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Wireless Sensor Network, 2010, 2, 538-554 doi:10.4236/wsn.2010.27066 Published Online July 2010 (http://www.SciRP.org/journal/wsn) Copyright © 2010 SciRes. WSN Stable Sensor Network (SSN): A Dynamic Clustering Technique for Maximizing Stability in Wireless Sensor Networks A. B. M. Alim Al Islam1, Chowdhury Sayeed Hyder2, Humayun Kabir3, Mahmuda Naznin3 1Purdue University, West Lafayette, Indiana, USA 2Michigan State University, Michigan, USA 3Bangladesh University of Engineering and Technology, Dhaka, Bangladesh E-mail: razi_bd@yahoo.com, hydercho@msu.edu, mhkabir@cse.buet.ac.bd, mahmudanaznin@cse.buet.ac.bd Received April 26, 2010; revised May 12, 2010; accepted May 15, 2010 Abstract Stability is one of the major concerns in advancement of Wireless Sensor Networks (WSN). A number of applications of WSN require guaranteed sensing, coverage and connectivity throughout its operational period. Death of the first node might cause instability in the network. Therefore, all of the sensor nodes in the net- work must be alive to achieve the goal during that period. One of the major obstacles to ensure these phe- nomena is unbalanced energy consumption rate. Different techniques have already been proposed to improve energy consumption rate such as clustering, efficient routing, and data aggregation. However, most of them do not consider the balanced energy consumption rate which is required to improve network stability. In this paper, we present a novel technique, Stable Sensor Network (SSN) to achieve balanced energy consumption rate using dynamic clustering to guarantee stability in WSN. Our technique is based on LEACH (Low-Energy Adaptive Clustering Hierarchy), which is one of the most widely deployed simple and effec- tive clustering solutions for WSN. We present three heuristics to increase the time before the death of first sensor node in the network. We devise the algorithm of SSN based on those heuristics and also formulate its complete mathematical model. We verify the efficiency of SSN and correctness of the mathematical model by simulation results. Our simulation results show that SSN significantly improves network stability period compared to LEACH and its best variant. Keywords: Network Stability Period, Clustering, Energy Consumption Rate 1. Introduction With the emergence of highly dense fabrication technol- ogy and low production costs, wireless sensor networks (WSN) prove to be useful in myriad of diversified appli- cations. In a typical WSN application, sensor nodes are scattered in a region from where they collect data to achieve certain goals. Data collection may be continuous, periodic or event based process. WSN must be very sta- ble in some of its applications like security monitoring and motion tracking. Death of only one sensor node may disrupt coverage or connectivity and thus may reduce stability in this sort of applications. Therefore, all of the deployed sensor nodes in WSN must be active during operational lifetime. However, sensor nodes are gener- ally equipped with one-time batteries and most of the batteries are of low energy. For this reason, each sensor node must efficiently use its available energy in order to improve the lifetime of WSN. Different techniques are used for efficient usage of this low available energy in a sensor node. Clustering is one of these most well-known techniques. In some related research works, lifetime of WSN is considered as the time required for the last sensor node to die. Some other related research works also consider lifetime of WSN as the time required for half of the de- ployed sensor nodes to die. However, lifetime can be termed as stability period of WSN when it considers the time required for the first sensor node to die. There is an impact of efficient usage of available energy in a sensor node on stability period of WSN. This period is mainly A. B. M. A. A. ISLAM ET AL. 539 controlled by balanced energy consumption rate throug- hout the network. Therefore, we have to ensure balanced use of the available energy throughout the network along with the efficient use of the available energy in a sensor node to assure stability in WSN. In this paper, we pro- pose a novel technique Stable Sensor Network (SSN), which ensures balanced use of the available energy throughout the network. It also achieves the efficient use of the available energy in a sensor node by exploiting clustering technique. Clustering is a technique in which deployed sensor nodes are grouped into some clusters. Only one sensor node is solely responsible to communicate to the base station in a cluster. This sensor node is called cluster head and the remaining sensor nodes in the cluster are called followers. The followers collect data and send it to their corresponding cluster heads. The cluster heads agg- regate its own data with the data received from its fol- lowers. Aggregated data is then sent to a sink to acc- omplish a specific goal. Cluster heads remain closer to their follower sensor nodes compared to the sink. It takes less energy to transmit data to the cluster head instead of the sink, which allows the sensor nodes to conserve more energy and live longer in WSN. There are different clustering techniques already established for ad-hoc networks. However, those techni- ques cannot be directly used in WSN because of the fact that WSN imposes strict requirements on the energy efficiency than that ad-hoc networks do. As a result, many techniques have been proposed for clustering in WSN. Dynamic clustering techniques are more useful for WSN because of the dynamic variation in residual en- ergies of the sensor nodes. LEACH [1] is one of the simple but popular dynamic clustering techniques used in WSN. LEACH rotates cluster headship very effectively among the sensor nodes of a network based only on some locally available information. However, LEACH does not consider the variation in residual energies of the sensor nodes when it selects the cluster heads. There are some already proposed modifications of LEACH to incorporate the variation. We consider this variation in more efficient way in SSN. We also incorporate the bal- anced use of residual energy in the network with the help of some heuristics in SSN. We formulate mathematical model for SSN. We prove that SSN has a significant improvement in network stability over LEACH and its best variant by simulation results. In the next section, we briefly describe some related works. Then, we briefly describe the underlying app- roach of our technique along with its variants in Section 3. We present our novel clustering technique SSN with three heuristics and complete mathematical model in the next section. In Section 5, we evaluate SSN by simula- tion results. In last two sections, we conclude the paper shedding some lights on our future works. 2. Related Works Several techniques have already been proposed to imp- rove network lifetime in WSN. Clustering in one of the widely accepted techniques among them. Clustering is also used in wireless ad-hoc networks, mobile ad-hoc ne- tworks along with sensor networks. Several clustering te- chniques have already been introduced for partitioning nodes in these areas. Some of the early clustering techni- ques are—Hierarchical Clustering [2], Distributed Clu- stering Algorithm (DCA) [3], Spanning Tree (or BFS Tree) based Clustering [4], Clustering with On-Demand Routing [5], Clustering based on Degree or Lowest Iden- tifier Heuristics [6], and Distributed and Energy-Efficient Clustering [7], Adaptive Power-Aware Clustering [8]. Some of the recently developed clustering techniques are PEGASIS (Power-Efficient Gathering in Sensor Inform- ation Systems) [9], Energy Efficient Clustering Routing [10], PEACH (Power Efficient And Adaptive Clustering Hierarchy) [11], Optimal Energy Aware Clustering [12], ACE (Algorithm For Cluster Establishment) [13], HEED (Hybrid Energy-Efficient Distributed Clustering) [14], PADCP (Power Aware Dynamic Clustering Protocol) [15], LEACH (Low- Energy Adaptive Clustering Hierar- chy) [1], SEP (Stable Election Protocol) [16], and LEA- CH with Deterministic Cluster Head Selection [17]. In [9] PEGASIS introduces a near optimal chain-based protocol. Here, each node communicates only with a cl- ose neighbor and takes turns transmitting to the base stat- ion, thus reducing the amount of energy spent per round. It assumes that all nodes have global knowledge of the network and employ the greedy algorithm. It maps the problem of having close neighbors for all nodes to the traveling salesman problem. PEGASIS is a greedy chain protocol that is near optimal for a data-gathering problem in sensor networks. Greedy approach considers the phy- sical distance only, ignoring the capability of a prospec- tive node on the chain. Hence, a node with a shorter dist- ance but less residual energy may be chosen in the chain and may die quickly. In [10] a routing algorithm is proposed which com- bines hierarchical routing and geographical routing. The process of packet forwarding from the source nodes in the target region to the base station consists of two pha- ses—inter-cluster routing and intra-cluster routing. For inter-cluster routing, a greedy algorithm is adopted to fo- rward packets from the cluster heads of the target regions to the base station. For intra-cluster routing, a simple flo- oding is used to flood the packet inside the cluster when the number of intra-cluster nodes is less than a predeter- mined threshold. Otherwise, the recursive geographic forwarding approach is used to disseminate the packet inside target cluster, that is, the cluster head divides the target cluster into some sub-regions, creates the same number of new copies of the query packet, and then diss- eminates these copies to a central node in each sub reg- Copyright © 2010 SciRes. WSN 540 A. B. M. A. A. ISLAM ET AL. ion. Like [9], it uses greedy algorithm based on the dist- ance only but not on the capability or the residual energy. Although it deals with the optimal forwarding approach the criteria to choose the cluster heads optimally is not clearly explained. PEACH [11] is a cluster formation technique based on overheard information from the sensor nodes. Acco- rding to this approach, if a cluster head node becomes an intermediate node of a transmission, it first sets the sink node as its next hop. Then it sets a timer to receive and aggregate multiple packets from the nodes in the cluster set for a pre-specified time. It checks whether the dist- ance between this node and the original destination node is shorter than that of between this node and already sele- cted next hop node. If the distance is shorter, this node joins to the cluster of the original destination node and the next hop of this node is changed to the original des- tination node. PEACH is an adaptive clustering approach for multi-hop inter-cluster communication. However, it suffers from almost the same limitations of PEGASIS due to the choice of physical propinquity. Optimal energy aware clustering [12] solves the ba- lanced k-clustering problem optimally, where k signifies the number of master nodes that can be in the network. The algorithm is based on the minimum weight matching. It optimizes the sum of spatial distances between the me- mber sensor nodes and the master nodes in the whole network. It effectively distributes the network load on all the masters and reduces the communication overhead and the energy dissipation. However, this research work does not consider of residual energy level while choosing a node as the master. Hence, the choice of the master or cluster head is far away from the optimal energy efficient distribution of the cluster heads. ACE [13] is a distributed clustering algorithm which establishes clusters into two phases-spawning and migra- tion. There are several iterations in each phase and the gap between two successive iterations follows uniform distribution. During the spawning phase, new clusters are formed in a self-elective manner. When a node decides to become a cluster head, it will broadcast a message to its neighbors to become its followers. During migration phase, existing clusters are maintained and rearanged, if required. Migration of an existing cluster is controlled by the cluster head. Each cluster head will periodically poll all of its followers to determine which could be the best candidate to elect as a new leader for the cluster. Current cluster head will promote the best candidate as the new cluster head and abdicate itself from its position. ACE results in uniform cluster formation with a packing effi- ciency close to hexagonal close-packing. However, ACE does not consider the residual energy of the nodes while selecting cluster heads. Hence, the clustering is far away from the optimal energy efficient. HEED [14] introduces a distributed algorithm cons- idering the residual energy of sensor nodes. It results in some clusters by uniformly distributing the cluster heads across the network. It periodically selects cluster heads according to a hybrid parameter which consists of a pri- mary parameter, the residual energy of a node, and a secondary parameter, such as propinquity of a node to its neighbors or node degree. HEED converges in O(1) iter- ations using low messaging overhead and achieves fairly uniform cluster head distribution across the network. Ho- wever, it chooses the initial percentage of cluster heads randomly. This random choice remains as a severe limi- tation of this algorithm. PADCP [15] uses several adaptive schemes like dy- namic cluster range, dynamic transmission power and cluster head re-election to form clusters. In this approach, the sensor nodes are assumed to have the same transmis- sion capability and the ability to adjust transmission power in five levels. PADCP has four major phases— neighbor information collection, cluster head election using a cost function, cluster formation using HEED, and cluster head re-election in case of residual energy lower than a pre defined threshold value. The mobility of the sensor nodes is considered in cluster formation. However, it suffers from the same randomly chosen initial probab- ility limitations of HEED as it completely follows HEED algorithm for cluster formation in its third phase. More- over, there is no suggestion about the optimal weights of the cost function used in cluster head selection and the threshold used in cluster head re-election. LEACH [1] introduced a simple mechanism for loc- alized coordination and control for cluster set-up and op- eration. It also introduces the randomized rotation of the cluster heads and the corresponding clusters. However, it does not consider the variation of the initial energy nor the residual energy of sensors during cluster head selec- tion. SEP [16], a LEACH variant, modifies the equation of the threshold. However, it considers two types of nod- es only, normal and advanced, instead of many types that can be encountered in the wireless sensor network after a significant amount of time of operation. Deterministic Cluster Head Selection [17], another variant of LEACH also modifies the threshold to accommodate the hetero- geneity of residual energy based on some heuristics. LE- ACH-C, proposed by the same authors of LEACH in [18], is a centralized technique which selects the cluster heads based on their positions. It considers uniform dist- ribution of the cluster heads based on their positions and the average residual energy in the network. They did not consider the relative residual energy in each sensor node. Adaptive Cluster Head Selection [19], a distributed clus- tering technique based on LEACH, considers the posi- tions but not the relative residual energies of the sensor nodes. There are a number of different research works that maximize network lifetime other than clustering. Lifet- ime is defined in a various ways in those works. In [20], functional lifetime is analyzed solving the linear progra- Copyright © 2010 SciRes. WSN A. B. M. A. A. ISLAM ET AL. 541 ms only for simple and regular network topologies. Fun- ctional lifetime of a sensor network is defined as the ma- ximum number of times a certain data collection task can be performed without the death of any sensor node. In [21], average network lifetime is maximized for a sensor network which is under physical node destruction by deriving deployment plan. In [22], α-lifetime of a wirel- ess sensor network is maximized. α-lifetime is the time duration during which at least α portion of deployed sen- sor area is covered. In [23], a mathematical model is dev- ised for sensor network, where data generation events are spatially and temporally independent. Based on the mo- del, it also introduces a routing protocol for optimal ave- rage lifetime. In [24], a method is introduced using the k-shortest simple path algorithm and a dynamic program- mming method rooted in operational rate-distortion (RD) theory to increase the operational lifetime of a multi-hop 802.15.4 wireless sensor networks. In [25], sensor trees with desired properties are constructed from fusion cen- ter and then these sensor trees are scheduled to maximize network lifetime. It considers network lifetime as the time passed before the death of first node in the network. Load Balancing Protocol (LBP) [26] makes the number of live sensor nodes as large as possible by the enforce- ment of load balancing. Deterministic Energy-Efficient Protocol for Sensing (DEEPS) [27] allows higher energy consumption for sensors with higher total supply and mi- nimizes energy consumption rate for low energy targets. Deterministic Energy-Efficient Protocol for Adjustable Range Sensing (ADEEPS) [28] is an extension of DE- EPS. ADEEPS controls sensing range with the underly- ing approach of DEEPS. In [29], lifetime as time till the death of first node is improved by real time classifier using ART1 neural network model along with co-opera- tive routing. In [30], network lifetime in terms of the death of first sensor node or the first failure of a transmit- ssion in the network is maximized by optimal sensor sch- eduling. It maps the problem to a stochastic shortest-path multi-armed bandit problem and thus chooses the sensor with the largest Gittins index for optimal transmission. In [31], Maximum Lifetime Data Aggregation (MLDA) pr- oblem is solved by selecting the best data aggregation tree using integer programming. It considers lifetime as the time during which information from all the sensors can be gathered to the base station. In [32], a combina- tive measurement is defined based on information utility, communication cost, and energy level. Weights of these factors are self-optimized using autonomic computing. In [33], average lifetime is maximized by reducing energy consumption through the enforcement of disjoint sets of sensor nodes. This approach maps Disjoint Set Cover problem to Maximum Flow Problem and then solves the Maximum Flow Problem by mixed integer programming. In [34], average lifetime is maximized by near optimal routing protocol which performs two shortest path com- putations to route a message. In [35], average lifetime is maximized by optimal routing through the formulation of linear programming problem. It considers both commu- nication energy consumption rates and residual energy levels of two end nodes in the computation of link cost. In [36], lifetime of a fault tolerant sensor network in te- rms of death of first sensor node in the network is maxi- mized by using multipath diversity and erasure codes. SPINDS [37] maximizes lifetime in terms of time till the failure of first Aggregation and Forwarding Node (AFN) in two steps. It formulates joint problem of energy provi- sioning and relay node placement into a mixed-integer nonlinear programming (MINLP) problem. Then it trans- forms MINLP problem into linear programming (LP) problem with maintaining all critical points in the search space. In [38], sensing ranges of sensor nodes are consi- dered as adjustable. It finds maximum number of set co- vers and the sensing ranges of sensor nodes to achieve maximum lifetime in terms of time until BS detects the first failure. MLDR [39] attempts to improve network lifetime based on the death of first sensor node in the network by efficient routing using integer programming. This research work also uses data aggregation. In [40], network lifetime based on the death of first sensor node in the network is improved by distributed optimal routing technique using linear programming and sub-gradient al- gorithm. A number of research works [20,25,29-31,36,39,40] attempts to improve network stability period by various techniques like—routing, scheduling, aggregation etc. However, in this paper we attempt to improve the netw- ork stability period using clustering as it can serve as a better platform for upper layer functionality such as bro- adcasting, aggregation etc. Our novel algorithm SSN ex- ploits the underlying method of LEACH due to its wide acceptability. In experimental analysis, we compare SSN with LEACH and its best variant. For this reason, we de- scribe LEACH and its variants in detail in the following section. 3. Leach LEACH is a self-organizing and adaptive clustering prot- ocol [1]. It dynamically creates clusters in order to distr- ibute the energy load evenly among all of the sensor no- des. This algorithm needs time synchronization. Cluster heads are randomly rotated during each time interval. The resultant cluster heads directly communicate with the base station. 3.1. Mechanism In LEACH, the lifetime of the network is divided into some discrete, disjoint time intervals. Each interval is ag- ain divided into some subintervals or rounds as shown in Copyright © 2010 SciRes. WSN 542 A. B. M. A. A. ISLAM ET AL. Figure 1. Each subinterval begins with an advertisement phase followed by a cluster set up phase. In the adverti- sement phase, each node independently decides whether to become a cluster head or not. In the cluster set-up ph- ase, the clusters are organized based on the decisions made in the advertisement phase. Then a steady-state phase follows. In this phase, the followers, i.e., the sen- sor nodes except cluster heads, will send data to the corr- esponding cluster head. The cluster heads accumulate and compress the received data with its own data. Cluster heads send the compressed data to the base station. In order to minimize cluster establishment overhead, the duration of steady-state phase must be longer than that of cluster set-up phase. At the very beginning of advertisement phase, each node decides whether it wants to become a cluster head for the current round. This decision is based on the sug- gested percentage of cluster heads for the network, which is set a priori. This decision also depends on the number of times the node has already been a cluster head. This decision is made by a node n choosing a random number between 0 and 1. If the number is less than a threshold T(n), the node decides to become a cluster head. The threshold is calculated as follows: otherwise Gnif P rP P nT 0 1 mod1 )( where, P = the percentage of nodes that can become cluster heads (e.g., P = 0.05); 1/P = the number of subintervals in an interval; r = the current subinterval; G = the set of nodes that have not been cluster heads yet in the current interval. Using this threshold, a node can be a cluster head in any one of 1/P subintervals in an interval. At the first su- binterval of an interval (r = 0), each node has a probabil- ity P to become a cluster head. The nodes that are cluster heads in the first subinterval cannot be cluster heads in the next (1/P – 1) subintervals of the same interval. Thus the probability that the remaining nodes are becoming cluster heads is increasing. After the completion of 1/P subintervals, a new interval will start and all the nodes are again eligible to become cluster head. Each node that has chosen itself as a cluster head in the current subinterval, broadcasts an advertisement me- Figure 1. Discrete and disjoint intervals in the whole netw- ork lifetime; discrete and disjoint subintervals in an interval. ssage to the rest of the nodes. The non-cluster-head nodes will choose the cluster to which it will belong in this subinterval. This decision is based on the received signal strength of the advertised message. Assuming symmetric propagation channels, the cluster head whose advertisements have been heard with the largest signal strength will be selected by a non-cluster-head sensor node as its cluster head. In case of a tie, a cluster head is chosen randomly. 3.2. Mathematical Models There are some incomplete mathematical models avai- lable on LEACH. In [18], a mathematical model is prop- osed to compute the total energy dissipation in the sensor network for the transmission of a frame. Taking the deri- vative of the total energy it finds the optimum number of clusters, kopt as: 2 2BS mp fs opt d MN k where, N is the total number of sensor nodes, M is the dimension of the sensor area, dBS is the distance between cluster head and base station, fs and mp are the amp- lifier energies. In [41], a mathematical model is proposed to compute the total energy consumption in the sensor network dur- ing a single round. Taking the derivative of the total ene- rgy it also finds the optimum number of clusters, kopt as: 2 BS mp fs opt d MN k In [42], a mathematical model is proposed to calculate the total energy consumption in the sensor network dur- ing a single round. It also finds the optimum desired clu- ster head probability, popt as: DAelecBSmp fs opt EEd p 4 2 1 where, λ is the intensity of homogeneous spatial Poisson process that indicates the sensor node density, Eelec is the electronic energy required for coding, modulation, filteri- ng etc. and EDA is the energy required for data aggregation. However, the lifetime of a sensor node is directly the inverse of its long run rate or expected rate of energy co- nsumption. Therefore, in order to elongate network life- time, the long run rate of energy consumption must be given more importance than other metrices (for example, energy required to transmit one frame [41] or total ener- gy consumption in an interval [42]). Moreover, none of these models consider the situation in which all the sen- sor nodes in the network can pick a random number hig- her than its respective threshold and become a temporary Copyright © 2010 SciRes. WSN A. B. M. A. A. ISLAM ET AL. 543 follower. In this case, no sensor node will find any other node to choose as its cluster head under which it can ke- ep its follower status. In this circumstance, every node changes its state from follower to cluster head, i.e., all the sensor nodes will become a one-member cluster head. In [43,44], a complete mathematical model is proposed incorporating all these factors. In [48], Heinzelman First Order Radio Model [21] is used as the energy model and Renewal Reward Process [26,48] is used as the underlying stochastic process to calculate long run rate of energy consumption. It defines the following parameters in the model: 1) P be the desired percentage of cluster heads, 2) s be the number of subintervals in an interval, therefore s = 1/P, 3) Ph be the probability of becoming cluster head of a follower node at the start of any subinterval, 4) Ph′ be the probability of becoming cluster head of a cluster head node at the start of a subinterval in the next interval, 5) Φ0 be the probability of becoming cluster head of a sensor node at the start of any subinterval, 6) T(n) be the currently considered threshold value. 7) N be the total number of sensor nodes in the net- work. 8) a × b be the two dimensions of rectangular sensor area. According to Renewal Reward Theorem, the rate of reward will be: XE RE t tR t lim (1) where, R is reward and X is cycle length. It considers the energy consumed by the sensor as the reward and the dif- ference between two consecutive subintervals in which a sensor node becomes cluster head as the cycle. It considers different state transition diagrams for a se- nsor node between two states while changing the subin- terval in an interval and between two states while chang- ing the subinterval as well as the interval to compute E(X). Figure 2 shows those state transition diagrams. Using these state transition diagrams, the probability of becoming a cluster head, Φ0, at the start of any subint- erval is calculated as follows: 01 h h h P P Ps s s (2) After a number of steps, the long run rate of energy consumption is calculated as: 2 0_ lim 1 1 2 t elecamp F Rt ER tEX ab Ek k (a) (b) Figure 2. State transition of a node while (a) Changing sub- interval without changing Interval, (b) Changing subinter- val as well as the interval. 1 0 10 11 , 1 NN ni1 Ni n g npi nn qin (3) where, ab n n N ng nNn 2 100 , BSHampDAelec dkiEEkiip _ )1()()12()( , 00 ,,1, 1 , N ni i Nn n Nn qinhrn hrn i N n and 1 22 1, n aa p ab r p ab r nrh . Here, Eelec is energy required per bit to run the cir- cuitry in transmitter or receiver, E DA is the energy re- quired for data aggregation, amp_F is the energy con- stant for the radio transmission of a follower node, amp_H is the energy constant for the radio transmission of a cluster head node, k is number of bits in a message, λ is the path loss exponent, dBS is the distance between cluster head and base station, and pa is the percentage of the circular area (centered at a follower and with radius equals distance to a cluster head) falls within the sensor area. As we cannot get any closed form for derivative of Equation 3, we can get the optimal percentage of cluster heads by plotting the value of long run rate of energy consumption from the equation. 3.3. Limitations This algorithm introduced a fairly simple strategy whi- Copyright © 2010 SciRes. WSN 544 A. B. M. A. A. ISLAM ET AL. ch is more efficient than the direct transmission and the minimum-transmission-energy (MTE) protocol that cho- oses the route to minimize the transmitter energy. How- ever, it has some limitations: 1) LEACH always wants to achieve an even distribu- tion of energy consumption which might not be rational. Residual energies in different nodes do not remain same after a significant amount of time of operation. Nodes with higher residual energy should get preference to be elected as cluster head. Otherwise, longer network stabil- ity as well as longer network lifetime cannot be ensured. 2) When the number of live nodes becomes small, the number of prospective cluster heads which is equal to the number of live nodes multiplied by desired percentage of heads will also become very small and in some cases it may become less than one. For example, if the initial nu- mber of sensor nodes is 100 and the desired percentage of heads P is 0.05 then the initial number of prospective heads is 100 × 0.05 = 5. However, with the same P when the number of live nodes becomes less than 20 the num- ber of prospective heads will become less than one. Un- der this condition in most of the subintervals, none of the live sensor nodes can become a cluster head by choosing a random number which is less than the current threshold. In other words, there will be no cluster head available to the sensor nodes to which they can become followers. Rather, all the live sensors will force themselves to bec- ome a one member cluster head. In this particular case, the resultant cluster setting will behave like a setting which does not have any clustering. For this reason, no energy efficiency will be gained. A number of variants have already been proposed for LEACH to overcome its limitations. Some of them are briefly summarized in the following section. 3.4. LEACH Variants SEP [16] is variant of LEACH, which elects the clust- er heads based on weighted probabilities according to the residual energy of the sensor nodes. It assumes that a pe- rcentage of the sensor nodes are coming with higher ene- rgy resources and studies the impact of heterogeneity of nodes based on their energy levels. It follows the underl- ying synchronization approach used in LEACH. In addi- tion, it considers the variation in the residual energy as- suming two types of nodes—normal and advanced. It assumes m fractions of the nodes are advanced nodes, which have α times energy than that of the normal nodes. As a result, it assumes n(1 + α m) number of virt- ual normal nodes in the network. It extends the number of subintervals from 1/P to (1 + α m)/P in an interval. The objective of this extension is to elect a normal node once and an advanced node (1 + α) times as the cluster head in an interval. The probability equation to become cluster head has been modified. In fact, two different eq- uations are used for the normal and the advanced nodes. The weighted election probabilities for the normal and the advanced nodes are pnrm and padv respectively. Their equations are as follows: m p popt nrm 1 and, )1( 1 m p popt adv where, popt is the optimal probability of a node to become a cluster head. It also uses two different equations for the threshold. One for the normal nodes called T(snrm) and the other for the advanced nodes called T(sadv). T(snrm) and T(sadv) are calculated as follows: otherwise Gsif p rp p sT nrm nrm nrm nrm nrm 0 1 mod1 )( and, otherwise Gsif p rp p sT adv adv adv adv adv 0 1 mod1 )( where, G' is the set of normal nodes that have not bec- ome cluster head yet within the last 1/pnrm subintervals and G″ is the set of advanced nodes that have not bec- ome cluster head yet within the last 1/p adv subintervals in an interval. This works introduced the heterogeneity to LEACH in terms of two levels of residual energy. However, it has some limitations: In SEP, the percentage of cluster heads is optim- ized based on the energy consumption in an in- terval. However, this value should be optimized on the basis of the long run rate or expected rate of energy consumption for achieving the higher network stability period. SEP considers two types of nodes only in terms of residual energy. However, during the life cy- cle of the network the different levels of the res- idual energies may exist which will not be cove- red by only two types. More types of nodes are necessary to consider covering numerous resid- ual energy levels in different nodes to achieve maximum network stability. It did not attempt any improvement to enhance the network stability. Deterministic Cluster Head Selection [17] introduces the heterogeneity to LEACH in terms of residual energy. It considers the residual energies of the sensor nodes in order to manage rational power consumption throughout the network. It follows the underlying mechanism of LE- ACH exactly. It has changed the equation of the thresh- Copyright © 2010 SciRes. WSN A. B. M. A. A. ISLAM ET AL. 545 old value only to incorporate the residual energy in clus- ter head selection process as follows: max_ _ 1 mod1 )( n currentn new E E P rP P nT where, En_current is the current energy, En_max the initial energy of the node. The other parameters have the same definitions as of LEACH. After a significant amount of time of operation, the re- sidual energies of the sensors would become very low and then this threshold value will be very low. This can result in a situation where all the live sensors are one member cluster head. In this case the energy consump- tion rate will be very high. To break this stuck condition another modified equation of the threshold value has been proposed: _ _max _max () 1 1 mod P 1 1 new n_currentn current s n P Tn Pr E rdiv EPE n E where, rs is the number of consecutive rounds in which a node has not been cluster head. This works introduced the heterogeneity to LEACH in terms of different levels residual energy. However, it has some limitations: Deterministic Cluster Head Selection uses a random value for the percentage of heads pa- rameter like LEACH. Therefore, it does not consider the optimal value of this parameter. It does not suggest any optimum value for rs. It did not attempt any improvement to enhance the network stability. LEACH-C [18] is a centralized technique to cluster se- nsor nodes based on their positions. In this approach, ba- se station selects cluster heads to get uniformly distribu- ted clusters. In LEACH-C, sensor nodes detect their curr- ent locations using GPS (Global Positioning System) receiver or any other technique. At the beginning of each interval, each node informs the base station its current location and residual energy level. After receiving the in- formation from all the sensor nodes, base station comp- utes the average residual energy in the network. It prec- ludes those sensor nodes whose residual energy is below the average residual energy from attaining cluster heads- hip. Base station selects the cluster heads from the rema- ining nodes using the simulated annealing algorithm [47]. Base station also selects corresponding followers for the clusters while selecting the clusters and cluster heads, and the base station broadcasts a message into the net- work informing these selections. This algorithm minimizes the total sum of squared dis- tances between all the non-cluster-head nodes and the corresponding closest cluster head node. Thus, it minim- izes the amount of energy necessary to use to transmit data to the cluster head nodes by the non-cluster-head no- des. However, it suffers from the following limitations: In LEACH-C, the base station selects the cluster heads based on their positions and the average residual energy in the network. Like LEACH, the individual residual energy in each sensor node has little impact on the cluster head selec- tion process in LEACH-C. This centralized al- gorithm also suffers from non-scalability. Incorporating GPS receiver or similar device in the sensor nodes increases sensor node cost. It did not attempt any improvement to enhance the network stability. Adaptive Cluster Head Selection 19 assumes that a sensor node knows its distance from another sensor node by observing the signal strengths in the received mes- sages. At first, this approach randomly selects cluster heads following LEACH. Next it reselects the cluster heads considering the distance between each cluster head and the sensor nodes farthest from the cluster heads. The reselection is done in order to distribute the cluster heads uniformly in the network. When a sensor node is selected as a cluster head by LEACH, it broadcasts an advertise- ment message to all other nodes. Other sensor nodes re- spond to the broadcast. From the received responses, a cluster head calculates its distance to its farthest follower node and its distance to the nearest cluster head of neighbor clusters. It subtracts the first distance from the later. Three cases may arise as follows: Case 1: The result is positive. Case 2: The result is negative. Case 3: The result is zero. In order to place the cluster head in an optimum loca- tion, the cluster head is moved to the direction of the closest head in Case 1 and to the direction of the farthest sensor node in Case 2. Cluster head position remains the same in Case 3. This approach ensures uniform distribution of the cluster heads. However, it has the following limitations: It completely ignores the relative residual ene- rgy of each sensor node in the network while selecting the cluster heads. It also suffers from other LEACH limitations. In this work cluster head movement, if necess- ary, is not clearly defined. It did not attempt any improvement to enhance the network stability. Therefore, none of the research works mentioned in this section makes any attempt to improve network stab- ility. In the next section, we propose a novel technique, Stable Sensor Network (SSN) to improve this metric. Copyright © 2010 SciRes. WSN 546 A. B. M. A. A. ISLAM ET AL. 4. Stable Sensor Network (SSN) In this section, we propose a new algorithm to cluster se- nsor nodes in a network to improve network stability in terms of death of the first sensor node. We follow the underlying approach of LEACH. In LEACH, each sensor node is given equal chance to get cluster headship and thus its lifetime depends only on its own residual energy. Therefore, a sensor node with low residual energy dies within a short period. However, there may be some other sensor nodes alive after its death. If that sensor node could exploit the residual energies of the live sensor nodes then it would live longer. Therefore, we should use the total residual energy of the network to increase the lifetime of the sensor node which dies first. We present three heuristics to achieve this goal. We illustrate our complete clustering algorithm SSN in details after des- cribing those heuristics. We also adapt the mathematical model derived in [44] for SSN incorporating the heuris- tics accordingly. 4.1. Heuristics We propose three heuristics for SSN. First two heur- istics basically attempt to use the residual energy of the network in a sensor node. A sensor node needs residual energy status of other sensor nodes in the network for the second heuristic. It can get that information from unac- knowledged broadcasts from other sensor nodes. Some of the information will not be available to the sensor node due to unacknowledged broadcasts. Third heuristic attempts to make up this missing information. Heuristic 1: Energy consumption of a cluster head no- de is higher than that of a follower node. Therefore, sen- sor nodes with higher residual energy should be elected as cluster heads. In the original LEACH algorithm, if a node becomes cluster head in a subinterval it cannot bec- ome cluster head again in any of the subsequent subint- ervals of the same interval. However, if a sensor node with higher residual energy can become cluster head ag- ain in other subintervals in the same interval then a sen- sor node with lower energy can escape from being clus- ter head. In that case, the lifetime of this lower energy sensor node will increase by using residual energy of a higher energy sensor node. For this reason, we make the subintervals completely memory less and eliminate the use of the separate set of nodes that have not been cluster head yet in the current interval. With this modification, the probability of becoming cluster head of a sensor node in a subinterval does not depend on its status in the prev- ious subintervals. This heuristic partially increase net- work stability period. Heuristic 2: We can expect higher stability period of a sensor network if we increase the probability to become cluster heads for sensor nodes with higher residual ener- gies. We should consider relative residual energy of a sensor node to determine whether it is with higher resi- dual energy or not. For this reason, we judge the relative residual energy of a sensor node while selecting it as a cluster head. We map the relative residual energy of a sensor node in its threshold computation so that it keeps its expected value at the optimal percentage of cluster heads P. At the beginning of each subinterval, each node knows its own residual energy (Ecur) along with maxi- mum (Ecur_max), minimum (Ecur_min), and average (Ecur_avg) residual energies of all sensor nodes alive in the network. Considering average residual energy (Ecur_avg) corre- sponds to expected percentage of cluster heads (P), we map Ecur_min, and Ecur_max to (1 – Prange) and (1 + Prange) respectively, where Prange is the minimum between P and (1 – P). If P ≤ (1 – P), (P – Prange) becomes zero and if P ≥ (1 – P), (P + Prange) becomes one. This has been shown in Figure 3. We define deviation from P for a sensor node based on the difference between its residual energy Ecur and the average residual energy Ecurr_avg in the network. Hence, the deviation is: range r PP E (4) where, avgcurcur avgcurcur avgcurcur avgcurcur avgcurcur curavgcur avgcurcur r EEif EE EE EEif EEif EE EE E _ _max_ _ _ _ min__ _ , ,0 , In order to make the threshold value proportional to the residual energy of a sensor node, we assign threshold value equal to P plus ∆P, i.e. PPnT (5) This heuristic along with the previous one enable a se- nsor node to become cluster head according to its relative residual energy in the network. A sensor node with hig- her residual energy is ensured to be more probable and a sensor node with lower residual energy is ensured to be less probable in the selection of cluster heads. Heuristic 3: To apply the previous heuristic, a sensor node must know the maximum, minimum, and average residual energies of all sensor nodes alive in the network. To calculate these values it must know residual energies P + P range P P-P range Threshold R esidual ener gy E cur_min E cur_max E cur_avg Figure 3. Distribution of Threshold Value according to Res- idual Energy. Copyright © 2010 SciRes. WSN A. B. M. A. A. ISLAM ET AL. 547 of all other sensor nodes. Therefore, each node must bro- adcast its residual energy level. For guaranteed availabil- ity of this information, some acknowledgement based data transmission technique should be followed. Howe- ver, this will incur a significant energy cost. For this reason, we make a trade-off between the accuracy of this information and the energy required to transmit them. We simply adopt one pass broadcast and to overcome the accuracy problem we multiply the threshold by the ratio between total number of deployed sensor nodes (N) and number of sensor nodes (Nlive) from whom residual ene- rgy information is received. This will increase the proba- bility of a sensor node to become cluster head when it finds a lower number of live sensor nodes in the network. This ultimately ensures the preservation of overall opti- mal percentage of cluster heads among those reachable sensor nodes irrespective of the statuses of the unreach- able sensor nodes. This heuristic changes the equation of the threshold as the following way: live N TnP PN (6) 4.2. SSN Algorithm We divide the lifetime of the network into some discrete and disjoint equal length intervals in SSN. Each interval has three consecutive phases—advertisement, cluster-set- up, and steady-state phase. The algorithm depicted in Fig- ure 4 runs independently in each sensor node in each interval. The parameters are initialized at the start of the algorithm. Ecur is set to its current residual energy level. Ecur_max, Ecur_mi n, and Ecur_avg are set to its own current re- sidual energy level, i.e., equal to Ecur. The number of live sensor node, Nlive, is set to one assuming it is the only live sensor node in the network. Advertisement, cluster- setup, and steady-state phases are executed as follows: 1) Advertisement Phase: During this phase, each no- de executes two parallel processes. In one process, each node waits for a uniformly distributed random amount of time and then broadcasts its current residual energy level. This random delay reduces the probability of collision. Another process receives the current residual energy lev- els of other sensor nodes. A sensor node may receive multiple copies of a current energy level advertisement me- ssage from the same sensor node due to multi-path effect. A receiver sensor node detects these duplicate receptions and ignores them. A receiver sensor node up- dates the parameters—Ecur_max, Ecur_min, Ecur_avg, and Nlive using the fresh advertisement messages only. 2) Cluster Set-up Phase: In this phase, each sensor node independently decides whether to become a cluster head or not based on the information gathered in the ad- vertisement phase. At first, it calculates the threshold T(n) using Equation 6. Next, it picks a random number and compares the random number with the threshold. Three cases may arise as follows: CASE 1: The random number is less than the thres- hold. In this case, the sensor node becomes a cluster head and broadcasts HEAD_EXPOSURE message. CASE 2: The random number is not less than the threshold and it does not receive any HEAD_EXPO- SURE message from other sensor nodes. In this case, the sensor node becomes a one member cluster head. CASE 3: The random number is not less than the threshold and it receives one or more HEAD_EXPO- SURE messages from other sensor nodes. In this case, the sensor node becomes a follower of the nearest cluster head and sends a FOLLOWER_ACCEPTANCE: Mes- sage to the nearest cluster head. 3) Steady-state Phase: In this phase, the followers send data to the corresponding cluster head. The cluster heads accumulate, aggregate, and compress the received data with its own data. Cluster heads send the aggregated and compressed data to the base station. The duration of steady-state phase is significantly longer than the sum- mation of the durations of the advertisement and clus- ter-setup phases in order to minimize cluster establish- ment overhead. 4.3. Mathematical Model of SSN The difference between underlying mode of operations of LEACH and SSN arises because of three new heuris- tics. The last two heuristics make change only in the thr- eshold value (T(n)). This change merely affects the prob- ability of becoming cluster head of a follower node at the start of any subinterval (Ph). Otherwise, there is no imp- act of these two heuristics on Equation 3, which is the latest mathematical formulation of LEACH. However, heuristic 1 of our new clustering algorithm makes the subinterval completely memory less. For this heuristic, the first state transition diagram of Figure 2 is no longer applicable. However, Φ0 is formulated form the weighted combination of two state transition diagrams of Figure 2 in the mathematical model of LEACH. Therefore, the fo- rmulation of Φ0 needs to be changed in the mathematical model of SSN. With the introduction of heuristic 1, any sensor node can become cluster head irrespective of its status in the previous sub interval. Therefore, the probab- ility of becoming cluster head of a follower node at the start of any subinterval (Ph) will no longer differ from the probability of becoming cluster head of a sensor node at the start of any subinterval (Φ0). As a result, formulation of Φ0 in the changed mathematical model of SSN will be Φ0 = Ph. With this change, we can use Equation 3 as the mathematical model of SSN. Copyright © 2010 SciRes. WSN A. B. M. A. A. ISLAM ET AL. Copyright © 2010 SciRes. WSN 548 Algorithm SSN () Set the value of Ecur Initialize Ecur_max, Ecur_min, and Ecur_avg to Ecur, Initialize Nlive to 1 Advertisement(); broadcasts and receives current energy levels Cluster_Set_Up(); generates the clusters Steady_State(); receive and transmit data Algorithm Advertisement() Transmit_Current_Energy_Residual_Level() Receive_Current_ Residual_Energy_Level() Algorithm Transmit_Current_ Residual_Energy_Level() Wait for a random time Broadcast own current residual energy level Algorithm Receive_Current_ Residual_Energy_ Level() For each received current residual energy level, E’cur if E’cur is not a repetition from an already received node Update_Parameters(Nlive, E’cur) endif Algorithm Update_Parameters(Nlive, E’cur) if E’cur > Ecur_max Ecur_max = E’cur endif if E’cur < Ecur_min Ecur_min = E’cur endif 1 ' _ * _ live N cur E avgcur E live N avgcur E Increment Nlive Algorithm Cluster_Set_Up () PP range P1,max if Ecur < Ecur_avg min_ _ _ cur E avgcur E avgcur E cur E r E else if Ecur > Ecur_avg avgcur E cur E avgcur E cur E r E _max_ _ PP E range r else Er = 0 endif N TnP P Nlive Choose a random number r if (r < T(n)) then status=head broadcast HEAD_EXPOSURE message else Receive HEAD_EXPOSURE messages from other sensor nodes if ( no HEAD_EXPOSURE message received) then status=head else status=follower send FOLLOWER_ACCEPTANCE message to nearest cluster head endif endif Algorithm Steady_ State () if status=follower send self originated data to own cluster head else receive messages from own followers aggregate and compress them with own message send to base station endif Figure 4. Algorithms for Stable Sensor Network (SSN). A. B. M. A. A. ISLAM ET AL. Copyright © 2010 SciRes. WSN 549 We compare these mathematical models from simul- ation results in the next section. We also analyze the eff- iciency of SSN in that section. 5. Simulation Results We conduct our simulation runs on a randomly deployed wireless sensor network. Our simulation program is wri- tten in visual C++. In this section, we first describe our network settings along with various parameters used in energy rate calculation. Then, we compare mathematical models of SSN with that of LEACH. Finally, we evalu- ate network stability in SSN with that of LEACH and its high performance variant. 5.1. Network Settings We use network settings as shown in Figure 5 in our simulation runs. The network settings do not make any impractical assumption to simplify the analysis. The set- tings are as follows: ● The dimension of sensor area is 200 × 200 m2. ● Total number of sensor nodes in the network is 100. ● The sensor nodes are randomly distributed over the sensor area. ● Each sensor node is initially equipped with a bat- tery of 5 Joule. ● The base station is located at position (400 meter, 100 meter). We use the following parameters in the simulation ru- ns for verification of mathematical models and in the fir- st runs of the subsequent analyses: 1) The amount of energy per bit to run sensor node circuitry, Eelec is 5 × 10–8; 2) The value of energy constant, Єamp, for radio trans- mission, is 1 × 10–10; 3) The number of data packets generated during each subinterval by a sensor node is normally distributed in the range of [0, 50], with the value of mean equal to 25. We applied Box-Muller transformation [48] to achieve this normal distribution from the uniform distribution of the built-in rand() function in visual C++. 4) Each data unit contains 8 bits data; 5) The probability that a message successfully arrives at its destination is 90%. 5.2 Verification of Mathematical Model We first plot the long run rate of energy consumption from Equation 3 versus the percentage of heads for a LE- ACH node in Figure 6. The value of the probability of becoming cluster head of a sensor node at the start of any subinterval Φ0 must not exceed 1 and the value of Φ0 can be computed from Equation 2. According to Equation 2, if the value of P exceeds 0.61 then the value of Φ0 will exceed 1. In order to avoid this, we plot the graph against the percentage of cluster heads P up to 0.61. According to the graph: 1) Energy consumption rate initially decreases very sh- arply with the increase of the percentage of cluster heads. 2) There is an optimal point for which energy cons- umption rate is the lowest. After this point the energy consumption rate increases with the increase of the perc- entage of cluster heads. In our simulation runs this opti- mal point is (0.045, 0.000337). We also plot the long run rate of energy consumption from Equation 3 versus the percentage of heads for a SSN node in Figure 7. Here, the probability of becoming clu- ster head of a sensor node at the start of any subinterval Φ0 is no longer computed from Equation 2 as in SSN Φ0 directly maps to Ph. Therefore, we plot the graph against the percentage of cluster heads P up to 1. The graph in Figure 7 exhibits almost the same trends found in the graph in Figure 6. Energy consumption rate initially decreases very sharply with the increase of the percentage of cluster heads and after an optimal point the energy consumption rate increases with the increase of the percentage of cluster heads. In Figure 7, the optimal point for SSN is (0.045, 0.000331) which gives lower long run rate of energy consumption than the optimal point for LEACH found in Figure 6. This improvement is only due to heuristic 1 as only this heuristic modifies the mathematical model. Base station at (400, 100) a = 200 0 50 100 150 200 200 180 160 140 120 100 80 60 40 20 0 b = 200 Figure 5. Netw or k Settings: Uniformly distributed sensor nodes w i th a base station. A. B. M. A. A. ISLAM ET AL. Copyright © 2010 SciRes. WSN 550 Figure 6. Long run rate of energy consumption against Dif- ferent Percentage of Heads according to the Mathematical Model of LEACH. Figure 7. Long run rate of energy consumption against Dif- ferent Percentage of Heads according to the Mathematical Model of SSN. We evaluate network stability of SSN against that of LAECH and its best variant. The authors of Determinis- tic Cluster Head Selection [17] claimed that it improves the network stability period by 30% over LEACH where- as the authors of SEP [16] claimed that it does the impro- vement over LEACH by 26%. These two are the most improved LEACH variants claimed so far. For this rea- son, we take Deterministic Cluster Head Selection [17] as the best LEACH variant instead of SEP in our perfor- mance comparison. We already find P = 0.045 as the optimal percentage of cluster heads from the mathemati- cal models of both LEACH and SSN. We use this value for all of the three techniques under evaluation. Our eva- luation is based on three metrics: 1) Data rate of a sensor node, 2) Position of base station, and 3) Initial energy of a sensor node. In the evaluation process, for each simulation run we take average of values found from fifty simulation passes. Each simulation run generates a point in a graph. We st- art with already described network settings for the first point in each of the graphs. I. Data rate of a sensor node In the initial network settings, number of data packets generated by a sensor node in a subinterval is normally distributed in the range of 0 to 50, with mean 25. We conduct fifteen simulation runs varying this range. We change the upper limit of the range from 50 packets with step of 10 packets in each simulation run. We plot the values of network stability periods in terms of FND in Figure 8 and the values of HND in Figure 9. Figure 9 indicates that HNDs of SSN, LEACH and LEACH vari- ant are comparable. However, there is a significant ste- ady improvement in FND for SSN over LEACH and its variant. We plot these improvements in Figure 10. The average improvement over LEACH and its variant is 53.42% and 35.62% accordingly. Figure 8. Network stability period in terms of First Node Dies (FND) for different data rates. Figure 9. Half of the Nodes Die (HND) for different data ra- tes. A. B. M. A. A. ISLAM ET AL. 551 II. Position of base station In the initial network settings, base station is located at (400 m, 100 m). Therefore, distance of the base station from the center of network area is 300 meter. We cond- uct fifteen simulation runs varying this distance. We cha- nge the position of base station in first dimension from 400 meters with step of 25 meters in each simulation run. We plot the values of network stability periods in terms of FND in Figure 11 and the values of HND in Figure 12. Figure 12 indicates that HNDs of SSN, LEACH and LEACH variant are comparable. However, there is a sig- nificant steady improvement in FND for SSN over LE- ACH and its variant. We plot these improvements in Figure 13. The average improvement over LEACH and its variant is 48.55% and 30.22% accordingly. III. Initial energy of a sensor node In the initial network settings, initial energy of a sen- sor node is 5 Joule. We conduct fifteen simulation runs Figure 10. Improvement in network stability period in ter- ms of First Node Dies (FND) in SSN for different data rates. Figure 11. Network stability period in terms of First Node Dies (FND) for different positions of base station. Figure 12. Half of the Nodes Die (HND) for different posi- tions of base station. Figure 13. Improvement in network stability period in ter- ms of First Node Dies (FND) in SSN for different positions of base station. Figure 14. Network stability period in terms of First Node Dies (FND) for different initial energies of a sensor node. varying this initial energy. We change the initial energy of a sensor node from 5 Joule with step of 1 Joule in each simulation run. We plot the values of network stability periods in terms of FND in Figure 14 and the values of Copyright © 2010 SciRes. WSN 552 A. B. M. A. A. ISLAM ET AL. HND in Figure 15. Figrue 15 indicates that HNDs of SSN, LEACH and LEACH variant are comparable. However, there is a sig- nificant steady improvement in FND for SSN over LEA- CH and its variant. We plot these improvements in Fig- rue 16. The average improvement over LEACH and its variant is 52.04% and 34.25% accordingly. These values clearly indicate that, SSN provides sig- nificantly higher time before first node dies in compare- son to LEACH and its variant irrespective of data rate of sensor node or position of base station or initial energy of a sensor node. 6. Conclusions We propose a novel self-organizing and adaptive clust- ering protocol SSN in this paper. We use three heuristics Figure 15. Half of the Nodes Die (HND) for different initial energies of a sensor node . Figure 16. 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