria of degree of failure, the number of

retransmission by routers and number of sensors to

neighbouring routers. The algorithm allows each

criterion is enabled at a time or that they be

combined with weights. Comparison between the

results obtained in this paper and those known from

the literature are not straightforward to produce

since their criteria were not the same as ours. Our

criteria considered as a top priority the fault tolerant

aspect guaranteeing, for instance, in the case studies

presented, at least two paths to the gateway for each

sensor node. The affinity function, which works as

an objective function, is multi-objective so several

other objectives could be jointly considered.

Another alternative could be to use some sort of

workbench problem and try to compare other

methods with ours, but the definition of a suitable

workbench problem has issues which are difficult to

deal with.

REFERENCES

Zheng, J., and Lee, M. J., 2006. A Comprehensive

Performance Study of IEEE 802.15.4. Sensor Network

Operations, IEEE Press, Wiley InterScience, Chapter

4, pp. 218-237.

Costa, M. S., Amaral, J. L.M., 2010. A tool for node

positioning analysis in wireless networks for industrial

automation. In XVIII Automation Brazilian Congress.

Bonito, pp. 1521-1527, in portuguese.

Moyne, J. R. and Tilbury, D. M., 2007. The Emergence of

Industrial Control, Diagnostics, and Safety Data.

Proceedings of the IEEE, 95(1), pp. 29-47.

Cannons, J., Milstein, L. B., Zeger, K., 2008. An

Algorithm for Wireless Relay Placement. IEEE

Transactions on Wireless Communications.USA.

Nov.2006. vol.8, n°11, pp. 5564-5574.

Coelho, P. H. G., Amaral, J. L. M., Amaral, J. F. M.,

Barreira, L.F.A. and, Barros, A. V., 2013. Deploying

Nodes for Industrial Wireless Networks by Artificial

Immune Systems Techniques. In 15

International

Conference on Enterprise Information Systems,

Angers, France.

Gersho, A., Gray, R. M., 1992. Vector Quantization and

Signal Compression. Norwell, MA. Kluwer Academic

Publishers.

Hoffert, J., Klues, K., and Orjih, O., 2007. Configuring the

IEEE 802.15.4 MAC Layer for Single-sink Wireless

Sensor Network Applications, Technical Report

http://www.dre.vanderbilt.edu/~jhoffert/802_15_4_Ev

al_Report.pdf.

Youssef, W., and Younis, M., 2007. Intelligent Gateways

Placement for Reduced Data Latency in Wireless

Sensor Networks. In ICC’07 International Conference

on Communications, Glasgow, pp.3805-3810.

Molina, G., Alba, E., and Talbi, E. G., 2008. Optimal

Sensor Network Layout Using MultiObjective

Metaheuristics. Journal of Universal Computer

Science, Vol.15, No. 15, pp.2549-2565.

Coelho, P. H. G., Amaral, J. L. M. and Amaral, J. F. M.,

2012. Node Positioning in Industrial Plants Wireless

Networks. In WES’12 International Conference on

Communications, Rio Grande, R.S., in portuguese.

Shi, Y. , Jia,F., Hai-Tao, Y., 2009. An Improved Router

Placement Algorithm Base on Energy Efficient

Strategy for Wireless Network. In ISECS International

Colloquium on Computing, Communication, Control

and Management (CCCM2009), pp. 421- 423.

Silva, L. N. C., 2001. Immune Engineering: Development

and Application of Computational Tools Inspired by

Artificial Immune Systems, Ph. D. Thesis, State

University of Campinas, Campinas, in portuguese.

Amaral, J. L. M., 2006. Artificial Immune Systems Applied

to Fault Detection, Ph. D. Thesis, Pontifical Catholic

University of Rio de Janeiro, Rio de Janeiro, in

portuguese.

Jerne, N. K., 1974. Towards a Network Theory of the

Immune System. Ann. Immunol. (Inst. Pasteur), 125C,

pp. 373-389.

Howard, A., Mataric, M. J., and Sukhatme, G. S., 2002.

Mobile Sensor Network Deployment using Potential

Fields: A Distributed, Scalable Solution to the Area

Coverage Problem heuristics. In DARS’02, 6th

International Symposium on Distributed Autonomous

Robotics Systems, Fukuoka, Japan.

Poduri, S., Pattem, S., Krishnamachari, B.; Sukhatme, G.,

2006. Controlled Deployments of Sensor Networks.

In Press.

Howard, A., Mataric, M. J., Sukhatme, G. S., 2002.

Mobile Sensor Network Deployment using Potential

Fields: A Distributed, Scalable Solution to the Area

Coverage Problem. Proceedings of the 6th

International Symposium on Distributed Autonomous

Robotics Systems (DARS02), Fukuoka, Japan, pp. 299-

308.

Timmis, J., and Neal, M. , 2001. A Resource Limited

Artificial Immune System for Data Analysis.

Knowledge Based Systems, Vol.3-4, No. 14, pp.121-

130.

Neal, M., 2002. An Artificial Immune System for

Continuous Analysis of Time-Varying Data. In 1

ICARIS.

RouterNodesPositioningforWirelessNetworksUsingArtificialImmuneSystems

421