IMPACT OF HETEROGENEITY ON THE NETWORK LIFETIME OF A WIRELESS SENSOR NETWORK Maninder Pal Kaur1
IMPACT OF HETEROGENEITY ON THE NETWORK LIFETIME OF A WIRELESS SENSOR NETWORK
Maninder Pal Kaur1, Gaurav Bathla2
1Computer Science & IT, Chandigarh University, Gharuan, [email protected]
2Computer Science & IT, Chandigarh University, Gharuan, [email protected]
ABSTRACT
The most challenging issue in the Wireless Sensor Networks is the constraint on the energy level of the sensor nodes. Energy is required by the sensor nodes for their complete functionality. During the transmission of data, energy is utilized for transferring the data packets from the nodes to the central aggregation point i.e. Base Station. Clustering is a key technique used to extend the lifetime of a sensor network by reducing energy consumption. Clustered sensor networks can be classified into two broad types; homogeneous and heterogeneous sensor networks. In homogeneous networks, all the sensor nodes are identical in terms of battery energy and hardware complexity. On the other hand, in a heterogeneous sensor network, two or more different types of nodes with different battery energy and functionality are used. There are two desirable characteristics of a sensor network, viz. lower hardware cost, and uniform energy drainage. While heterogeneous networks achieve the former, the homogeneous networks achieve the latter. In this paper, a novel technique is proposed to measure the impact of heterogeneity of the nodes over the lifetime of the network and compare the performance by comparing with the homogeneous sensor network.
Keywords
Select the significant words of the chapter. The keywords should be separated by commas (Max 6).
INTRODUCTION
The advancements in the technology have led to the development in the field of WSNs. WSNs is now a day considered as the most important area of research. A WSN is said to be composed of a sensor field, where a large number of sensor nodes are deployed for the purpose of collecting the information, and a sink or base station which is either located inside the sensor field or outside it. An increment in the fame of inventions like portable workstations, PDAs, mobile phones, GPS gadgets and other sharp computational creations has been seen in normal life. Late advances in the field of small-scale sensors creations have assisted advances in sensor system field which has at last prompt the development of Wireless Sensor Networks (WSN) 1. The advances in the innovation have speeded up the mass utilization of the sensor nodes, which, notwithstanding their small size, have successful recognizing, taking care of, transmitting and accepting potential 2. The detecting hardware present on these gadgets measures the conditions related to the surroundings evading the sensor nodes and proselytes them to electrical signs. The signals processed further reveals some properties related to the objects that are located in the sensor node’s vicinity 3.
WSNs ordinarily comprise of little, economical, asset con-strained gadgets that communicate among one another utilizing a multi-hop remote communication. Every node of WSN is called as a Sensor Node which contains one sensor, installed processors, restricted memory, low-power radio, and is ordinarily worked with battery. Each SN is in charge of detecting the desired event and for handing-off, a remote event detected by different SNs so that the event detected is accounted for to the destination through BS. As SNs have constrained energy so applications and conventions for WSNs ought to be precisely intended for enhanced utilization of energy for prolonging the system lifetime 4.
Particular capacities, for example, detecting, following, and alarming, can be acquired through collaboration among these nodes. These capacities make remote sensors exceptionally valuable for checking normal phenomena, natural changes, controlling security, assessing activity streams, checking military application, and following cordial strengths in the front lines. These tasks require high reliability of the sensor networks. To make sensor networks more reliable, the attention to research on heterogeneous wireless sensor networks has been increasing in recent past 5.
A sensor network can be made adaptable by grouping the sensor nodes into groups alluded to as clusters. Every cluster in the network has a head node, often referred to as the cluster head (CH) which may be elected either by the sensors in a cluster or pre-assigned by the network designer. The member present in a cluster may be fixed or variable. The concept of cluster-based routing is also utilized to perform energy efficient routing in WSNs. In a hierarchical architecture, higher energy nodes (cluster heads) can be used to process and send the information while low energy nodes can be used to perform the sensing 5.
In the WSNs, the nodes are operated through batteries and these nodes are deployed in the areas where it is difficult or sometimes impossible to replace or recharge these batteries. Without these batteries, the nodes are not able to survive for a long time in the network, which further affects the system lifetime. This is the reason why the power should be controlled in an energy efficient manner such that lesser amount of energy is consumed by the sensor nodes. If the energy consumed is reduced the sensor nodes can survive in the network for a longer period of time 6.
WSNs play an important role in the understanding of the various physical phenomenon occurring in the environment around us. These networks are capable of providing better and more reliable results related to the events happening in our surroundings. Power consumption and energy efficiency are the major and essential considerations of WSNs.
The lifetime of the sensor network relies on various factors such as:
The individual energy capacity of the sensor node.
The topological arrangement of the overall sensor network.
The number of the sensor nodes present in the network.
The techniques used to gather the information in the sensor network.
The total number of processing that is allowed in the network.
The path selected for routing of the gathered information from the sensor nodes to the BS.
Preserving and saving the power with respect to every sensor node in the network can altogether impact the total lifetime of the network. When there is conservation of energy at each node level, so the nodes survive in the network for a longer period of time and as such the lifetime of the network is increased considerably. Due to the energy constrained nature of the sensing devices, usually, a large number of sensor devices are deployed in the sensor field. In order to build an energy efficient sensor network and to enlarge the network lifetime usually two methods are proposed by the researchers:
Global Level: A certain quantity of sensor nodes are used as alternative nodes in place of the dying sensor nodes, such that the process of sensing and signal communication continues and the overall network lifetime is boosted. These sensor nodes are referred to as backup nodes or redundant nodes.
Local Level: By altering the schedule of sensing time, sleep time, communication time for each sensor node.
Homogeneous vs Heterogeneous WSN 4
HETEROGENEOUS MODEL FOR WIRELESS SENSOR NETWORKS
Researchers generally suppose that the nodes in the wireless sensor network are homogeneous in nature i.e each node has all parameters in common like their energy level. But in actual homogeneous networks exists very rarely as homogeneous sensors may have different capabilities such as energy, response time, reduction rate, etc. For this the sensor networks are heterogeneous. In a heterogeneous network, a small fraction of nodes with comparatively high energy than the other nodes perform complex tasks that require a large amount of energy consumption like data fusion, transmission, etc. Heterogeneous networks are becoming popular and can be used for extending the network lifetime as well as reliability 7.
In heterogeneous networks, there are usually two types of nodes i.e. normal nodes and advanced nodes. The normal nodes are inexpensive and constrained in terms of resources as their main task is to sense the data and issue data reports. The advanced nodes are expensive and have more capabilities. The advanced nodes may be powered by the line or they may contain replaceable batteries. The advanced nodes may be configured with high memory capacity and powerful microprocessor. The presence of heterogeneous or advanced nodes in the network can increase the reliability as well as the lifetime of the network 7.
In this section, we will present a paradigm of the heterogeneous wireless sensor network, types of resource heterogeneity and also discuss the impact of heterogeneous resources.
Paradigm Of Heterogeneous Wireless Sensor Network 7
One type of real-time application where heterogeneous sensor networks are used is indoor air monitoring system. In order to ensure an appropriate environment for the growth of the plants, various sensor nodes are deployed in order to sense the prevailing environmental conditions like temperature, humidity, the concentration of various gases as CO2 and O2 in the air etc. Certain actuators are also deployed in order to maintain suitable environmental conditions of temperature and pressure. These actuators regulate the temperature inside as well as outside the greenhouse by opening or closing the valves etc. In order to reduce the cost of installation, the sensors are powered using batteries and they use the wireless channel for their communication purpose. Certain heterogeneous nodes with a high-speed microprocessor, high bandwidth, and long distance transceivers are deployed in the area where charging point or socket is available for the charging of the batteries of the heterogeneous nodes. These nodes provide high-performance data processing as well as longer-term storage.
Types of heterogeneous resources 7
There are basically three types of resource heterogeneity in sensor nodes that are explained below:
Computational heterogeneity: It means that the heterogeneous nodes have comparatively powerful microprocessor and greater memory than the normal nodes. With greater computational resources these nodes provide complex processing of data and long-term data storage.
Link heterogeneity: It means that the heterogeneous nodes have higher bandwidth for data transmission and have high-performance transceivers that can send as well as receive data over longer distances as compared to the normal nodes. It provides consistent data transmission.
Energy heterogeneity: The last yet most important type of resources heterogeneity is energy heterogeneity in which heterogeneous nodes are equipped with replaceable batteries or are line-powered where the sockets are available. This type of heterogeneity is important since both the computational as well as the link heterogeneity will use extra energy sources.
Impact of Heterogeneous Networks7
By deploying a few heterogeneous nodes in the network, the following benefits are provided:
Increased Network Lifetime: The network lifetime is defined as the time interval between the start of the operation of data transmission until the time when the first node in the network becomes dead. In the type of network, all the normal nodes can forward their data to the BS through the nearest advanced node. By using the advanced nodes in the network, the average consumption of energy in order to forward the data from the normal nodes to the BS is comparatively less than that consumed in the homogeneous networks. As the size of the networks increases, the energy usage between the two types of the network becomes bigger.
Reliable Data Transmission: As the nodes in the network are energy constrained in nature, so it may happen that while transmitting the data to the BS they may fall short of energy and this may lead to the loss of data. This causes unreliability. With the deployment of advanced nodes, that has more energy than the normal nodes, in the network the task of transmission is carried out by these nodes. As they have greater energy so there are no chances of loss of data during the transmission. The use of heterogeneous nodes in the network ensures reliability in the transmission of data from the normal nodes to the BS.
2. RELATED WORK
The most customary methodology for the transmission of information and also data from the sensor nodes to the BS was direct transmission approach in which each of the sensor nodes would recognize ; transmit its data to the BS solely. The greater distance of the BS from the nodes further increases the expense of the transfer of data. The nodes drain off their energy faster due to increased transmission cost. This became a shortcoming of direct transmission approach. To overcome this shortcoming in Direct transmission approach, protocols that are based on clustering were proposed.
In these protocols, small groups of nodes were created called as clusters. These clusters consisted of a head node called the cluster head (CH) and other nodes called the member nodes. All the member nodes sense the data from the environment and instead of transmitting the information received by them directly to the BS, they send it to the nearest CH. The CH collects the information from its member nodes and forwards it to the BS. In this way, the expense of transfer of data from the nodes to the BS was considerably reduced. This is because the nodes now spend less energy to transfer their data, as each node sends its data to the nearest CH which is located at very less distance from the node. As less energy is spent to transfer the data that is why the network lifetime is considerably increased as the nodes will survive for a longer period of time in the network. One of the most important clustering based protocols is LEACH.
LEACH is an adaptable group-based protocol that dispenses the load uniformly between the nodes in the network in a random fashion. The main goal of this protocol is to reduce the number of nodes involved in the process of transmission of information from the node level to the BS. For reducing the number of nodes involved, the nodes are grouped into clusters. These clusters consist of a leader node called the CH which is responsible for the actual transfer of information to the BS. The clusters consist of member nodes as well as a head node. The member nodes sense the data from the target area in which they are deployed and send the information to their nearest CH. This CH then forwards the received information from the nodes to the BS which is used there for the decision-making process. Each node takes a turn in becoming the CH. A threshold t(n) is set which is used for the CH selection process:
tn=P1-P*r mod1P , n?GIf a node, from the desired percentage P of nodes that can become CH, wishes to become a CH then it chooses a random number between 0 and 1. If the value of the random number chosen by the node is less than the threshold value, then the node can become the CH in the present round ‘r’ otherwise not. In this way when nodes take a turn to transfer the data from their member nodes to the BS, the load on a single node which was earlier involved in the direct transmission of data is reduced to a great extent. Now each node handles the responsibility of transferring the data from the deployment area to the BS. There are certain disadvantages of LEACH. Firstly the cost of forming the clusters is high. Secondly, some of the CHs transfer the data to the BS placed at a distant location which increases the energy cost of data gathering. In order to overcome these shortcomings of LEACH protocol, a new protocol named PEGASIS was introduced 8.
PEGASIS 9 was introduced as an improvement over LEACH as the key idea in PEGASIS is to connect the sensor nodes using a chain of shortest length. The nodes can construct the chain either themselves using Greedy Algorithm or the BS computes the chain for the nodes and broadcasts the information to the nodes. This protocol follows a token passing approach in which one node that is designated as the leader node passes a small size token starting from the end nodes to transmit the data. This token passes from node to node and in this way gathered information will move from node to node, get fused with the data of the receiving node that possesses the token, and eventually reach a node designated to transfer this fused data to the BS. Information combination is performed at all the nodes except the end nodes. In order to reduce the average energy that each node spends per round, the nodes take a turn in transmitting the data to the BS. This provides an improvement over LEACH as in this protocol just one node transmits the data to the BS instead of several cluster heads per round. This improvement reduces the energy cost for data fusion and transmission.
PEDAP 10 protocol is a further extension of PEGASIS protocol. The PEGASIS protocol connects each of the sensor nodes using a chain with the most limited length while in the PEDAP protocol, each of the sensor nodes are connected to each other through a minimum spanning tree. PEDAP protocol expects that the locations of all the sensor nodes are known by the BS in advance. The route for transferring the information from the nodes to the BS is calculated with the help of Prim’s minimum spanning tree algorithm in which the BS becomes the root of the tree. The base station removes the dead nodes after regular interval of time and again computes the routing information and forwards it to the node which requires it. Thus PEDAP protocol dissipates less energy than the other two protocols. The drawback of PEGASIS is that the nodes which are placed at a large distance from the BS on the chain suffer from an excessive delay in the transfer of their data to the BS 11.
Minimum Spanning Tree Multi-Tier Protocol (MSMTP) 12 protocol separates all the sensor nodes into diverse tiers, as per their distance towards the BS. Each of the sensor nodes advances its detected, amassed information to that neighbor node which is joined with it in MST structure. At this point, a node of the highest rank of the tier closest to the base station starts transmitting the summarized data to the BS. This process continues until the threshold level is maintained. When the energy level of the nodes of the first tier becomes less than the threshold level, then the nodes of the next tier begin sending the summarized information to the BS. Furthermore, when the energy of the last tier goes beneath the edge level then a new threshold is defined. This process of redefining the threshold is repeated until the threshold becomes less than the dead energy of the nodes.
Minimum Spanning based Clustering Tier Technique (MSCT2) 13 is an improvement of MSMTP protocol. An improvement is made in the MSMTP protocol by introducing the concept of clusters within the tiers which will further increase the system lifetime. In this, the cluster heads of the same tier are connected to each other as well as the other tier cluster heads using MST. By using this arrangement lesser number of nodes is used in the transmission of amassed data to the BS.
In TBMSTP protocol, the whole network is segmented into 3 tiers according to the distance of the nodes from the BS. Each tier contains a fixed number of clusters i.e one cluster in Tier 1, two clusters in Tier 2 and 4 clusters in Tier 3. The nodes are allocated tier IDs and cluster IDs at the initial setup stage. Clusters are formed using the Minimum spanning tree (MST) approach. In 12,13 authors proposed a scheme in which, each tier contains clusters and the data was transmitted first between the CHs of the same tier which was connected to each other through a MST and then the data was forwarded to the next tier by the one of the CH of the previous tier. This arrangement increased the load on a single CH that was connected via MST to the next tier, as all the clusters send their data to this cluster head which then forwarded their data to the next tier. In order to improve this situation, it is required that any cluster which wants to send data to the other tier be connected with the other tier directly through MST so that it could transmit its data to the next tier CH nearest to it. In this way, the transmission cost is reduced. This requirement is fulfilled in the proposed work. The protocol is named as Tier Based Minimum Spanning Tree Structured Protocol (TBMSTP).
3. PROBLEM FORMULATION
3.1 Problem Statement
A sensor node in the network can continue to communicate along with the other nodes in the network as long as they have enough energy capacity. In order to maintain the system lifetime, the modulation in the network parameters, such as the number of nodes in the network or power scheduling, is required. In such cases, if there is a need to use the power efficiently then the sensor nodes should be programmed for sensing the event at different time intervals or at the different sample as asked. But the drawback of power scheduling is that if the nodes are programmed to sense the event at a particular time interval, then in some cases the sensor nodes might not transmit any information even if there is some environmental event occurring. This happens because the sensor node may not be in the waken state when the event happened. In order to improve the network lifetime, the concept of heterogeneity in the energy level of the nodes has to be used. This work tries to investigate and analyze a novel technique for increasing the lifetime of a wireless sensor network by introducing the concept of heterogeneity in WSN. Simulation for this respective algorithm is done using MATLAB and compared with the existing approaches to calculate the lifetime of the network.
3.2 Objectives
The main objective of this thesis work is to prolong the lifetime of the network by increasing the survival time of the sensor nodes in the network which can be achieved in the following manner:
To study & analyze the existing routing techniques.
To propose a new energy efficient routing scheme to maximize the lifetime of the sensor network.
To compare the proposed technique with the existing techniques.
Proposed Work
In the proposed work we have partitioned the whole network into three tiers based on the distance of the nodes towards the base station. Each tier contains fixed number of clusters and both normal nodes and advanced nodes having different levels of energy. The nodes are assigned tier IDs and cluster IDs at the initial setup stage. Clusters are formed using the Minimum spanning tree (MST) approach. In the previous work any cluster which wants to send data to the other tier be connected with the other tier directly through MST so that it could transmit its data to the next tier nearest to it. In this way the transmission cost is reduced. This requirement is provided in our proposed work. The protocol is named as Tier Based Minimum Spanning Tree Structured Protocol (TBMSTP)
Energy consumption is the main area of concern in wireless sensor network. As sensor in wireless sensor networks works on battery and have limited energy, therefore they have a limited lifetime. To overcome this issue many protocols have been proposed. Each protocol tries to overcome the issue of limited lifetime of the network by increasing the network lifetime by one way or the other 14. In order to improve the network lifetime a new protocol named Hybrid Tier Based Minimum Spanning Tree Protocol (TBMSTP) with heterogeneous nodes is being proposed which by using the concept of heterogeneity fulfills its purpose of prolonging the stability period of the network. The aim is to transmit the aggregated data to base station with minimum loss of energy which in fact increase system life time in terms of rounds.
METHODOLOGY
START
To study & analyze the existing routing techniques
Setup the Network for deployment of nodes along with pre-requisite parameters by using MATLAB
Partition the network into tiers containing normal as well as advanced nodes
Connecting network nodes via Minimum Spanning Tree (MST) for transmission of data to BS
To analyze & compare the results of the proposed technique with the existing routing schemes
END
Fig 4.1 Methodology Used
4.1 Methodology
Step 1: To study & analyze the existing routing techniques
Various protocols have been proposed in order to fulfill the most important concern of the Wireless Sensor Network i.e the network lifetime which depends the time until the first node in the network is alive. The time from the start to the time when the first node of the network becomes dead due to drain of its energy, the region marks the stability region of the network and thus represents the lifetime of the network. The protocols analyzed are LEACH, PEGASIS, PEDAP, MSMTP, MSCT2 & TBMSTP. Each protocol has advantages as well as limitations. By analyzing the existing techniques, a new protocol named Hybrid Tier Based Minimum Spanning Tree Protocol (TBMSTP) is proposed.
Step 2: Setup the Network for deployment of nodes along with pre-requisite parameters by using MATLAB:
Simulation is done for a wireless sensor network in a field with dimensions 100m × 100m using MATLAB. The total number of sensors n = 100. The nodes are randomly distributed over the field. This means that the horizontal and vertical coordinates of each sensor are randomly selected between 0 and the maximum value of the dimension. The sink is in the center i.e 50mx50m and so, the maximum distance of any node from the sink is approximately 70m. The initial energy of a normal node is set to E = 0.25, 0.5 & 1 Joules. The size of the message that nodes send to their cluster heads as well as the size of the (aggregate) message that a cluster head sends to the sink is set to 2000 bits. In this model, a radio dissipates Eelec = 50 nJ/bit to run the transmitter or receiver circuitry and Eamp = 0.0013 pJ/bit/m2 for the transmitter amplifier. The parameters are given below in the tabular form as:
Table 4.1 Parameters Used
Parameters Value
Electronics energy (Eelec ) 50 nJ/bit
Energy for data aggregation (EDA) 5 nJ/bit/signal
Initial energy of sensor node (Einit ) 0.25J,0.5J, 1J
Communication energy (Efs) 10 pJ/bit/m2
Communication energy (Emp) 0.0013 pJ/bit/m4
Threshold value of distance (d0) 75m
Sensing Area (M x M) 100×100
Number of nodes 100
Base Station 50×50
Network Model 14
The protocol assumes that 100 sensor nodes are distributed randomly in the network area of diameter 100m. In addition to data aggregation, each node of the network has the capability to transmit data to other sensor nodes as well as to BS. The aim is to transmit the aggregated data to base station with minimum loss of energy which in fact increase system life time in terms of rounds. In this work we consider sensor network environment where:
• Each node periodically senses its nearby environment & likes to send this data to BS.
• Base Station is placed at a fix location i.e center of the field.
• Sensor nodes are homogeneous & energy constrained.
• Sensor nodes are stationary & are uniquely identified.
• Data fusion & aggregation is used to reduce the size of message in the network. We assume that combining n packets of size k results in one packet of size k instead of size nk.
Radio Model
Based on energy level used in 8, we have:
ETxl,d=Eelec*l+Efs*l*d2 d? doEelec*l+Eamp*l*d4 d? doWhere l is the number of transmitted bits, Eelec is the energy consumption to run the transmitter or receiver. Eamp or Efs depends on do. In the simulation, a packet length k of 2000 bits is considered.
Step 3: Partition the network into tiers
Hybrid TBMSTP partitions all sensor nodes into three different tiers, according to their distance towards the base station. The system assigns a tier ID and cluster ID to each node during the initialization stage. Those sensor nodes having the same tier ID are treated to be in the same tier. They approximately have the same distance towards the base station, and they consume approximately the same energy to communicate with the base station. Nodes closer to the base station are assigned lower tier IDs.
Each tier contains different number of clusters. We have taken one cluster in the Tier 1, two clusters in Tier 2 and four clusters in Tier 3. The tier partitioning is done in the following manner:
Tier1 = Distance of the node from BS is upto 15m
Tier2= Distance of the nodes from the BS is greater than equal to 15m to less than 35m
Tier3= Distance of the nodes from the BS is greater than 35m
Clusters are formed within the tier where non-cluster head nodes are connected to the CHs with the help of Minimum Spanning Tree (MST).
Step 4: Connecting network nodes via Minimum Spanning Tree (MST) for transmission of data to BS
Prim’s Algorithm is used for the MST construction between the nodes and CHs as well as between CHs of different tiers. A Spanning Tree of a graph is a connected sub graph in which there are no cycles. The Minimum Spanning Tree for a given graph is a Spanning tree of minimum cost for that graph.
Fig 4.2 Minimum Spanning Tree
The MST is created between the node to node as well as CH to other CHs. This concept is called two level MST, one at the level of nodes to the CHs and other between the CHs of different tiers.
Prim’s Algorithm works faster when the number of nodes as well as edges is large. This algorithm starts with a node & spans from one node to another. Weights are assigned to the nodes by calculating the distance between the nodes. Adjacency matrix is formed containing the distance of one from the other nodes in the field. This adjacency matrix is taken as input in the Prim’s algorithm to calculate the minimum weighted spanning tree. The cost of transmitting the data from a node to the base station is calculated through the use of MST. The path constructed by the MST is used for transmission of data to the BS with minimum cost and thereby increasing the stability period of the network.
Fig4.3 Proposed Architecture of TBMSTP
Cluster Head Selection with Heterogeneous Sensor Nodes
In this section, we calculate the probability of electing a sensor as a cluster head in the case of multilevel heterogeneity. Different initial energy levels for different types of sensors are considered as heterogeneity factor. First we derive the probability of electing a sensor as a cluster head with two types of sensors: normal and advance sensors. Assume that there are m advance sensors and n (1-m) normal sensors. The energy of each advance sensors is a times more than the energy of each normal sensor, where a is the energy factor. The total energy of the network is increased by a factor of (1+ a * m). The weight is defined as the ratio of the initial energy of a sensor to the initial energy of normal sensor. The average number of cluster heads from normal sensors equal to popt *n= pnrm *n 1+a*m where pnrm is the weighted election probability for normal sensor and 1+a popt *n= padv *n 1+a*m where padv is the weighted election probability for advanced sensor as given by 16.
4.2.2 Data Transmission
In this TBMSTP, each sensor node forwards its sensed, aggregated data to the CH which is connected to it in MST structure. Then the CH of topmost rank tier will transmit the aggregated data of all nodes of the cluster to the nearest CH in the next tier and finally to the Base Station (BS). CH of tier1 continues to transmit aggregated data to base station until all nodes of tier1 have energy greater than defined threshold level, when all nodes of tier1 have energy below threshold energy then CH of tier2 will transmit data to base station and same procedure will be shifted to nodes of tier3. This procedure is known as TOP TIER SHIFTING 17. When all nodes of tier3 have energy below threshold energy then a new threshold is defined. This procedure is continued until threshold goes below dead energy, at that moment all nodes of network are dead so the network is assumed to be dead.
RESULTS ; DISCUSSION
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SUMMARY OF CHAPTER
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ACKNOWLEDGEMENT
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REFRENCES
Author (s) should cite publications in the text: (Singh, 2006) using the first named author’s name or (Singh and Kumar, 2006) citing both names of two, and (Singh et al., 2006), when there are three or more authors. At the end of the paper a reference list in alphabetical order should be written in following format only:
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