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Scientific Reports
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Nature Publishing Group UK London

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10.1038/s41598-024-71902-5
Article
Energy and throughput aware adequate routing for wireless sensor networks using integrated game theory method
Vivek Kumar M. vivekkumar3987@gmail.com

1
Saraniya O. 2
1 https://ror.org/02f1z8215 0000 0004 1788 0913 Department of Electronics and Communication Engineering, Sri Eshwar College of Engineering, Coimbatore, Tamilnadu 641 202 India
2 grid.252262.3 0000 0001 0613 6919 Department of Electronics and Communication Engineering, Government College of Technology, Coimbatore, 641013 India
9 9 2024
9 9 2024
2024
14 209965 5 2024
2 9 2024
© The Author(s) 2024
2024
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A Wireless Sensor Network (WSN) is usually made up of a large number of discrete sensor nodes, each of which requires restricted resources, including memory, computing power, and energy. To extend the network lifetime, these limited resources must be used effectively. In WSN, clustering constitutes one of the best methods for optimizing network longevity and energy conservation. In this work, we proposed a novel Energy and Throughput Aware Adaptive Routing (ETAAR) algorithm based on Cooperative Game Theory (CGT). To achieve the energy efficient and improved data rate routing in WSN, we are applied two game theories of CGT and coalition game. The main part of this routing mechanism is cluster head selection and clustering the nodes to perform energy efficient and throughput effective communication between the nodes. In first stage, CGT based utility function which adopts both energy and throughput is utilized to handpick the CH nodes. In the second stage, along with the energy and throughput, average end-to-end delay is considered for the adaptive time slot transmission to avoid collision in the coalition game approach. MATLAB tool is used for simulation. The simulation results shows that the proposed ETAAR protocol is outperforms than earlier works of routing in terms of residual energy, PDR, energy due ratio, average end-to-end delay, dead nodes. The network lifetime of 48% extension, energy saving of 60% and 52.5% of delay shortage attained in ETAAR.

Keywords

WSN
Routing algorithm
Scheduling in nodes
Network lifetime
Energy efficiency
Throughput
Game theory
Clustering
Cluster head selection
Subject terms

Electrical and electronic engineering
Computational science
Computer science
Information technology
issue-copyright-statement© Springer Nature Limited 2024
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pmcIntroduction

The term "wireless sensor network" (WSN) refers to a type of network in which individual nodes, or sensors, collaborate to collect data through sensing, computing, and communication. Many applications, including the observation of ecological processes (e.g., air pollution levels and warming temperatures), can be supported by the deployment of WSNs. A base station receives the information collected from each of the sensor nodes and processes it further1. Energy saving is a crucial architectural criterion for WSNs as they are usually installed in distant locales or across wide distances2. Regardless, it is usually not a practical choice to swap out exhausted batteries for an enormous number of networks or perhaps a small number of difficult-to-access nodes3.

Sensor nodes, base stations, and monitoring events, that is, incidents that must be detected in the surrounding environment are the parts of a WSN4. Four components typically comprise a sensor node: an energy system, the communication system, a unit that processes data, and a sensor device5. A node's sensing element evaluates expected environmental characteristics, such as temperatures or moisture content of the soil, in the environment in which it is installed. The data processing element is in charge of gathering and handling information that has been acquired from its surroundings6. A sensor node's wireless connectivity element is in charge of sending and receiving collected information to and from additional sensor nodes, as well as to end users. Energy is necessary for the sensor node's computing and communication features to operate as intended, and the electrical component, which has a restricted supply is the only one accountable for supplying all three additional elements with energy5. The structure of a WSN is depicted in Fig. 1.Fig. 1 WSN architecture.

Each component of the system needs to be thoughtfully built to be ecologically conscious in order to sustain the sensors in the network over extended periods of time. One way to reduce energy usage in wireless sensor networks is to cluster nodes that sense into groupings such that the sensors only provide data to the cluster heads, which then relay the collected data to the base units.

We need to find innovative approaches to improve the energy balance and efficiency in WSNs because the node power supply are limited and non-rechargeable. Because of the finite lifespan of sensor batteries, researchers are attempting to extend the useful life of these devices by developing more efficient routing protocols. The scalability of a WSN is ensured by grouping sensor nodes into clusters, which is a common practice in WSNs. Additionally, it ensures that the network's limited resources are used efficiently, which helps to save energy and maintain network stability. In order to minimize interference among the SNs, decrease the system's total energy consumption, and make optimal use of resources, clustering algorithms are implemented in sensor networks. Cluster Head (CH) information pooling technique lowers SN energy consumption by reducing communication-related energy utilization. Deploying clustering also helps with load balancing, which means the network will last longer. The goal of clustering is to increase the lifetime of the network by distributing the work among the CHs in an equitable manner.

Sensors must be positioned in clusters, particularly for wireless sensor networks with a high number of electricity-constrained sensors, in order to minimize the amount of energy used during data transmission from terminals to the base station6. A tremendous amount of study has been done on clustering techniques to lower node usage of energy in a wireless network switch. The multilevel navigation method used in the LEACH protocol allows nodes to be arranged into groups or collections. For the purpose of developing clusters and cluster head election, these procedures simply include residual energy into account. The low-rate-high-energy issue may result from this. For this reason, Rotating Energy Efficient Clustering for Heterogeneous Devices7 has been designed to take into account node operations and remaining energy while electing and rotating leaders. There is also other works of heterogeneous WSNs like ER-HEED8, RUHEED9, UHEED10, FMUC11 and M-LEACH12 for routing problem.

The primary functions of LEACH are divided into two distinct phases. The two processes in the initial stage, often known as the beginning stage, are clustering and cluster head determination. The term "second stage" refers to a stable stage in which data collection, gathering, and transmission to a destination are the main objectives. A dynamic clustering technique called BCDCP13 enhances network longevity and average savings on electricity by equitably distributing the loss of energy between every sensor node. According to simulation data, BCDCP outperforms LEACH, LEACH-C14, and PEGASIS in terms of network longevity and total energy usage. A multilevel energy-efficient routing system is called HEARP15. HEARP is built upon the PEGASIS and LEACH protocols. It is better to develop the protocol for routing for WSNs utilizing game theory. To the greatest extent of our understanding, game theory-driven protocols for routing in WSNs have only been explored in two previous survey publications16,17. Four protocols were evaluated in16: the Nash equilibrium method for integrated flow management and routing21, flowing and networking control policies with multiple users competing for resources19, evaluation of a multi-stream games for routing with multiple paths20, and competing networking with exponential expense18. A game theory-based collaborative, energy-aware, and information-aware navigation algorithm was studied in17. Four protocols have been investigated in22: using game theory for dependable routing exhibiting in WSNs25, game theory-driven energy-balanced routing algorithm for WSNs24, extending the network lifespan via nodes energy distribution in diverse WSNs23, and anticipated energy-aware routing that employs dynamic game theory in WSNs26.

In this paper, we design a novel and efficient clustering-based routing algorithm named as Energy and Throughput Aware Adequate Routing (ETAAR) algorithm. In this ETAAR protocol, we applied the cooperative game theory for selection of cluster head (CH). The main contributions of the work as follows:With the support of game theory in WSN, an energy-balanced partitioning algorithm is proposed to split the whole network into multiple small clusters. In each clusters, there is only one CH, and every node can communicate with the CH directly and BS via CH.

Selection of CH node in the segmented cluster using energy as one of the metric, it incorporates the proficient utilization of restricted energy assets of nodes present in WSN to prolong the network lifetime.

An energy-efficient and throughput balanced routing algorithm is developed to optimize the performance of inter-cluster communications.

The proposed work is segmented as four stages. It started with prediction of neighboring nodes of each sensor node. Once the forwarding nodes set is tabulated, selection of cluster head node is performed by using cooperative based game theory (CGT) with the utility and payoff function. This payoff function is derived by relating the energy, throughput, distance and channel path loss. In third stage of implementation, CH will be evaluating the sensor node to form cluster with cluster member of each CH. Finally, data transmission with adaptive time slot allocation for each communication is defined. This proposed algorithm resolves the issue of energy sufficient and proper packet transmission using ETAAR.

The enduring paper is structured as follows. Section II stated the literature review of the clustering-based routing in WSN. Section III holds the detailed information about methodology of proposed ETAAR algorithm with mathematical modelling of each stage. Section IV is results and discussion of simulated implementation of ETAAR with comparison of earlier works. Section V concludes the session.

Related works

We discussed the variety of routing methods used in WSN in this part. Following an extensive analysis of every one of the protocols that have been released thus far, we discovered that three different game types cooperative, uncooperative, and evolving games were utilized in WSNs to design routing protocols. A method for choosing actions in tactical contexts where it's important to take different players' opinions and logical options into consideration is cooperative game theory27. For shared assistance, the creation of coalitions is encouraged if working together yields additional benefits. In cooperative games, our attention is directed toward the coalitions that will determine the team's actions that are taken together and the group reward that follows. We refer to coalitions that consist of multiple actions from the particular action set as joint actions. Coalitions are thought to provide a collective benefit since they include several players.

We examine the non-cooperative gaming concept when player collaboration is prohibited. Necessitating a separate action by any player to reach a solution position where nobody can enhance the outcome is called a non-cooperative a state of equilibrium or Nash equilibrium. The actions of an enormous number of individuals that frequently communicate strategically is explored in evolving game theory. The many activities requiring collaboration of different species in a population are the fundamental ideas of adaptive games. Since the interactions that any of these creatures have with one another play a major role in their success, the viability of an individual should not be evaluated in isolation but rather in the context of its whole community.

Reputation is among the most useful instruments for evaluating partnerships and motivating their actions28. Although cooperative, this method is heavily reliant on the networks' reputations. Because of this, we have decided to categorize it as a distinct kind of game and apply it to the creation of routing protocols for WSNs. The comparison of these game-based routing is tabulated in Table 1. To focus on our main objective energy efficiency is attained in cooperative game theory-based routing than the other methods. The cooperative game-based routing methods are compared in the Table 2.Table 1 Game based Routing protocols.

Game	Key Characteristics	Comparative Attributes	Routing Measures	
Cooperative

game theory

	Taking into account the logical decisions as well as needs of additional nodes in a WSN's routing game	In games intended for routing, legally enforceable contracts are required for mutually advantageous outcomes	Taking into account the packet delivery proportion and energy as routing measures	
Non-cooperative

game theory

	Examines the scenario in which, if an individual follows specified methods, neither of the nodes with sensors may profit more from any action made after a specific moment	Achieving Nash equilibrium is a prerequisite for effective implications	Takes energy into account as the primary routing measure for the majority of protocols	
Evolutionary

game theory

	Does not have to take into account alternative routing nodes' choices	The consequence of this kind of approach requires an evolutionary sustainable one	Takes network lifespan into account as the main routing measure	
Reputation-based

games

	In this kind of game, the nodes cooperate	Evaluates the standard of the partnerships and provides incentives for their actions	Takes into account the network lifespan and the mean throughput in the navigation protocol	

Table 2 Cooperative Game Based Routing Algorithms.

Protocol	Algorithm	Clustering Method	Communication method	Advantages	Disadvantages	
CH-C-TEEM 129	To create such small networks for collaborative transfer of information, CH-based collaborative MIMO	Centralized	Single path	Energy conservation is the result of CH cooperation

Taking into account network safety through the removal of harmful nodes

	No consideration is given to routing parameters such as packet delivery ratio and end-to-end latency

In terms of significant routing metrics, compare with a greater percentage of the current cutting-edge routing methods

	
RCFR 230	The cost-effectiveness concept is used by the Consistent Coalitions Construction Routing protocol to choose an acceptable path inside the network	Centralized	Multi path	Continual route management and information transfer

Interoperability with additional standards

	No consideration for node failure scenario	
Assignment game

approach31

	Established an identifiable purpose in addition to the utilitarian function to assess the communication nodes' cost-effective capabilities	Distributed	Single path	Exceptionally energy-effective and capable of handling a large number of connected devices	Disregard for the subsequent connections	
PRGT 332

_

	A probability incentivized routing strategy for OppNets transmitting messages	Distributed	Multi path	Preventing egotism and fostering collaboration between nodes to improve routing and reduce energy consumption	Unsuitable for architecture that has distributed components	
ASFO-IEHO33	Fuzzy adaptive sailfish optimization for CH selection and IEHO for energy efficient shortest path selection	Centralized	Multi path	Energy conservation is high

Fast route prediction

	The complexity of the system is high	
K-IABC & CL-HHO34	K-medoids based clustering and cross layered optimization based routing	Centralized	Single path	Energy efficient

Reduced transmission delay

	Selection of path is based only on power which degrades the PDR of system	
CGC35	Cooperative game theory to form the cluster by self-configuration	Distributed	Single path	Energy saving

Reduced transmission time

	Not concentrate on the transmission security	
EECGTC36	Energy efficient clustering based on CGC	Distributed	Single path	Prolonged lifetime	No support for long distance transmission	

In order to reduce the unnecessary energy consumption of sensor nodes during the idle listening stage and avoid the energy burden caused by frequent switching between the active and sleep states, we employ game theory to discuss the transition of the node from the active to the sleep state in this paper. The result is an energy and throughput efficient clustering algorithm (ETAAR). The use of dynamic scheduling to allocate transmission slots also improves PDR. This accomplishes the goal of increasing the network's throughput and making the most of sensor nodes, which in turn increases the network's life cycle.

Proposed methodology of ETAAR based routing using game theory

In this proposed model of ETAAR, we are implemented the effective routing protocol of WSN by utilizing the concept of Game Theory. In this section, we described each stage of methodology in the ETAAR routing protocol.

Preliminaries of game theory

A basis for identifying the character of an interactive decision-making scenario is provided by game theory. In collaborative applications, where players attempt to achieve maximum or decrease payoffs according to tactics, it offers a technique to forecast the types of participants. The games fall into one of two categories: cooperative or non-cooperative. Cooperative games are essentially defined as sharing the costs games that prioritize achieving aggregate benefits while taking different expenses and motivations into account37,38.

A game typically has three components: a group of players, a collection of individual player tactics, and a set of related utility functions. A 3-tuple H =  < M, R, V > gives the typical format games of a WSN with n sensor nodes. Here, M = {m1, m2,…, mm} is a finite collection of the sensor nodes, and H is a specific game. The solution category of the sensor node that K can choose from, denoted by Rk (k = 1, 2, …, m), is R = {R1, R2, …, Rm}. The equivalent payout function of node k, denoted by vk (k = 1, 2,…, m), is V = {v1, v2,…, vm}. The utilitarian value that each node gets at the conclusion of an action is vk.

For a player, an approach is a comprehensive plan for taking action for every scenario that might arise throughout the game. In an attempt to optimize their outcomes in accordance with their desires, the participants attempt to act unjustly. The reward functions must be created in an approach that will assist node K in choosing a course of action. It stands for the optimal reaction to the tactics chosen by the remaining k-1 nodes. In this case, rk represents the specific strategy selected by node K, while r-k represents the specific strategies selected by every other node in the game. It is referred to as a technique characteristic or occasionally a strategy combination for approaches r = {rk, r − r}. Each unique mix of a person's chosen tactics might result in a distinctive approach profile. The nodes responsive to a Nash Equilibrium (NE) must be placed using the technique profiles r = {r1, r2, …, rm∣ rm ∈ Rk, i = 1, 2, …, m}. It is a notion for a solution that depicts the constant state of a game comprising multiple players, where each player is said to be aware of other players' equilibrium plans and neither player stands to benefit by independently altering its plan of action39. NE is defined as the situation in which none of the nodes will logically decide to change from his selected course of action since doing so will reduce its utility, i.e., vk (rk, r-k) ≥ rk (rk*, r-k) for every rk* ∈ Rk.

Every conceivable game result is assigned an integer determined by a utility coefficient that describes the needs for a specific player, with the characteristic that a larger number indicates a more favored result.

Basics of cooperative game theory

Several nodes will band together and create a coalition in order to lower the overall energy usage of the WSN and increase its lifespan. The theory of collaborative games is also referred to as coalitional game theory since it is one of the most significant types of cooperative game theory40. Cooperating organizations develop in a WSN that adheres to the cooperative game theory, and participants make decisions based on how best to optimize the utilities of their respective groupings. By establishing coalitions, coalitional game theory enables a decrease in energy usage in WSN.

Transferable-utility games41 and non-transferable-utility games42 are two more areas of cooperative game theory. The evaluation of the distribution game's payout is convertible in the TU game. In accordance with the theory of coalitional games, m sensor nodes form the game through a triplet H =  < M, v, R > distinctive form, where M = {1,…, M} is a predetermined group of players known as the big coalition (the coalition that includes all nodes; it is not ideal), R = {R1,…, Rl} indicates a coalitional organization and the division of M, and v is a distinctive parameter related to coalition value that determines the significance of a coalition in a game. In the cooperative coalitional game H, players aim to fortify their advantages by forming cooperation coalitions. Every coalition Rk(k = 1,.., l) denotes a consensus among the participants in R to behave as a single unit. Nodes within a coalition exchange measures in order to determine a specific location.

Assuming a clustering-based routing procedure, nodes with sensors determine their remaining energy to determine whether or not to become the cluster head (CH). Game theory states that a game can be expressed as G = (P, A, S, ui), where i = 0, 1, 2, : : :, n, and Q = {MG, ML} is a set of players, MG representing higher energy nodes and ML representing low-energies nodes. Methods are denoted by S = {Choice about becoming a cluster head, maintaining as a typical cluster participant}, and decisions and actions are portrayed by B = \MG, ML}. When a node has more residual energy, or energy remaining in the node. This reasoning is the one that players in this type of game must possess. There are two activities mentioned in the set A description. This collection is referred to as a game's activity characteristic. For node i which has greater energy, the return on function ui is provided by,1 ui=ri-ci

Hence, for the procedure that node K selects, sk and dk stand for the benefit and retribution, respectively. For instance, the return on investment is 10 if the node receives a 20 payment and 10 penalties for being a CH. In this case, nodes must evaluate their residual energy to one another and choose who should be the CH as a group. They employ two acts collectively in the procedure collection, which we might refer to as collaborative actions. Because they are accomplished by cooperative coalition, the benefits they produce are shared benefits. Nash equilibrium is reached when two players select two separate approaches and there fails to be another which will increase the benefit if one selects another approach, and the remaining players keeps the approach they first selected.

Basics of non-cooperative game theory

In contrast to cooperative game theory, non-cooperative game theory operates on the premise that players act independently and do not form alliances, making decisions solely based on their self-interest without binding agreements. The central focus in non-cooperative games is on finding strategies for individual players to maximize their personal payoff or utility. If a non-cooperative game reaches equilibrium, it typically manifests as the Nash Equilibrium (NE), where each player's strategy is optimal given the strategies chosen by others. While this approach doesn't guarantee the most efficient outcome (as opposed to the optimal Pareto utilization), it provides insights into decision-making processes among players with diverse interests. Notably, in non-cooperative games, any form of cooperation must emerge organically, without direct communication among players43.

The designed game consisted of N players (sensor nodes), where N = {i1, i2, i3, : : : , in}. Each player i had its own finite set of possible strategies. The strategies declared were the combination of the next forwarding node and transmission power level. A pay-off function to map the strategies was also designed. All the players in the game were bound to choose a strategy that would reduce the long-term cost and increase longevity. Consequently, the game was mentioned as an incomplete information game. The nodes could maximize their benefit by choosing the transmission energy level and optimal path towards the sink node. In every iteration of the game, pay-offs were generated based on the mentioned parameters. The utility of a chosen strategy for the ith node was addressed as Si. All the other players had a strategy S-i. The designed utility function of the game model in this routing scheme was:2 UncoSi,S-i=LRpi+fγi-EEr+DelayDr

3 fγi=1-2Pe2

where R bit rate of L information bits, fγi is the efficiency function, E is initial energy and Er is reference energy, Dr is reference delay, pi is the power level of nodes i and Pe is the BER of bit 2.

Network model

Figure 2 depicts the Network topology which we considered for the implementation. Sink node is placed at the center top of the network surface and sensor nodes are formed as clusters with each Cluster Header. Number of nodes in each cluster except CH is called as member nodes.Fig. 2 WSN Network Structure Model with Clustering.

The assumptions considered in the network model of WSN as follows,Every node is dispersed independently to gather information regarding environmental conditions.

Every node's geographical position remains constant, making it possible to determine the distance between any node and the base station.

Every node's information gathered packet dimension is equal.

Every node can function as either a cluster head or a sensing node, but not both, during each round.

Every sensing node's primary responsibility is to gather information and anticipating it to the appropriate cluster header.

The entire network employs the identical quantity of energy, and each one node's remaining energy can be calculated at BS employing power transmitting and the associated transmission expenses.

CHs are in charge of obtaining information from sensing nodes, combining it, and transmitting it to BS

BS is in charge of carrying out every computation for every round.

The cluster-head node is in charge of generating the Time-Division Multiple Access plan, which establishes the period of time during which the sensor nodes can broadcast.

Nodes energy model

The initial ordering energy structure of LEACH44 and the suggested protocol's energy structure are comparable. A few energy-intensive tasks performed by the sensors located in the network are shown by the symbols {G,T}: G stands to indicate data collecting from various nodes, and T stands for communicating data to the nodes within the CH45.In addition, each cluster head nodes performs three distinct tasks, denoted by the symbols {R, A, T}, where R stands for accepting information from nodes with sensors, A for combining the collected information, and T for sending the information it has collected to BS.4 EiSN=Ei-eic+eis

5 EiCH=Ei-eir+eig+eis

Thus, the residual energy Ei at any node ni can be obtained by Eq. (4) if it is a sensor node, or by Eq. (5) if the node acts as clusterhead.

In WSN, modelling of energy is obligation to measure the energy consumption for every transmission which is done in each sensor nodes46. For a single hop or direct transmission, propagation model is designed with wireless channel of d2 power loss, where d is distance between one nodes to another. The same way of one hop, multi hop also structured via distance in multipath fading medium propagation model with distance of d4power loss for pack broadcast. Consequently, the energy used in this type of long-distance packet transfer of a JK-bit packet is computed as,6 eis=lEdis+lEampd2,d<d0lEdis+lEmpd4,d≥d0

where,Edis is energy dissipated per bit,Eamp is the energy consumption and d0 is edge distance which is calculated as,7 d0=EampEmp

The amount of energy used to send the communication over the radio is described as8 eir=lEdis

As a result, Fig. 3 illustrates how the quantities of energy for transmitting and acquisition of energy are constructed.Fig. 3 Energy model of WSN.

Optimal CH count

During this stage, the ideal number of CHs and the optimum number of transmitted phases are calculated in this work using the information provided in the research25. The following formula determines the ideal amount of cluster heads (kopt) for a round:9 kopt=N2π×eampemp×MdBS2

where dBS is the Euclidean distance of a node from its base station, the value of N is the total number of nodes that are deployed and M is the dimension of deployed region.

Methodology of ETAAR routing algorithm

In any routing algorithm of WSN, the implementation comes under two stages: Start-Up Stage and Steady Stage. The process involved in these phases using our method is described as follows.

Step 1: Start-Up Stage.

The sensor nodes perceive according to their sensing category, and the neighboring nodes are identified according to their communications frequency. To increase the dependability of WSNs, ETAAR uses game theory to choose nodes that relay messages from the forwarded nodes set, which is made up of a portion of the sender's nearby nodes. Since it significantly impacts the choice of CH node and protocols efficiency, the routing nodes set selection is therefore very crucial in ETAAR. Algorithm 1 provides the routing nodes set method.Algorithm 1 The Detection of Forwarding Nodes Set.

Step 2: Steady phase

In this phase, based on the proposed ETAAR routing protocol, we evaluate the selection of CH nodes and the corresponding data transmission. Each cluster maintains the routing table to decide the optimal route of data using algorithm 2.

Cluster-head selection using cooperative game theory

Because WSNs have limited energy, they need routing methods that are power-efficient for fading environments. The effectiveness of this technique was evaluated using consumption of energy, and it depends on game theory. Sensor nodes may have a shorter network lifespan due to interfering and channel fading47. A CH-based Cooperative Game Theory approach was developed in order to extend the lifespan. As mentioned in31, small groups were formed using the cooperative game theory for cooperative transfer of information. In order to transmit information, the CHs collaborate with one another, and each node progressively becomes a CH. Utilizing a game-theoretic approach, the ETAAR also integrates a throughput-based architecture to minimize packet destruction and routing-related overhead by removing dead nodes, which frequently drop valuable information packets. The structure of a CH election game is as follows:

N is the number of players, or nodes of sensors. A = A collection of options from which a sensor node can choose to make a choice; L is a collection of methods, denoted as {l1, l2, l3, : : :, ln}. In the event that node n1 selects method l1, its value is "0" in the absence of a node's choice to be a CH and "1" otherwise.

The pay-off collection, which is made up of values that are numerically derived from the approach's characteristics, is {u1, u2, u3, : : :, un}. The CH election game's pay-off mechanism is as follows:15 Ui,j=ηErewardij+1-η∗Drewardij+τRrewardi-εn-C

where η is the weight parameter, τ is the weight parameter of thenode’s throughput, ε is the weight parameter corresponding to average path loss, Ereward is the node’s residual energy related cost function, Dreward is node’s distance related cost function and Ri,reward is node’s packet delivery ratio (PDR) cost function.

When choosing vacant nodes, the consequence can be adjusted using the penalty parameter C. The expense function of node I's energy data defines the residual power-related cost function E_reward, which may be expressed as,16 Erewardij=Ei+Ej

and17 Ei=1-eireseiinit&Ej=1-ejresejinit

The distance-related cost function Drewardij is defined as a costfunction of difference of depth between node I and node j, and can be formulated as,18 Drewardij=1-Dlinki,jR

where Dlinki,j represents the distance of link48 established between node i and node j using Eqs. (13) and (14), R represents the maximum transmission range.

The PDR of the node i (Rrewardi) is the ratio between number of packets received (Npr) to the node i and number of packets sent (Nps) from the certain node i which is formulated as,19 Rrewardi=NpsNpr

A coalitional activity is utilized in order to pick out a specific group of nodes for cooperative information transfer and reception. The game is developed utilizing the remaining energy levels of the nodes with sensors that function as players, and the collaborative sites that engage in the exchange of information are selected according to this game. Reducing overall power usage is the goal of this type of grouping. N is a collection of CH nodes, υ is an identifiable operation. The system's distinctive function, which was determined by the network lifespan, is demonstrated by20 vSj=xij=Nlife,∀iϵS

where the network's lifespan is represented by N life and the node's utility is represented by xtj inside the of nodes. Due to this procedure, the duration until the initial node with sensors runs out of power is the network's lifespan. The lifetimes of both of the initial nodes in a coalition that are collaboratively engaging in information exchange are assumed to be L_co1 and L_co2.21 Nlife=min(Lco1,Lco2,Lnon-co1,Lnon-co2)

As shown in Fig. 4, the CHs 3 and 4 work together to transfer data in pairs to the sink node. Additionally, the CHs in clusters 1 and 5 collaborate to transmit their data as a pair.Fig. 4 Cooperative Game based Clustering.

In our protocol, after receiving a packet, a node uses Algorithm 1 to identify whether or not it is a transmitting node. If this is the case, the node uses Eq. (15) to compute the U value and determines the holding time using the dynamic scheduling technique that is suggested in Section III-H. If not, the packet is discarded. When the holding period expires, nodes will modify the matching information in the message to reflect their current data and proceed on. As soon as the sink receives a packet, it ceases to relay it and broadcasts the information to nearby nodes. Algorithm 2 displays the pseudo code for the cooperative game-based CH node selection.Algorithm 2: ETAAR: CH selection based on Cooperative Game Theory

Cluster formation

The cluster formation remains the same as in the traditional LEACH i.e., the nodes selected as the cluster leader advertise itself and the nodes become the member of the cluster on basis of the strength of the signal received from the cluster leaders as in algorithm 3.Algorithm 3: Cluster Member Formation

Adaptive time slot allocation for dynamic scheduling

After the retention phase has passed, the ACH node forwards packets. Nevertheless, when a packet of data is carried by several CH nodes at once, it will eventually collide, and choosing a less-than-ideal CH node to forward also reduces WSN efficiency. Thus, we must provide each CH node a forwarding priority and make absolutely certain that the best one can transmit packets initially in order to allow packets to proceed over the international optimal routing pathway and minimize packet collisions. The ETAAR procedure exhibits a negative correlation between the holding time and the U value, meaning that a higher U value is associated with a shorter period of holding. In order to increase time effectiveness, we take use of data exchanges between neighboring nodes, take into account node i's relative U value, and construct as23 fU=U-Ulast,U<Ulast0,U≥Ulasts.t.U<0

where Ulast is the U value of the optimal relay node sender in final transmission. Considering that the maximal propagation delay (tmax) with propagation speed v can be represented by,24 tmax=Rv

The waiting period makes guarantee that node 2 has access to the data packet that node 1 delivered before forwarding it and suppresses redundant transmission with the constraint of,25 δ≥tanh-fU1-tanh-fU2

The holding time of each node i is derived by,26 ti=tanh-fQi.2tmaxδ

Packet transmission algorithm

The method of transmitting information is explained by Algorithm 4. Initially, devices that have zero or less remaining energy have been classified as dead and are unable to send information. However, devices can connect immediately to the base station without the need for an intermediary device if they are in the transmission range of the base station and have the greatest U-value in their area. However, if the CH is also far away, devices that are located far from the base station remain capable of sending packets to it by way of another nearby device that is a part of the same cluster.Algorithm 4: Packet Transmission Scheme

The flowchart of cooperative game theory-based clustering is shown in Fig. 5. In this figure, the red highlighted parts are the conventional LEACH and shown the overall steps of the CGT clustering with cooperative CH named as CCH included with LEACH steps.Fig. 5 Cooperative Game Theory based clustering.

The heads of the cluster are responsible for creating and disseminating the TDMA schedule. Each cluster node is given a transmission window by the TDMA schedule. So, the sensor nodes can go into sleep mode to save power. Using the TDMA method further guarantees that the cluster will not have any collisions. When communicating with the base station, the cluster-heads provide the aggregated data via the CSMA/CA MAC protocol.

Results and discussion

Simulation settings

For simulation of this proposed algorithm ETAAR, we considered platform of MATLAB 2020a version with 64-bit operating system of 8 GB RAM and Inter core i3-5005U CPU @ 2GHZ configuration. The performance comparison of proposed ETAAR is considered along with recent existing routing algorithms of EECA49, PECR50, PEG-RDA51, and GCEEC52. The simulation environment variables specifications are listed out in Table 3.Table 3 Network Model Configurations.

Parameter	Value	
Network Length x Width	250 × 250 m	
Coverage Range	50 m, 100 m, 150 m	
Number of Sensor Nodes	50 to 450	
Number of Sink Nodes	1	
Sink Coordinate(X,Y)	(125,275)	
Nodes Mobility	Static	
Percentage of CH	0.1	
Initial Energy (E1)	0.5 J	
Energy dissipate per bit (Edis)	50 nJ/bit	
Energy loss of amplification fading (Eamp)	10 pJ/bit/m2	
Energy loss of multi path fading (Emp)	0.0013 pJ/bit/m4	
Data Aggregation Energy (Eg)	5nJ/bit	
Packet Size (lbits)	3200, 6400, 12,800	
Number of Rounds	1000	
Weight coefficient of node’s residual energy (η)	0.2	
Weight coefficient of node’s Throughput (τ)	0.4	
Weight coefficient of node’s average path loss (ε)	0.1	
Penalty Constant (C)	0.1	

Performance metrics

(i) Packet Delivery Ratio27 PDR=PrPt

where, Pr is the overall packets that the sink received and Pt is the overall packets sent from the sensor nodes.

(ii) Average End-to-End delay28 Tdelay=Tr-TsPt

where, Tr is the packet received time at the sink successfully and Ts is the packet transmitting time at the source node. Average time delay is calculated as the ratio of total time consumption to the total packets transferred.

(iii) Energy due ratio

The Energy Due Ratio can be described as a combination of the amount of deployed networks (n) and the amount of packets that are received by the sink (Pr), divided by the amount of energy used. It is provided by29 Edue=Econsn∗Pr

(iv) Number dead nodes

The network lifetime is calculated by certain nodes sustainability with residual energy for the number of rounds. When the residual energy of specific nodes is empty, it will be denoted as dead node at the corresponding round of routing.

(v) Residual Energy

The residual energy of each node is the difference between initial energy and consumed energy.30 Eres=Einit-Econs

Simulation of network configurations and clustering

Figure 6 illustrates the network topology of 100 nodes with the area of 250 × 250 m. Red circled points are sensor nodes and green squared marker is Sink node of the WSN. As we stated in the network model, the position of each nodes under the area is randomly distributed in Fig. 6. In Fig. 7, we can see that the link availability between one node to another in the network. The communication range of the topology we considered that 50 m. Each blue lines are shown in Fig. 7, is the transmission line established.Fig. 6 Network Nodes positioning of WSN.

Fig. 7 Network neighbor detection with R = 50 m.

The CGT based cluster head selection for proposed ETAAR routing is implemented for the above topology of WSN and selected CH nodes are highlighted as black marked square and mentioned with CH.id in red font bold in Fig. 8. The highest U value nodes are elected as CH nodes in Fig. 8. Once the cluster head is selected, the cluster members ofparticular CH nodes to be predicted to form the number of clusters and for an efficient transmission, the clustering should be in proper and effective manner to accumulate the energy efficiency performance all over the rounds of processing.Fig. 8 Cluster Head Selection using ETAAR.

As per the algorithm 3, cluster member formation is implemented for the selected CH nodes are shown in Fig. 9. In each cluster every cluster head is shown in magenta color and the corresponding cluster members are linked with transmission to their respective CH nodes in Fig. 9.Fig. 9 Cluster Member Formation after CH Selection using ETAAR.

Performance comparison of proposed ETAAR

As the number of nodes in the WSN increasing, the dead nodes in the process of routing will increase as shown in Fig. 10. The performance is captured under the 1000 rounds of routing for each method. ETAAR achieved less dead nodes than other earlier works which means it retains the network lifetime of WSN compared to EECA, PECR, PEG-RDA and GCEEC of 23, 52, 65 and 100 nodes reduced in ETAAR respectively.Fig. 10 Performance of Number of Dead Nodes.

Figure 11 depicts the performance of residual energy with different number nodes configuration of WSN. Compared to EECA, PECR, PEG-RDA and GCEEC of existing methods, ETAAR achieved the highest residual energy. ETAAR attains energy efficiency even at the highest round of routing. With the initial energy of 0.5 J, at 50 nodes of network, ETAAR has the residual energy of 0.3 J and at 450 nodes it is 0.2 J. This energy level is 100% higher than GCEEC and 25% higher than the PECR as in Fig. 11.Fig. 11 Performance of Residual Energy Vs Number of Nodes.

Throughput is denoted as the successful PDR which increase when the amount of nodes in the network increasing. The PDR performance is illustrated in Fig. 12. The PDR of ETAAR is 0.971254 at the lowest network nodes of 50 and it reaches 100% of PDR at 250 nodes itself.Based on the Energy and throughput reward highest value the process of transmission fixed in the ETAAR. So, it enables the success packet forwarding to improve PDR effectively.Fig. 12 Performance of PDR Vs Number of Nodes.

The five procedures' end-to-end delays steadily drop, as seen in Fig. 13. This is because a node's neighbors also rise in tandem with the amount of deployed nodes. Packets might then be forwarded by using the more suitable CH nodes. ETAAR outperforms the other four approaches in terms of end-to-end delay. Due to its lack of a global viewpoint, GCEEC has trouble determining the best routing path, which results in a significant end-to-end latency. The suggested protocol has a minimal end-to-end latency because ETAAR adjusts transmission time based on the relative U values.Fig. 13 Performance of Average Number of Nodes Vs End-to-End Delay.

The energy due proportion of the ETAAR and the four current protocols grows gradually, as seen in Fig. 14. This is due to the fact that as sparse nodes are deployed into dense nodes, more nodes become qualified to forward packets, resulting in increased energy usage during packet sending and receiving. Because our suggested ETAAR performs routing choices at receivers and does not require information maintenance, it has a low energy due ratio and uses less energy overall. As shown in Fig. 14, the energy due ratios for ETAAR, EECA, PECR, PEG-RDA, and GCEEC for the design of 450 network nodes are 3, 4.5, 4.7, 5.5, and 5.9.Fig. 14 Performance of Energy Due Ratio Vs Number of Nodes.

Performance of different parameter variations

Different transmission ranges

In this section, we are evaluating the effectiveness of suggested and existing protocols with different transmission range of R = 150 m, R = 100 m and R = 50 m.

Figure 15 shows the performance of network lifetime with number dead nodes counting as increasing N from 50–450 for proposed ETAAR with different R values. As increasing R from 50 to 150, the dead nodes of network will reduce. This is because when we increasing the transmission range, the nodes which involved in the transmission and reception from source to sink decreases.Fig. 15 Network Lifetime of ETAAR for different Transmission Ranges at round of 1000.

Due to energy consumption increases as increasing the transmission range as stated in last figure, residual energy getting reduced for the same case of scenario. Figure 16 shows the residual energy of ETAAR at different ranges of R from 50–150. Low transmission range R = 50 m retain the low residual energy than remaining two conditions.Fig. 16 Residual Energy of ETAAR for different R, at round of 1000.

Figure 17 illustrates how the end-to-end latency rapidly reduces as the communication distance increases. This is due to the fact that as communication range increases, fewer connections are needed to reach the sink, which lowers node transmissions and computation delays. Conversely, the communication area includes better-suited nodes, which may lead to the selection of more suitable CH nodes.Fig. 17 Average End-to-End Delay of ETAAR for different R, at round of 1000.

The PDR of an enhanced communication length grows steadily, as seen in Fig. 18. This is essentially a growing communication range includes more neighboring nodes of the recipient for packet forwarding, expanding the routing path and enhancing transmission efficiency.Fig. 18 PDR of ETAAR for different R, at round of 1000.

The power due ratio of an expanding communication range grows progressively, as Fig. 19 illustrates. This is due to the fact that as communication range increases, fewer hops are needed to transfer data from the node that originates to the sink, which lowers the number of packets that need to be forwarded and, therefore, the energy used during transmission.Fig. 19 Energy Due Ratio of ETAAR for different R, at round of 1000.

Different packet sizes

At the same time, we are analyze the results of routing mechanism under different packet size of l = 3200bits, l = 6400 bits and l = 12,800 bits.

When the packet size of transmission increases, it will increase the energy consumption of each node which involved in the transmission route and mainly selected CH nodes. Because, CH nodes performing the receiving of packets from the sensor nodes and transmitting it to the sink. So automatically the dead nodes increased when packet size increases. This performance is shown in Fig. 20 for proposed ETAAR with three different packet sizes.Fig. 20 Network Lifetime of ETAAR for different Packet Sizes, r = 1000.

When the packet size increases the energy dissipation at every stage of processing for each node in the network increases and Fig. 21 depicts the residual energy of proposed ETAAR with the different packet sizes. It shows that the residual energy reduced when the packet size increased to 12,800 bits of processing.Fig. 21 Residual Energy of ETAAR for different Packet Sizes, r = 1000.

The end-to-end latency with growing packet dimensions grows steadily, as seen in Fig. 22. This is because the end-to-end delay and additional time cost at each CH node are caused by the transmission delay increasing with packet size. Figure 23 illustrates how the PDR resemble one other as packet size increases. This fact is mostly due to several neighbors receiving packets and working together to forward them, which effectively lowers the packet loss rate. The energy due ratio of rising packet size grows progressively, as seen in Fig. 24. This is mostly due to the fact that when packet sizes rise, so does the energy cost involve in packet transmission. Furthermore, the formation of superior CH nodes as the total amount of nodes rises has increased the efficiency of the network, as seen by Figs. 22, 23, 24.Fig. 22 Average End-to-End Delay of ETAAR for different Packet Sizes, r = 1000.

Fig. 23 PDR of ETAAR for different Packet Sizes,r = 1000.

Fig. 24 Energy Due Ratio of ETAAR for different Packet Sizes, r = 1000.

Conclusion

To improve the energy efficiency along with throughput of transmission in routing of WSN, we proposed a novel cooperative game theory based ETAAR protocol in this work. By concentrating on both energy and throughput in the selection of CH nodes and unique time slot allocation mechanism, we achieved optimal solution for low complex routing for WSN. The simulation results of different metrics such as dead nodes, residual energy, PDR, average end-to-end delay, energy due ratio is carried in this work to prove the efficiency of the proposed ETAAR. In all these aspects, ETAAR provides the best results than the literature works. Especially our objective of increasing the residual energy to prolong the network lifetime by 0.1 J to 0.2 J than existing methods, and increasing the throughput by 20% to 30% with 1000 rounds of execution. Also, the major factor of delay to complete the communication between nodes and sink is also reduced to 50%, i.e., 6 s of delay with 50 nodes in GCEEC is reduced to 2.85 s in ETAAR algorithm. For future work, we can concentrate on void region mechanism to increase the secured and drop less transmission of packets.

Author contributions

M.V.K. wrote the main manuscript text and O.S. prepared Figs. 1–24. All authors reviewed the manuscript.

Data availability

The datasets used and/or analysed during the current study available from the corresponding author on reasonable request.

Competing interests

The authors declare no competing interests.

Publisher's note

Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.
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