Proceeding of the 2011 IEEE Students' Technology Symposium

14-16 January, 2011, IIT Kharagpur

EER: Energy Efficient Routing in Wireless Sensor

Networks Indrajit Banerjee#, Prasenjit Chanak

*, Biplab Kumar Sikdar$, Hafizur Rahaman#

"Department of Information Technology, $ Department of Computer Science, *Purabi Das School of Information Technology

Bengal Engineering and Science University, Shibpur, Howrah, India. Email: ibanerjee@it.becs.ac.in, prasenjit.chanak@gmail.com

bipla@cs.becs.ac.in, rahaman_h@it.becs.ac.in

Abstract-Sensor Networks are usually large collections of

sensing nodes. The main constrain of sensor network is that the

sensor nodes have constant power source. They cannot be

recharged or replaced once deployed. Topological control is a

popular technique for energy conservation in sensor networks.

Therefore, numbers of cluster base energy conservation

technique are defined previously. In cluster base technique, main

problems are proper data aggregation and a large amount of

energy wastage to make cluster. In this paper we study the

problem of efficient data propagation with proper data

aggregation model in wireless sensor networks. The EER

(Energy Efficient Routing in Wireless Sensor Network)

technique define optimal size of clusters where data are

aggregated properly and data routing occurs in energy efficient

way. In EER, clusters are generated with the help of L-system

CA scheme. Data routing path is also decided by L-system CA scheme. The simulation result depicts that life time of the nodes

increases with respect to other existing energy conservation

techniques.

I. INTRODUCTION

wireless sensor network comprises of a large amount of A distributed sensors and processing networks. In WSN each node is capable of sensing an event, actuating the

data, computing the results and communicating with other nodes using multi-hop communication [1]. In proposed scheme each sensor node has a common structure. This is called homogeneous wireless sensor network [2]. In wireless sensor network, it is almost impossible to change or recharge batteries attached with the sensor nodes, since sensor nodes are usually small sized and are distributed in a large inaccessible area [3]. Therefore, various types of energy­conservation techniques have been proposed, for example Simulating Large Wireless Sensor Networks Using Cellular Automata [4], Cellular Automata Based Method for Energy Conservation Solution in Wireless Sensor Network [5], An Energy Efficient monitoring of Ad-Hoc Sensor Network with Cellular Automata [6], LEACH [7], UCCP (A Unified clustering and Communication Protocol for Wireless Sensor Network [8], EECS(An Energy Efficient Clustering Scheme in Wireless Sensor Network) [9].

The main objective of our paper is to maximize the life time of the sensor nodes using topological control. The energy consumption of sensor node can be minimised by converting number of sensor nodes to the stand-by mode and other to

active mode. The change of state (active/stand-by) is done with the help of cellular automata (CA). The active nodes make clusters with the help of L-system CA scheme without any message/signal passing. The effective routing is most important for energy saving of sensor network otherwise large travel path exhausts more energy [10]. The energy efficient routing (EER) scheme also generates a short routing path between cluster head and base station for effective data transmission to base station. The proposed technique selects the active node in such a way that the whole network is covered without any overlapping of coverage area. EER focuses on the achieving a longer lifetime of the network by reducing the number of active node and by reducing the transmission distance of the sensor nodes with the help of efficient routing technique.

This paper is arranged as follows. Section II gives preliminary concept of cellular automata (CA) and L-system. Section III gives the motivation of network model and also discussing the proposed L-system cellular automata. Section IV describe mathematical energy consumption model and in Section V we have introduced our EER algorithms. In Section VI we have compared the results between EER and other energy saving algorithms. Finally, the section VII concludes the paper.

II. CELLULAR AUTOMATA

In cellular automata cells are changing their states according to the condition of the neighbouring cells [6] and [11]. If any cells present in active state they go to stand-by state according to their neighbouring cells' condition. The Greenberg-Hastings Model (GHM) is perhaps the simplest CA prototype. The GHM is a family of multi-type cellular automata that emulate excitable media, exhibiting the nucleation and spiral formation characteristic of such complex systems. The Greenberg-Hasting Model is briefly described below. A. Greenberg- Hasting Model in Z2

The Greenberg-Hasting Model describes cellular automata that emulates on excitable medium [12] and [13]. In GHM model every cells change their states according to their neighbouring cells. Cells in GHM are changing their states according to given rules [19].

l. If Pt(x) = i > 0, then Pt+1(x) = i + 1 mod k.

TS 11 COMS02128 978-1-4244-8943-5/11/$26.00 ©2011 IEEE 92

2. If Pt(x) = 0 and at least e neighbours are in state 1, then Pt+1 (x) = 1 ; otherwise, there is no change in statePt+1(x) = O.

According to this rule nodes are generating a spiral cell pattern. But in the L-system cellular automata we have modified the Greenberg-Hasting Model, where the cells are changing their states according to L-system concept. The L­system cellular automata produce tree type cells pattern. B. L-system.

Lindenmayer (In 1968) first proposed a new type of grammar where every rule is applied simultaneously, rather than the other grammar where one rule is applied at a time. This type grammar also called L-system [14]. The main difference of L-system from Chomsky grammars production [15] is it applied sequentially, whereas in L-system they are applied in parallel and simultaneously replacing all letter in an initial given word. In L-system initial string is called axiom which is changed according to some given production rules and the initial axiom produce a new string after some derivation. We are designing here the L-system cellular automata with the help of Greenberg-Hasting model and L­system concept which is described in section III. With the help of L-system cellular automata we have divided the nodes of entire network into some clusters without any message passing.

III. MOTIVA nON

The load of cluster heads is affected by the number of cluster member nodes and the load of communication between the cluster heads. On the basis of load on cluster head we are calculating the effective cluster size. In each cluster sensor nodes are arranged into a tree pattern with the help of L­system cellular automata. The data of cluster members are routed through the tree path in an energy efficient manner. The EER technique also saves the routing energy with the help of data aggregation.

Cluster Size

2500

"C " 2000 :J

l: .!: 1500 � .. "C 0 1000 "

'0 :S 500

0

0% 10% 20% 30% 40% 50% 60%

Numberof cluster members nodes

Fig.1 Cluster head life span with respect to cluster head load.

A. Cluster formation with minimum load

Load of the cluster head affects the rate of energy loss in cluster head. Another reason of energy loss is high transmission range of the cluster heads. In EER technique, transmission range of the cluster heads are reduced by

TSllCOMS02128

Proceeding of the 2011 IEEE Students' Technology Symposium 14-16 January, 2011, IIT Kharagpur

formation of a tree structure with the help of L-system CA. On the other hand a minimum data transmission path is also identified between cluster member nodes and cluster head within a cluster. Load of the cluster head is defined by, fmax

(1) LCluster -load = 1 (Oa + Tt + flt)dt Where Oa represent transmission energy loss. The Tt represent data aggregation energy loss and flt denoted the receiving energy loss by the cluster head. The cluster head load depends on three factors. With the help of equation number I, we are calculating the load on a cluster. The experimental results show that if 15% nodes of the network of size 1800 (active nodes) will form a cluster then the energy loss is minimal (Fig. 1). Within a cluster the nodes are then arranged in tree structure by the L-system CA. In EER technique every cluster member node is arranged in a sub-tree and all the sub-tree form a global tree which can perform efficient data routing. The global tree defines the shortest route of data transmission for each cluster head.

1+1

3 neighbors CA

• 5 neighbors CA

9 neighbors CA

Fig.2. 20 cellular automata neighbour cell structure.

B. L-system Cellular Automata

In L-system cellular automata a new type of cells pattern is generated according to some production rules. In L-system cellular automata any 0 (stand-by) state cell change its state according to nine neighbouring cells state (Fig. 2).

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10

Fig.3. L-System CA implementation

At initial condition in L-system cellular automata some random positions of cells are chosen as active state this is called Axiom. The cells are changing their states according to

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the nine neighbours' condition. The pattern is starting to generate from axiom and after time t all nodes are arranged in tree type pattern. Node states are changing according to rules as defined below.

1. It(x) = i > 0, Then It+1(x) = i + 1 = i = k - 1, Then It+l(X) = 0

2. It(x) = 0 check its own nine neighbours condition if at list 8number nodes are in active state then change their state It+l = 1; otherwise there is no change in state : It+l = o.

Where It (x) represent the cell condition at time t and It+1(x) represent the cell condition at time t+ I. The number of states are {O, l... k-I} and any intermediate position i= {l . . . k-I}. In L-system cellular automata tree patterns are generated according to the initial axiom condition (Fig.3).

Algorithm 1: L-system Cellular Automata

FOR i = I: nil n is the number of repetition AXIOMINCELLS = cellstr (AXIOM); FOR j = I: K II K Number of rule check

II Neighbours cells state value calculation Sum (x, y) = cells(x, y-l) +cells(x, y+l) +cells(x-I, y)

+cells(x+ 1 ,y)+cell(x-l ,y-l )+cells(x-l ,y+ 1) +cells(x+l, y-l) +cells(x+l, y+I);

II Active Neighbours cells check IF (Sum>=Threshold)

I I Initial condition to start to state change M = strafing (AXIOM, rule G).vorher); IF (length (M) >= I)

FOR k =M AXIOMINCELLS {k} = rule G).danach;

END FOR END IF

END FOR II when no cell is active in initial condition

AXIOM = NULL; FOR j = I: length (AXIOMINCELLS)

AXIOM = [AXIOM, AXIOMINCELLS {j}]; END FOR

END FOR

The L-system cellular automata are running in every sensor node which has prior knowledge of its neighbour; arrange the sensor nodes into tree structure without any message or signal passing. In EER technique, nodes are randomly changing their states from active to stand-by state by following Algorithm I.

IV. FORMULATION

This section initially deals with the network modelling approach in sensor network for wireless communication. Then we propose an efficient data aggregation model for every cluster head in sensor network. An energy efficient data communication model for wireless sensor network is discussed next and finally the data collection model is discussed.

TS 11 COMS02128

Proceeding of the 2011 IEEE Students' Technology Symposium

14-16 January, 2011, IIT Kharagpur

A. Sensor Network model

Our main target is very fast data gathering in energy efficient wireless sensor network model. A large number of sensor nodes are deployed in monitoring environment. Sensor nodes are communicated to base station and between each other by multi-hop communication with the help of L-system cellular automata. The nodes are arranged in tree structure. Every sensor node has two states - active and stand-by state. In active state, sensor nodes are sensing and transmitting data but in stand-by state, sensor nodes are not able to sense or transmit data. Periodically the nodes are checking their neighbouring nodes condition and according to L-system cellular automata they are changing their states. The L-system cellular automata generate a tree type nodes pattern shown in FigA. The main sub-trees act as a cluster. The root of the sub­tree is acting as cluster head. In a cluster every node is communicating with their upper level node (Fig. 5). In this way cluster member node's data are routed to the cluster head and cluster head's data is routed to the base station. In this model cluster member nodes transmit their data with minimum energy loss because transmission range of node is very low and receiving energy of the node is also minimal. The EER model organizes overlapping of sensing region problem, which means one node's sensing region are not overlapped with other node's sensing region. The overlapping nodes are changing their states to stand-by state with the help of L-system cellular automata scheme. In EER model data are aggregated by the active nodes. Therefore, a large amount of routing energy is saved by the nodes due to relatively small amount of data transmission.

Base Station Dedicated node for Routing

���������

......

Cluster Member nodes

Fig.4. Tree base clustering and routing in EER model

B. Data Aggregation Model

Data aggregation is significant for cluster based topological network management. In sensor network large amount of energy are lost for same data transmission in sensor network. With the help of data aggregation, we discard the draining of extra energy of sensor nodes due to transmission of same data. Aggregation accuracy depends on the number of cluster member nodes. If cluster size is large then the error in data aggregation is very high. On the other hand, if cluster area is small then there is no meaning of aggregation or clustering. In EER technique the effective size of cluster is established

94

where data is aggregated properly by the cluster head and cluster member nodes.

Level 0

Level I

Level 2

Level 3

Leafnodes Level 4

Fig.5. Sub-tree of cluster member nodes.

Different types of algorithms are available for data aggregation [16], [17] and [18]. Data correlation based algorithms are more popular. We have used data correlation based algorithm for aggregation. We have considered the sub­tree (Fig. 5) content v s numbers of nodes in ith level, i= 1... k. The length of the message in the t level node is

P; = L{-l L; (2) Li is the single message size, which is sent by one cluster member nodes and k is the highest level of the sub-tree. When all message come into cluster head of the tree, then aggregated message size is Pi. This is represented by the following formula

P; = r L7(P; + C) (3) Here i represent the number of level in a sub-tree. The C corresponds to the overhead of aggregation and r is compression ratio, which is always less than one. At level k the compression ratio is zero because all nodes of that level are leaf nodes. C. Data communication model.

The energy consumption by each node for single message transmission is represented by the linear equation

E(d;) = (at + adyn)L; (4) Where at is the energy loss per bit by the transmitter electronics circuit, and ad is the dissipated energy in the transmitter op-amp. Transmission range is y. The parameter n is power index for the channel path loss of the antenna. Li message size which is transmitted by each sensor nodes.

Receiving energy loss of each node is represented by the following formula

E(dr) = (arL;) (5) Where, ar is energy per bit which is consumed by the receiver's electronics circuit used by the node. Li message size which is received by each sensor node. D. Data collection by the cluster head

The cluster base data collection model is divided in two parts; cluster head coJlect data from the cluster member node that is sub-tree root which collects data from child nodes. Other is the cluster head which communicates to other cluster heads for data delivery to base station. The sub-tree data collection cost is Tsub -tree (cost). This is defined by following equation.

Tsub-tree (cost) = f E(d;) dt + f. E(dr)dt niE Tsub -tree n[ETsub -tree

TSllCOMS02128

Proceeding of the 2011 IEEE Students' Technology Symposium

14-16 January, 2011, IIT Kharagpur

The sub-tree data collection costs are depending on two things, receiving energy loss and transmission energy loss. The ni is number of nodes present in the upper level of the tree.

When each cluster head are routing their data through routing path then the energy loss by the root node of global tree is denoted by Ttree (cost).} this is defined by the following equation.

Ttree (cost) = f E(d;)dt + f E(dr)dt eiETtree eifTtree

= 1 (0'; (at + adyn))dt + L (ero';)dt eiETtree eLETtree

(7) Where 0'; is the message size received by the root of the

global tree T or transmitting message size of the root of sub­tree. Hence total energy loss by the network is

Ttotal = Tsub -tree (cost) + Ttree (cost) (8)

V. PROPOSED EER ApPROACH

This section describes our proposed L-system cellular automata based energy efficient routing scheme, referred to as the EER. First we determine the cluster size on the bases of cluster head load and generate clusters with the help of L­system cellular automata. A. EER Algorithms.

In EER model the cluster size is calculated depending upon the cluster load as defined in equation number 1. The sensor nodes are arranged according to the L-system CA scheme. The L-system CA scheme makes a tree likes nodes pattern. This tree is divided into some branches and these branches act as a cluster. All clusters have a cluster head and cluster member nodes. Within a cluster, cluster head collect data from cluster member nodes.

According to the network model which is described in the section IV. The sensor nodes are deploying in NxN monitoring environment. After deployment nodes are initialised to 0 states. Then some seed nodes are initialised according to the cluster size. The nodes are changing their states according to the L-system cellular automata scheme that is nodes are changing their state according to nine neighbour'S nodes state. The L-system cellular automata scheme arranges the active nodes into a tree type node pattern. After cluster formation every active node sends their data to its upper level active node in the tree. In this way cluster head collects all data and prepares an aggregate data for routing to base station. After data transmission every nodes calculate their remaining energy and continue the L-system cellular automata scheme for state change and transmitting data. B. EER Cluster Formation Algorithm.

In this algorithm the total network is divided in some efficient size clusters with the help of L-system CA scheme. The L-system CA scheme arranges the active nodes in a tree pattern. The clusters are formed with main sub-tree. All sub­trees are routed the data to base station with the help of main tree route. In L-system base clustering model tree structure are generated without any message/signal passing with the help of CA scheme. After cluster formation active nodes transmit and receive aggregated data from other nodes. Algorithm 3

95

calculate the remanning energy of the sensor nodes if nodes energy is less than threshold value then these nodes set as a dead node. The algorithm for cluster formation and nodes energy calculation is described below.

Algorithm 2 EER cluster formation

Initialise all nodes into an NxN array S Cluster Set = Null (empty set) Calculate the nodes energy (from Algorithm 3) WHILE S! = Null DO

Set current cluster (CC) = null Calculate minimum cluster size M Insert M into CC WHILE S! = null DO

IF size M in optimal THEN Break

END IF Divided S in to small part

END WHILE IF node is under covered of at least one node DO

Continue ELSE

Run L-system CA Algorithm 1 END IF

END WHILE

Algorithm 3 EER Nodes Energy Calculation

Calculate all nodes remaining energy IF remaining energy <= threshold THEN

Declare the node as dead ELSE

IF time is zero THEN

ELSE

Nodes are changing their state Set new timer

Timer is redefined END IF

END IF

Algorithm 2 establishes the optimal size cluster and the nodes are generating a tree type node pattern with the help of L-system cellular automata. In whole network active node to node distance are chosen such a way that the coverage areas of sensor nodes are not overlapped to each other. With the help of EER algorithm, we are monitoring whole network with minimum active nodes. Other nodes are in energy saving stand-by state. Algorithm 3 calculates the nodes energy, if the energy of any node is less than or equal to minimum threshold energy, then this node is declared as a dead node. In EER cluster head transmitted their data efficiently into the base station with the help of tree structured routing path. The EER technique defines the path according to the position of the base station. In sensor network nodes are deployed randomly, hence, there is a high chance that the sensing areas of the nodes are overlapped [4]. The EER technique also considers

TS 11 COMS02128

Proceeding of the 2011 IEEE Students' Technology Symposium

14-16 January, 2011, IIT Kharagpur

the sensing region overlapping problem. Sensing region of the sensor nodes are calculated as follows: R = 1 - e-2ar - zare-2ar (9) The r is common sensing range of sensor and a represents the density of the sensor nodes.

VI. PERFORMANCE ANALYSIS

The performance consequences of the EER algorithm is compared with other different well know algorithm like LEACH, UCCP, EECS, Three-phase algorithm and Eemca which are proposed for cluster base energy saving technique and CA base energy saving technique. In order to evaluate the performance of EER, described in Section V, four traditional metrics of WSN have been considered:

Active nodes: nodes that are sensing data from the monitoring environment and receive data from other active nodes and transmit data to other active nodes or to cluster head.

Stand-by nodes: nodes are not sensing any data from environment and not receiving or transmitting any data for a particular time period.

Network lifetime: the time elapsed from the start of simulation until all the nodes run out of energy.

First nodes dead: the first node reaches its threshold energy level.

In this simulation we have considered a 120x120 matrix of distributed sensor nodes. The energy loss in sensor nodes is mainly due to following: transmission loss and receiving energy loss, data aggregation energy losses. The values adopted for MA TLAB simulation are shown in table 1.

Sensor Deployment Area

Number of node

Data Packet Size

Initial Energy

TABLE I

SIMULATION PARAMETERS

a energy loss by transmitter electronics circuit

addissipated energy by transmit op-amp

Data aggregation energy loss

16000

14000

12000 '" w 0 10000 0 z OJ 8000 z ;;

\ \ '\ \ 6000

§ 4000 \ 2000

0

\ \ \

120xl20 14400 800bit

0.5J

50 nJlbit

10 pJlbiti m2

5nJibitimessage

-+-EER

-LEACH

-UCCP

-EECS

o 500 1000 1500 2000 2500 3000

ROUND

Fig.6 Network Life time of sensor network

Fig. 6 describes the network lifetime of a sensor network monitored by EER and the state-of-the-art algorithm. It is shown that the EER is better than other cluster base algorithms UCCP, EECS, LEACH, and HEED [19]. It also points to the fact that the proposed algorithm exhibits 65%

96

better performance than LEATCH [7], 53% better than UCCP [8] and 55% better than that of a similar algorithm EECS [9].

:c .., 0 z � '€ '" '0 0 z

16000

14000

12000

10000

8000

6000 � I

4000 I 2000

0

I

�-------------." ........ o 1000 2000

ROUND

3000

. • .•• . . EER

--Three Phased

Algorithem

- .... -ECCA

--Eemca

Fig.7. Number of Active nodes in the Network

Fig. 7 shows number of active nodes in EER compare to the other similar algorithm like Three-phased algorithms, EECA and An Energy Efficient Monitoring of Ad-hoc Sensor Network with Cellular Automata (Eemca). The graph shown in Fig. 7 establish that in EER technique less numbers of nodes are in active modes compared to Tree-phased algorithm, EECA and Eemca which leads to better battery utilization.

120

100 " .. !!l 80 c 1l � 60

.11 \;

" 10' :v 40 > 0

u 20

0 0

\111 V\

500 1000 1500 2000 2500 3000

ROUND

Fig.8. Coverage of Sensor Network

-EER

-Three-phased

Algorithem

-ECCA

----.- Eemca

The Fig. 8 shows that the EER scheme coverage of the sensor network for more number of rounds than that of other existing similar algorithm. In EER gives about 80% better coverage than Three-phased, ECCA and Eemca algorithm.

VII. CONCLUSION

In this paper, we propose an energy efficient routing technique with the help of L-system cellular automata concept. Our proposed technique EER arranges all sensor nodes in tree structure where every sub trees are making a cluster. The sub tree root is selected as a cluster head. The root node collects data from the child node and aggregates it. The aggregated data are transmitted to the base station in an efficient tree based routing path. In EER technique active nodes numbers are very small compare to the stand-by nodes, they are sufficient for energy efficient data collection, data aggregation and data routing. The simulation results establish that the proposed routing scheme gives better performance.

TS 11 COMS02128

Proceeding of the 2011 IEEE Students' Technology Symposium

14�16 January, 2011, IIT Kharagpur

REFERENCES

[I] Giuseppe Anastasi, Marco Conti, Mario Di Francesco, Andrea Passarella, "Energy Conservation in Wireless Sensor networks: A Survey", Ad Hoc Networks 7 (2009) 537-568

[2] I. Banerjee, H. Rahaman, B. Sikdar, "UDDN: Unidirectional Data Dissemination via Negotiation", IEEE International Conference on Information Networking 2008,23-25 January, Pusan, Korea.

[3] Hui-Ching Hsieh, Jenq-Shiou Leu, Wei-Kuan Shih "A fault­tolerant scheme for an autonomous local wireless sensor network" Computer Standards & Interfaces, Volume 32, Issue 4, June 201 0, Pages21 5-221 .

[4] R.O.Cunha, A'p'Silva, Antonio AF.Loreiro, Linnyer B. Ruiz., "Simulating Large Wireless Sensor Network Using Cellular Automata", In IEEE Proceedings of the 38th Annual Simulation Symposiums (ANSS'05), pp. 31 3-330, April 2005.

[5] S. Adabi, AK.Zadeh, ADana, S.Adabi, "Cellular Automata Based Method for Energy Conservation Solution in Wireless Sensor Network, IEEE, 978-1-4244-2108-4/08, 2008.

[6] I. Banerjee, S Das, B. Sikdar and H. Rahaman: "An Energy Efficient Monitoring of Ad-Hoc Sensor Network with Cellular Automata", IEEE International Conference on System Man and Cybernetics. Oct 8th -1 1 th 2006 Taiwan

[7] W.R.Heinzelman, Anantha Chandrakasan, and H. Balakrishnan, "Energy-Efficient Communication Protocol for Wireless Micro sensor Networks", IEEE International Conference on System SCiences, 2000.

[8] Nauman Aslam, William Phillips and William Robertson, "A Unified Clustering and Communication Protocol for Wireless Sensor Network". IAENG International Journal of Computer SCience, 35:3, IJCS_35_3_01 , 21 August 2008.

[9] M.Ye, C.F. Li, G.H.Chen, and 1.Wu, "EECS: An Energy Efficient Clustering Scheme in Wireless Sensor Network," IEEE Int'l Performance Computing and Communications Conference (IPCCC), pp. 535-540,2005.

[10] H.Long, YLiu, X.Fan, R.P.Dick, H.Yang, "Energy-Efficient Spatially­Adaptive Clustering and Routing in Wireless Sensor Networks", EDAA, 978-3-981080-5-5/DATE09,2009.

[II] I. Banerjee, S. Das, H rahaman, B. Sikdar, "CA Based Node Management Scheme: An Energy Efficient Approach", The 3rd IEEE International Conference on Wireless Communications, Networking and Mobile Computing. Shanghai, China, 21 -23 Sep 2007.

[1 2] 1. Greenberg and Hasting. "Spatial patterns for discrete models diffusion in excitable media" SIAM Journal of Applied Mathematics. 34:515.523.1978.

[13] R.Fisch, J. Gravner, and D. Griffeath. "Metastability in the Greenberg­hasting model", The Annals of Applied probability, 3(4):935-967, 1 993.

[14] A Stauffer, M.Sipper: "On the relationship between cellular automata and L-systems: The self-replication case", Physica D 1 1 6, p.71-80, 1 998.

[1 5] Curtis R. Cook, Patric shen-pei wang "A Chomsky hierarchy of isotonic array grammars and languages" Computer graphics and image proceSSing, Volume 3, Issuel, August 1 978.

[1 6] Lan Tien Nguyen, Xavier Defago, Razvan Beuran, Yoichi Shinoda, "An Energy Efficient Routing Scheme for Mobile Wireless Sensor Networks", IEEE , 2008.

[1 7] S. Lee, J. Lee, H.Sin, S.Yoo, S. Lee, 1.Lee, Y Lee, S. Kim, "An Energy Distributed Unequal Clustering Protocol for Wireless Sensor Networks", World Academy of Science Engineering And Technology 48,2008.

[1 8] Wei Ye, John Heidemann, Deborah Estrin, "Medium Access Control with Coordinated Adaptive Selling for Wireless Sensor Network" IEEE Transation on Networking, 2004.

[1 9] O. Younis, S. Fahmy, "Distributed clustering in ad hoc sensor network: a hybrit energy-efficient approach", IEEE transitions on Mobile Computing 3 (4) (2004).

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