1 Motivation
The implementation of a WSN is influenced by several design factors such as scalability, fault tolerant, topological layout, transmission media, and power consumption [SALEH2021, Alyousuf2019, Thi2019]. Fault tolerant, for example, ensures that a failure of a SN caused by a lack of power or physical damage should not affect the rest of SNs or severely degrade the overall performance. Since a WSN could be in the order of hundreds or thousands of SNs, scalable mechanisms are to be employed to help WSNs adapt to number and density of SNs [sharma2019heterogeneity, Guo2020, Shilpi2020]. Because each SN has limited power resources and may not be rechargeable, effective powersaving mechanisms are needed to extend network lifetime [Kirsan2019, Chen2019, Zhen2019]. Therefore, energy efficiency and network lifetime are primarily among the most important QoS obligations to consider in the design of a WSN [EACA2021, Pandey2021]. There is a need to formalize energyefficient strategies that preserve SNs’ residual energy, reduce the overall energy consumption, and consequently prolong the network lifetime [chan2020hierarchical, manuel2020optimization, Ateeq2020].
Energyefficient algorithms are proposed to address topological complications and energy concerns in WSNs. Heinzelman et al. [Heinzelman] present LEACH protocol that specifically merges “clustering and media access with applicationspecific data aggregation” to improve network lifetime, latency, and application quality. LEACH includes a distributed clustering technique that evenly rotates the clusterhead between SNs to avoid power depletion of a specific SN over others. They analytically compute the number of clusters expected per round to minimize the total energy consumption.
Disjoint clustering is accordingly an efficient mechanism effectively employed in WSNs. It is utilized to achieve scalability, stabilize network topology, minimize energy consumption, aggregate sensor data, and alleviate congestion rate. A clusterhead would potentially limit the scope of communication between clustermembers and Base Station (BS), as well as coordinate the channel time among its clustermembers so that the whole network is not burden with extra redundant information. Periodic clustering distributes energy evenly among all SNs, which consequently increases the energy efficiency and extends the network lifetime. With respect to energy consumption, a clustermember consumes energy when it transmits data to its corresponding clusterhead or directly to BS. On the other side, a clusterhead consumes energy when data is received from its clustermembers, and consumes more energy when data is aggregated and transmitted to the BS.
However, clustering approaches in the literature mostly focus on improving the process of selecting clusterheads, either randomly or according to SN’s residual energy. Some approaches form the best possible energy path toward BS such that network lifetime is increased. Nevertheless, such approaches do not account for variations in network state at runtime. In fact, the state varies often because of frequent changes in network configurations, and thus clusterheads would not potentially be elected depending on existing conditions of the network and distances between SNs.
To tackle such difficulties, this paper presents a LEACHbased adaptive clustering algorithm in which an adaptive probability function is employed to formulate clusters. A nearoptimal distance between each clusterhead and its corresponding clustermembers is formalized such that the overall energy consumption of the network is mitigated and accordingly the network lifetime is maximized. Distances between SNs and residual energy of each SN in the network are utilized to compute the maximum number of clusterheads elected per round. The clusterhead selection probability is adapted at the end of each round according to the maximum number of clusterheads permitted per round found in advance and the number of alive SNs currently interacting with the networking environment.
The proposed adaptive clustering scheme helps business organizations and building automation support realtime visibility and remote monitoring on their system operational data, so as to meet a highlevel of energyefficiency and costsaving. The design is robust to topology changes and can be utilized to tackle interoperability between heterogeneous SNs, so that to it manages security and privacy challenges incurred from a large volume of enterprise data reported from the working environment.
2 Contributions
The communication and computation energy model of the network is mathematically analyzed and examined, which is structured based on LEACH algorithm. An optimal distance () between each clusterhead and its clustermembers is formulated, found by deriving the total energy consumption with respect to the distance. The mitigates the total energy consumption of receiving, aggregating, and transmitting data, which as a result prolongs the network lifetime. Thus, the is utilized to formulate the maximum number of clusters permitted per round, . As a result, the clusterhead selection probability is adapted at the end of each round based on found a priori and number of alive SNs currently active in the network. Additionally, distance to and residual energy of clusterheads are both considered by each SN to select its potential clusterhead. Each SN joins a clusterhead that holds the maximum energydistance ratio, , where is the residual energy of clusterhead, is the distance between SN and clusterhead, and & are constants. Contributions of this paper are summarized as follows:

Formulating between each clusterhead and its clustermembers such that network lifetime is prolonged and the overall energy consumption is minimized.

Formulating based on found a priori and utilizing to optimize the maximum number of clusterheads permitted per round.

Adapting the clusterhead selection probability according to existing network’s state represented by and number of alive SNs .

Employing adaptive probability , jointly with and energy factor , to propose adaptive clustering algorithms.

Employing the energydistance ratio () to assist SNs effectively select the best clusterhead to join, and to propose adaptive energyefficient distancebased clustering algorithms jointly with , , and .

Verifying the performance of the proposed adaptive clustering algorithms, devised based on LEACH and Stable Election Protocol (SEP) algorithms, on randomly distributed heterogeneous SNs produced with different initial energylevels.
3 Background and Related Work
Clustering is a systematic practice in WSNs to facilitate routing and collecting data in a timely and energyefficient manner [Rajesh2020, DAANOUNE2021, RCHLEACH, Adnan2019, Dimple2019]. Clustering approaches are proposed to prolong the network lifetime, with their focus harnessed on devising clusterhead selection methods that evenly balance the energy consumption among SNs [sabor2017comprehensive, liang2019research, salam2020performance, alharbi2021towards, Adil2020]. To efficiently overcome the problem of energy consumption in clustering algorithms, LEACH protocol is proposed by Heinzelman et al. [Heinzelman] to enable selforganization of SNs and support clusterhead selection. In this protocol, a clusterhead is randomly rotated among all SNs to avoid fast energy depletion of a specific SN, so as to evenly distribute and balance the energy consumption among SNs and thus to prolong the network lifetime. The maximum number of clusters expected to minimize the total energy consumption of the SNs is calculated.
Similarly, Heinzelman et al. [Heinzelman2] evaluate the performance of LEACH algorithm with direct communication, Minimum TransmissionEnergy (MTE), and static clustering algorithms. The effectiveness of LEACH algorithm outperforms the other algorithms by reducing the communication energy and increasing SN’s lifetime. Nevertheless, LEACH algorithm suffers from numerous drawbacks in that it randomly selects clusterheads at each round. SNs have equal probabilities to become clusterheads regardless of their existing residual energylevels and number of remaining SNs in the network, which in turn may choose a clusterhead with low energylevel.
Smaragdakis et al. [SEP_SANPA04] propose SEP protocol that selects clusterheads such that time period to death of first SN is prolonged. SEP assumes SNs with different initial energy so as to tackle heterogeneity of the network. Improvements on SEP algorithm have been proposed to produce enhanced energy consumption and performance [SEP_2014]. Nurlan et al. [nurlan2021EZSEP] extends ZSEP routing algorithm to propose an EZSEP that connects SNs to BS via a hybrid method. Though, some SNs communicate with the BS directly while some other SNs form together clusters to transfer data. Clusterheads are selected based on residual energy of each SN.
Furthermore, Pranathi et al. [robust2020] present the centralized approach appeared in LEACH, in which a clusterhead is a singlepoint of failure that leads to information loss when it is transferred to BS. They propose a distributed, robust averageconsensus routing protocol that makes SNs exchange information directly to BS to overcome the problem of centralization. Despite the robustness of their consensus algorithm in collecting and transmitting data, it suffers from a high energy consumption required by each SN to transmit its data directly to BS. As such, the proposed algorithm is modified to present an energyefficient hybrid approach that mitigates the energy consumption to a level close to LEACH protocol.
Several clustering protocols for lifetime maximization of WSNs are also proposed in the literature to tackle such clustering issues. Rawat et al. [rawat2021novel] present an energyefficient LEACHbased routing protocol for network lifetime’s enhancement. Elmasry et al. [EESRA] propose a scalable energyefficient algorithm that adopts a threelayer hierarchy to minimize workload on clusterheads and randomize the clusterhead selection procedure. Loganathan et al. [loganathan2020energyCentroid] propose an energyefficient clustering algorithm that uses a distance centroid algorithm to design each cluster. The energy centroid of each cluster is computed and employed together with the energy threshold of each SN to choose a clusterhead. Muthukumaran et al. [K2018energy] present a hierarchical routing that uses cluster identification, multihop, and multilevel routing schemes to evaluate their effectiveness to produce energyefficient clustering. Priyadarshi et al. [priyadarshi2019energy] propose a clustering algorithm that uses threshold functions and residual energy of each SN to select clusterheads. Lin et al. [lin2021research] modify the threshold function of clusterhead selection to present a strategy for forming clusters of the network.
Qabouche et al. [qabouche2021hybrid] propose a static routing protocol that combines clustering and multihop routing. Data is transmitted in each round through independent SNs called gateways, which connect clusterhead SNs with the BS. Pour et al. [pour2021new] present an energyaware clusterhead selection based on residual energy of a SN, centrality of a SN, and number of neighboring SNs. In addition, Chauhan et al. [chauhan2020mobile] propose a clusterhead selection strategy that splits the WSN into rectangular regions, each of which is managed by a clusterhead. A natureinspired algorithm employs residual energy of each SN and distance from a SN to a sink node to select clusterheads of the network. Bhola et al. [bhola2020genetic]
adopts a geneticbased approach to optimally find route to destination nodes such that energy consumption is mitigated. The genetic algorithm utilizes its fitness function to optimize the network’s performance, thus if the network performance is decreased then the genetic algorithm alters the route such that network’s efficiency is increased. Wang et al.
[Wang2020GA] also present a genetic algorithm that selects the best clusterheads and combines them in a single chromosome to find the optimal routing path, with a fitness function that considers load balancing among SNs and minimum energy consumption.In addition, Lata et al. [Lata2020] propose a reliable clustering algorithm that adopts a fuzzybased clustering to formulate cluster, as well as select cluster heads and vice clusters, in a centralizedbased manner such that network’s lifetime is maximized and energy load is balanced. Antcolony optimization is utilized by Liang et al. [liang2019research] to present an optimized multihop routing protocol, where energy consumption per round is employed to compute number of clusterheads for an improved LEACHbased protocol. Shukry et al. [shukry2021stable] propose a Node Stable Routing protocol that stabilizes data transmission exchanged between SNs. The protocol characterizes a SN’s stability by its residual energy and number of successive hops required to reach a destination SN. The source SN formalizes a stable path to destination such that energy consumption is mitigated.
A missing factor in proposed clustering strategies of WSNs is to actively account for network state at runtime [SuleimanP1_2019, SuleimanP2_2019, SuleimanP3_2020]. Such a state varies very often because SNs by the time suffer from gradual decrements in their residual energy, which in turn affects the network’s configuration. Accordingly, clusterheads are not adaptively elected based on existing states of the network and hence the total energy of network would not be fairly distributed among SNs leaving network’s space proportionally covered. The clustering protocol in this paper employs an adaptive probabilistic function that formulates clusters so that QoS performance is enhanced. It computes a nearoptimal distance between SNs such that energy consumption is reduced and thus network lifetime is maximized.
4 Network Model
The network model comprises heterogeneous SNs with similar computation and communication capabilities. Such SNs are randomly distributed on a space of x area, with one BS positioned in the middle. The SNs and BS have fixed locations. However, all SNs are energyconstrained. Each SN starts with different initial amount of energy, has fixed Identifier (ID) address and position, and has enough power to reach the BS if a SN needs to act as a clusterhead. On the other side the BS works without energy constraint because it is assumed to have adequate energy supply; and as such the energy consumption of BS is not considered in the mathematical analysis and design evaluation. As in SEP protocol, SNs are divided into two types: normal and advanced SNs. Normal SNs start with low initial energylevel represented by . Advanced SNs start with high initial energylevel represented by , where is constant. Percentage of SNs that are advanced is . Table I summarizes notations used throughout the paper.
Notation  Definition 

Heterogeneity factor for advanced SNs  
Energy constant  
Distance constant  
Distance between two adjacent SNs  
Distance threshold  
Distance between a SN and a BS  
Distance between a SN and a clusterhead  
Optimal distance between a clusterhead and its clustermembers  
Energy dissipated by transmitter to run power amplifier using free space () model  
Energy dissipated by transmitter to run power amplifier using multipath fading () model  
Initial energylevel of normal SNs  
Initial energy of a SN  
Current residual energy of a SN  
Energy dissipated per bit to run the transmitter and receiver radio electronics  
Energy dissipated to transmit bits through a distance  
Energy dissipated to receive bits  
Energy dissipated to aggregate bits  
Energy dissipated by a clustermember  
Energy dissipated by a clusterhead  
Energy dissipated in each cluster  
Energy dissipated by all clusters  
Energydistance ratio  
Set of nonelected SNs  
Number of clusters per round  
Maximum number of clusterheads permitted per round  
Size of data packet in bits  
Percentage of advanced SNs distributed in the field  
Field’s dimension  
Number of SNs distributed in the field  
Probability of selecting a clusterhead  
Adaptive probability  
Current round number  
A selected SN from the set  
Threshold for selecting a SN as a clusterhead  
Threshold for selecting a SN as a clusterhead based on energy  
Number of alive SNs in the current round 
All clustermembers sense the environment at a fixed rate and always have data to send to their corresponding clusterheads. Each cluster has one clusterhead, and each clustermember is allocated to one clusterhead, i.e., fuzzy membership is not allowed. Clustermembers communicate with the BS via their corresponding clusterhead by means of symmetric communication channel, i.e., same energy is required to transmit data packets from source to destination SNs and vise versa for a given SignaltoNoise Ratio (SNR). Each clusterhead aggregates and then transmits data directly to the BS, and the BS receives compressed data.
The size of the transmitted and received data packet is fixed, bits. Each SN consumes energy when it receives (), aggregates (), and transmits () data packets of size bits. Such energy consumption only depends on a distance between source and destination SNs. For the distance between any two adjacent SNs, the free space model is employed if the distance between source and destination SNs is smaller than a threshold (), otherwise () the multipath fading model is employed. The network simulation parameters are shown in Table II, which illustrates the maximum number of rounds, field dimensions in meters, SN parameters, values for SNs’ heterogeneity, and parameters of the energy model.
Field Dimension  Maximum and (in meters)  

Maximum and coordinates in the field  
and coordinates of the sink node ()  
SN Parameters  
Maximum number of rounds  3000 
Number of SNs in the field ()  100 
Initial optimal election probability of a SN to become clusterhead ()  0.1 
Values for SNs Heterogeneity  
Percentage of advanced SNs in the field ()  0.1 
Heterogeneity factor () for advanced SNs  1 
Energy Model (All Values in Joules)  
Initial energy ()  
Transmitting () and receiving () energy  
Data aggregation energy ()  
Freespace model transmit amplifier energy ()  
Multipath model transmit amplifier energy () 
5 Mathematical Model
A SN typically consumes energy when it receives, aggregates, and transmits data packets. The mathematical model adopts the simple energy dissipation model explained in [Heinzelman]. A transmitter SN consumes energy to run the radio electronics and power amplifier, and a receiver SN consumes energy to only run the radio electronics.
(1) 
(2) 
The is the energy dissipated to transmit bits through a distance , whereas is the energy dissipated to receive bits. The is the energy dissipated per bit to run the transmitter and receiver radio electronics. Also, and are the energy dissipated by transmitter to run the power amplifier using the free space () model and the multipath fading () model, respectively. However, the free space () and multipath fading () models are used depending on the distance between the source and destination SNs. The distance is first compared with a threshold value, . The free space model () is employed if the distance is ; otherwise, the multipath fading model () is employed. Mathematically, the free space model () is used in this paper for intracluster communication because the distance is assumed to be , whereas the multipath fading model () is utilized for communication between clusterhead and BS because the distance is assumed to be .
5.1 Formalizing and
It is assumed that SNs are randomly distributed over an area of x. Since the number of clusters per round is , then each cluster comprises SNs. Each clusterhead dissipates energy when it receives data from clustermembers (denoted by ), as well as dissipates energy when it aggregates () and transmits () such data to the BS.
(3) 
where is the distance between a clusterhead and BS. Each clustermember dissipates energy when it transmits data to its clusterhead.
(4) 
where is the distance from a clustermember to its clusterhead. The energy dissipated in a cluster is equal to the energy dissipated by the clusterhead and its clustermembers .
(5) 
Then, the overall energy consumption dissipated by all clusters is
(6) 
The objective is to formulate a distance between each clusterhead and its clustermembers, such that the overall energy consumption of the network is mitigated. The network field is partitioned into equal circles, each of which is of size . The expected number of clusters per round is
(7) 
By replacing with its new value, replacing with , and deriving the overall energy consumption with respect to , then the final formulation becomes
(8) 
(9) 
(10) 
This means that maximum number of clusters permitted per round to avoid any potential increase in the overall energy consumption of the network is
(11) 
The value of achieved based on the distancebased clustering is compatible with the expected number of clusters calculated in [Heinzelman].
5.2 The impact of energy () and maximum number of clusters ()
The objective is to first design an energyefficient clustering algorithm that distributes the energy evenly among all SNs, such that no SN is frequently chosen to act as a clusterhead and runs out of energy before others. The and derived formerly are utilized to mitigate the overall energy consumption of the whole network. As explained in [Heinzelman], all SNs have equal probabilities to become clusterheads in each round. Each SN selects a random number between and elects itself to become a clusterhead in the current round if the random number is less than a threshold .
(12) 
where is the current round number, is the selected SN, is the probability of selecting a clusterhead, and is the set of nonelected SNs. Accordingly, a SN that has not previously been a clusterhead is assumed to have more residual energy than others and qualified to become a clusterhead in next upcoming rounds. In LEACH algorithm, the overall energy is calculated by multiplying the average amount of energy of all SNs in each cluster by the total number of SNs.
This is accomplished by modifying the clusterhead selection probability to become a function of current SN’s energy relative to its initial energy, so that more probabilistic weight is given to SNs that hold high residual energy to become clusterheads than others.
(13) 
where represents SN’s current residual energy and represents SN’s initial energy. In this case, SNs with high residual energy are more qualified and have high probabilities to become clusterheads in the upcoming round. As such, the number of clusterheads permitted per round developed based on are both employed to devise LEACHbased and SEPbased algorithms.
The number of clusters permitted per round is limited to so that qualified SNs are evenly distributed throughout the network operation. However, combined with manage and distribute the energy consumption evenly during the network operation instead of having several clusters in such a round. Tradeoff is obvious in applying which may sometimes negatively overload some clusterheads with extra data traffic and quickly drain their energy, especially when is small and there are many SNs joining the selected clusterheads. In this paper, the effect of appears when is computed as explained in the next section.
5.3 The impact of adaptive probability ()
In LEACH and SEP algorithms, the probability of a SN to become a clusterhead is fixed. Such a probability however becomes inappropriate by the time because of increasing the number of dead SNs; which leads to increase the total number of rounds and decrease the number of elected clusterheads per round. The probability of selecting a SN as a clusterhead should be adaptive and changed by the time depending on the network’s state represented by existing network conditions and structures.
In this paper, the probability of selecting a SN to become a clusterhead is adapted at the end of each round. The depends on the value of permitted per round (calculated a priori) and the number of remaining (alive) SNs in the network. Such a selection scheme in turn increases the probability of electing a SN from the remaining ones to become a clusterhead when the number of alive SNs in the network is decreased.
(14) 
Thus, LEACH and SEP algorithms are modified to have LEACH, LEACH, SEP, and SEP algorithms. In LEACH algorithm, the probability is adapted at the end of each round and the number of clusters permitted per round is limited to to independently study the effect of . In LEACH algorithm, the probability is adapted at the end of each round, the number of clusters permitted per round is limited to , and the factor is employed in the clusterhead selection probability function. The same thing is applied for SEP and SEP algorithms, respectively.
5.4 The impact of the energydistance ratio ()
In LEACH and SEP algorithms, a SN joins a clusterhead based on the distance between them. The SN first computes the distance between it and all available clusterheads, and accordingly the SN joins the nearest clusterhead. However, the difficulty of this practice is that a SN may join a clusterhead that does not have enough energy to serve all its clustermembers. Such a routine drains the energy of the selected clusterhead quickly and as a result leaves some regions uncovered. Though, as explained in [Jiao_2012], a SN selects a clusterhead based on the energydistance ratio , where a SN joins the clusterhead with the highest . The utilization of ratio is more energyefficient than joining a clusterhead based on distance only.
(15) 
The , , , and are employed. Values of and are varied, chosen to be to get LEACH11, and then is employed to get LEACH11. Also, values of and are chosen to be and to get LEACH12, and then is employed to get LEACH12. Same thing is applied for the proposed SEP algorithms to get SEP11, SEP11, SEP12, and SEP12, respectively. For figures of the number of dead SN, the round number period of comparison is chosen to be between , where the major difference between proposed algorithms appears. For figures of the remaining energy, the round number period of comparison is chosen to be between .
6 Evaluation
The adaptivebased clustering algorithms are developed by utilizing LEACH and SEP. The QoS performance impact of on the probability of dead SNs and the energy consumption are examined. The , , and performance parameters are employed and evaluated against each others.
6.1 The impact of on death rate of SNs by utilizing , , and
The QoS performance of the proposed LEACH algorithms is evaluated by computing the likelihood of dead SNs as shown in Figure 1. The impacts of , , and performance factors are examined and analyzed. Commonly, maintains a stable QoS performance throughout the network operation due to the limited number of maximum clusterheads permitted per round. In this condition, puts more constraints and controls on electing clusterheads per round by making it optimal, which preserves and defers some qualified SNs to become clusterheads in upcoming rounds and accordingly distributes the energy evenly among all SNs throughout the network operation. Consequently, positively influences the probability of dead SNs per round. That is because qualified SNs are evenly distributed throughout the network lifetime, instead of having most of them running early as clusterheads which in turn would deplete their energy rapidly. The effect of appears clearly when is adjusted at the end of each round, because accounts for and number of alive SNs exist in the network.
Examining the impact of utilizing , the formulation of LEACH algorithm developed from employing improves the QoS performance of LEACH algorithm. That is because the clusterhead probability is adapted based on existing network states. Since is fixed throughout the time of network operation, increases when number of alive SNs decreases. Increasing , however, puts less constraint on selecting a SN to become a clusterhead, and hence increases the likelihood of qualified SNs to act as clusterheads. The formulation of LEACH algorithm increases the stability period and decreases the probability of dead SNs, as compared to LEACH algorithm.
Exploiting factor to devise LEACH algorithm improves the stability period and decreases the probability of dead SNs, as compared to LEACH and LEACH algorithms. The probability function of LEACH algorithm employs the current SNs’ residual energy to thus offer more probabilistic weight to SNs with high energy to become clusterheads than others. Such energy considerations would in turn distribute the energy evenly among all SNs throughout the network lifetime. Overall, engaging and/or to LEACH algorithm improves the stability period and mitigates the likelihood of dead SNs.
The same thing is applied when SEP algorithms are assessed as shown in Figure 2. SEP algorithm surpasses the performance of SEP algorithm by enhancing the probability of dead SNs and stability period throughout most of the network lifetime. In contrast, SEP algorithm has the greatest stability period in comparison with SEP and SEP algorithms. As well, SEP algorithm improves the performance of SEP algorithms by decreasing the probability of dead SNs, due to combining the effect of and performance metrics.
Generally, SEP, SEP, and SEP algorithms outperform LEACH, LEACH, and LEACH algorithms, respectively. SEP algorithm basically has different probabilities for advanced and normal SNs; that is for advanced SNs and for normal SNs. SEP algorithm offers more weight to advanced SNs (by a factor of ) in the original probability function to become clusterheads than others due to their high residual energylevels, as compared to LEACH algorithm which allocates equal probabilities to all SNs. Overall, utilizing the effect of and performance factors together on LEACH and SEP algorithms improves the stability period and mitigates the likelihood of dead SNs per round.
The QoS performance of the proposed LEACH algorithms presented in Figure 3 is evaluated on the likelihood of dead SNs by considering the impact of , , , and . It is obvious that employing in combination with , , and improves the QoS performance of LEACH algorithm  apparently the stability period is increased and probability of dead SNs is decreased. As explained previously, SNs in LEACH algorithm join the nearest clusterhead. However, the nearest clusterhead does not necessarily have adequate energy to serve all its clustermembers for long time. Employing ratio improves the QoS performance because it also utilizes the residual energy of clusterheads. In this case, a SN joins a clusterhead with the highest ratio. combined with improves the stability period and probability of dead SNs. The same thing is applied when SEP algorithms in Figure 4 are compared together.
6.2 The impact of on death rate of advanced SNs by utilizing , , and
The probability of advanced deadSNs of the proposed LEACHbased algorithms is evaluated in Figure 5 by considering the effect of , , and . Employing such performance measures on LEACH algorithm gives advanced SNs high probabilities to become clusterheads and subsequently depletes their energy rapidly. LEACH algorithm by itself, however, selects clusterheads randomly and does not guarantee to select the most energyefficient SNs to become clusterheads.
In contrast, Figure 6 compares the QoS performance of the proposed SEPbased algorithms on the likelihood of advanced deadSNs by considering the effect of , , and . Though, SEP algorithm utilizes high residual energylevels of advanced SNs to accordingly elect them as clusterheads early during the network lifetime; which thus decreases the number of advanced SNs throughout the network operation.
However, employing increases the probability of electing advanced SNs and qualifies them more to become clusterheads in upcoming rounds, especially that advanced SNs have high residual energylevels as compared to normal SNs. This situation is obvious when SEP algorithm is compared to SEP algorithm, in which factor improves QoS performance of SEP algorithm. The combined with formulates SEP algorithm, which in turn improves the performance and stability period, as well as has more impact on enhancing the likelihood of death rate for advanced SNs.
When SEP and LEACH algorithms are compared together, SEP algorithm offers high probabilistic weights to advanced SNs because of their high residual energy as compared to normal SNs. Such weights qualify advanced SNs by increasing their probabilities of being elected as clusterheads and then die early. Most of advanced SNs are dead in case of SEP algorithm, whereas LEACH algorithm randomly selects clusterheads without considering SN’s residual energy which in turn may leave some of advanced SNs not being elected very often to act as clusterheads despite their high residual energylevels.
Furthermore, the performance impact of together with ratio for the proposed LEACHbased algorithms in Figure 7 is compared on the likelihood of advanced deadSNs. Advanced SNs die rapidly because of considering as a main factor in the modified LEACHbased algorithms to decide on clusterheads to be elected in each round. Holding has more impact on advanced dead SNs than it is in the case of and ; and the impact increases when is employed.
In contrast, Figure 8 assesses the performance of the proposed SEPbased algorithms on the number of advanced dead SNs by considering the effect of and . The proposed SEPbased algorithms improve the QoS performance of SEP algorithm by enhancing the stability period and number of advanced deadSNs. The reason is that the impact of energy and distance, instead of distance only, are considered at each SN to decide on a potential clusterhead to join in each round.
In addition, a clusterhead’s energy mostly decreases by increasing the number of clustermembers by the time, by that a clusterhead consumes energy ( and ) when it accepts a clustermember. When a distancebased procedure is employed, a clusterhead may keep accepting many SNs because such SNs join the nearest clusterhead, which in turn may rapidly deplete clusterhead’s energy. However the procedure of utilizing ratio makes a SN first look at the clusterhead’s energy relative to the distance between them, and then the SN joins the clusterhead with the highest . The latter procedure wisely distributes SNs evenly among existing clusterheads, each of which with its capacity represented by its residual energy, and hence positively affects the overall QoS performance.
6.3 The impact of on energy consumption
The energy consumption performance of the proposed LEACHbased algorithms is compared in Figure 9, considering the effect of , , and . Employing decreases the total energy consumption because it increases the probability of qualified SNs to become clusterheads by the time. LEACH shows an energyefficient performance because its clusterhead selection probability accounts for the energy factor. The same thing is applied for SEP algorithms as shown in Figure 10.
The impact of employing in the algorithms is demonstrated in Figure 11. The adaptive LEACH11 and LEACH12 algorithms enhance the QoS performance higher than LEACH algorithm. The same thing is applied for SEP algorithms in Figure 12, where adaptive SEP11 and SEP12 are the most energyefficient algorithms.
To conclude, Figure 13 assesses the performance of LEACH and SEP algorithms illustrating the best proposed algorithms according to probability of dead SNs, demonstrating the effect of and performance measures. As well, Figure 14 compares the mutual performance impact of such algorithms, utilizing with and measures. Overall, the proposed adaptivebased algorithms improve the probability of dead SNs and stability period of original LEACH and SEP algorithms.
Algorithm  Round Number  Algorithm  Round Number 

LEACH  999  SEP  1052 
LEACH  1063  SEP  1081 
LEACH  1164  SEP  1183 
LEACH11  1135  SEP11  1150 
LEACH12  1126  SEP12  1139 
LEACH11  1230  SEP11  1241 
LEACH12  1217  SEP12  1237 
LEACH11Learning  1308  SEP11Learning  1367 
LEACH12Learning  1277  SEP12Learning  1294 
6.4 Evolving and
Learning based algorithms are developed based on the former proposed algorithms, in which the clustering factor is frequently evolved at the end of each round according to the probability of alive SNs , instead of having it fixed a priori in the proposed adaptive algorithms. Accordingly, the probability is adapted according to the evolved clustering and number of alive SNs at the end of each round. Figure 17 compares such learningbased algorithms. The round number period of comparison for the likelihood of dead SNs is chosen to be between , where the major difference between the learning algorithms appears.
The evaluation of the original LEACH and SEP algorithms, the proposed adaptive algorithms, and the learning based adaptive algorithms are presented in Figures 1517. The learningbased adaptive algorithms demonstrate better performance and improve the stability period, as compared to both the proposed adaptive and the original LEACH and SEP algorithms. In this case, the round number period of comparison for the likelihood of dead SNs is chosen to be between , where the major difference between the proposed adaptive and learning algorithms appears. To summarize, Table III presents the stability period represented by death of the first SN for each clustering algorithm. The overall QoS performance is improved when , , , and are employed together with learning.
7 Conclusion
It is observed that incorporating the residual energy of a SN in the clusterhead selection probability and limiting the number of clusterheads permitted per round to improve the overall QoS performance, for LEACH and SEP algorithms. This, however, decreases the likelihood of dead SNs and the total energy consumption, which as a result prolongs the lifetime of network operation. In addition, it is found that improves the clusterhead selection probability because it is adaptive to existing network’s state; represented by number of remaining SNs per round and maximum number of clusters permitted per round. Adapting the probability of selecting a clusterhead by and limiting the number of permitted clusterheads per round to would both distribute the energy and defer qualified SNs evenly throughout the network operation, as well as improve the stability period and QoS performance. Such improvements involve probability of dead SNs and total energy consumption. In addition, incorporating the development of enhanced ratio improves the performance by considering the residual energy of a clusterhead relative to its distances with its members, instead of only accounting for the distance to compose clusters. Such a relation accounts for the mutual performance impact of member displacements from their corresponding clusterheads which in turn distributes existing SNs evenly among elected clusterheads.
8 Future Directions
The clusterhead selection probability will be modified to account for current SN’s position to comprise a hierarchical distancebased clustering. Furthermore, a densitybased clustering will be developed to formulate SN clusters that do not require a priori knowledge on . A sensitivity analysis will be conducted to study the effect and relationship between input and output performance parameters of the mathematical model. The study will mainly be focused on examining the effect of varying on the probability of dead SNs per round. The QoS performance of the proposed algorithms will be compared with the original LEACH and SEP algorithms, by varying the level of heterogeneity and percentage of advanced SNs in the WSN.
References
Author Biography
Husam Suleimanhusam received his PhD in Electrical and Computer Engineering from University of Waterloo, Canada in 2019. His MSc degree is in Computer Engineering from Khalifa University, UAE in 2011 in collaboration with the Massachusetts Institute of Technology (MIT). His BSc degree is in Electrical and Computer Engineering from Hashemite University, Jordan in 2007. Currently, he is an assistant professor in Applied Science Private University, Jordan. His research interests include QoS Optimization in MultiTier Cloud Computing, Load Scheduling & Balancing, Big Data Algorithms, Resource Allocation Methods, Performance Prediction Analysis, Security Requirements Engineering Methods for Smart Grids and Systems. Mohammad Hamdanmohamed received his PhD degree in Electrical Engineering from University of Southampton, Southampton, UK in 2019. His MSc degree is in Energy, Sustainability with Electric Power Engineering from University of Southampton, UK in 2014. His BSc degree is in Electrical Engineering from Jordan University of Science and Technology, Irbid, Jordan in 2010. Currently, he is an assistant professor in Applied Science Private University, Jordan. His research interests include smart grid and renewable energy applications.