# Modern Energy Optimization Approach for Efficient Data Communication in IoT-Based Wireless Sensor Networks

Authors: L. Sathish Kumar; Sultan Ahmad; Sidheswar Routray; A. V. Prabu; Abdullah Alharbi; Bader Alouffi; S. Rajasoundaran
Journal: Wireless Communications and Mobile Computing
 (2022)

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## Abstract

Many researchers are drawn to mobile wireless sensor networks (WSN) and the Internet of Things (IoT) because of the significant challenges of power consumption and network connectivity. A technique that takes into consideration the characteristics such as network probability, the identified region of individual nodes, and the radius of the whole identified region is presented in this article. Free-space propagation is carried out in the region of interest. This approach assures network connection, long-term communication sustainability, and maximum energy efficiency. It was discovered that a mathematical network model can be built using the probability theory. It has been possible to examine and evaluate the changes in sensor nodes as a function of distance from the detection region using this approach. As a result, a correlation has been established between a network’s communication radius and the identified region. Additionally, a novel method has been developed to reduce energy consumption and sustain connectivity through boosting the connectivity feature. Notably, IoT-based WSN architectures require more energy optimization than any other network, because they have resource-limited nodes. Also, a simulation plot of the proposed approach’s mathematical network scheme is shown to show if it works. The proposed method consumes much less energy averagely 40% compared to the existing methods, which are LEACH, ZTR, and DSR when the radius is 100.


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## Body

## 1. Introduction

Nowadays, wireless device and IoT device usage is increasing. For that reason, low power consumption and minimum cost systems are integrated with mobile applications. This integration happens with the support of low power and minimum cost sensor nodes. This system is defined as an IoT-based wireless sensor network because it self-organizes itself. It is common to practice to utilize these networks to monitor the environment, weather conditions, combat surveillance, structural health monitoring, and clinical factors. It all comes from the sensor nodes, which then send it to the IoT network’s control stations.The majority of the sensor network is powered by batteries, which are included in the package. Undersea communication, natural catastrophes, implantable nodes, and a variety of other critical circumstances are all possible. Battery life and energy consumption must be minimized while the appropriate level of network connectivity is maintained for the network to function properly [1]. As a result, a WSN’s ability to sustain its energy level is directly correlated to its ability to use less power [2, 3]. The battery life is also extended as a result of the reduced power usage, allowing the network to operate more effectively. At the same time, IoT-based networks use various types of sensor nodes and gateway nodes.In addition to determining network topologies and power allocations, network connectivity is a critical consideration in network planning and design. Several scholars have worked to improve network connection and minimize energy usage by proposing better solutions, both theoretically and practically. Percolation is a branch of graph theory and a probability that is used to investigate various network configurations [4]. There is a lot of scientific and social research that is used as a starting point for looking at different graphs based on how quickly things move.As a follow-up study to previous research, this paper investigates the optimal level of power for a given node and its coverage to ensure network connectivity. The most energy-intensive function for an IoT sensor node is data transmission. As a result, the transmit power of a sensor node directly affects its coverage area and the other way around. The node coverage and network connection will be harmed if the transmit power is reduced to extend battery life. As a last resort, more closely spaced nodes may be necessary. The location and distance between nodes in mobile sensor networks are stochastic, necessitating probabilistic modeling to estimate power coverage enhancement. The IoT-based MWSN’s main difficulty is to sustaining connectivity while upholding energy levels, by way of the fact of interaction changes at every point in the network. Data transfer is a critical part of this project, as it must be done quickly and efficiently while also ensuring that the network’s connectivity is maintained. This study presents an IoT WSN model that seeks to achieve this goal. The suggested model is tested using mathematical and simulation-based analyses.In the first half of this article, the fundamentals of IoT, wireless sensor networks, their main difficulties, and the necessity for specific parameters to make the network perform more efficiently are discussed. Some recent wireless sensor network research is presented in Section2. It is shown in Section 3 how to use mathematical models to model networks, which takes into account factors such as network probability and radius. Section 4 depicts the system’s network architecture and a proposed energy-efficient connection method. In Section 5, simulation results are shown on graphs, and the work is concluded with a section on the validation of the mathematical model. Power consumption and network connectivity are big challenges in mobility and IoT devices. A technique that takes into consideration characteristics such as network probability, the identified region of individual nodes, and the radius of the whole identified region is presented in this article. This approach assures network connection, long-term communication sustainability, and maximum energy efficiency. Also, this method consumes much less energy averagely 40% compared to the existing methods, which are LEACH, ZTR, and DSR when the radius is 100.


## 2. Related Work

Research in the domain of wireless sensor networks uses a variety of methods to examine various variables and circumstances. In this part, we will take a look at some connected pieces of literature. Ad hoc networks, a common method of building modular sensor networks, have been the subject of current studies into network coverage and routing algorithms. Naghibi and Barati [5] propose a method for geographically dividing a network into smaller cells.Single-hop and multihop cells can be found in each cell. There is a new energy-efficient geographic routing protocol (EGPRM) that utilizes two mobile sinks for data collection from sensor nodes. Conventional approaches are compared to EGPRM, as well. It is proposed that wireless sensor nodes use RL Sleep, a temperature-adaptive intelligent sleep scheduling approach. Reinforcement learning implies that the nodes examine the surroundings and respond accordingly, for example, by transmitting, listening, or sleeping, depending on the scenario. Improved network connections may also be shown in the simulation findings [6].According to [7], an efficient distributed MAC optimization strategy can cut energy consumption by 88%, node latency by 84%, and connectivity overhead by 80%. In addition, the method is associated with those already in use. Many different types of data centers examine the performance and power management of diverse clusters. An autonomous power management system has been proposed by Bithika et al. to increase the system’s efficiency as well as volume in terms of presentation and cost [8]. HF for single, multicore, and parallel architectures focuses on power-aware scheduling algorithm challenges [9].An EOSR (Energy Optimization Secure Routing Protocol) has been created to protect WSNs against rogue nodes. When compared to previous approaches, simulation findings demonstrate that EOSR is superior [10]. The current routing protocol for WSNs is compared in this paper (static and mobile). When conducting the investigation, the survey takes into account factors such as energy efficiency strategies, network life span, and network topology. Also, certain restricted routing systems are simulated and compared [11]. Based on current traffic circumstances, this study provides an energy-efficient ADMC-MAC protocol. The first method prioritizes the cluster head with the most energy, while the second is dependent on the current traffic situation and the node’s duty cycle. This enhances the system’s overall performance and efficiency. It has also been shown that ADMC is more energy-efficient than the S-MAC, M-Mac, and ADMC-Mac [12].Nodes, communication ranges, and connectedness are all studied in [13] using graph theory and statistical methods. In addition to the simulation findings, the authors of this work discussed the underlying mathematics. When assessing connectivity and coverage [14], it is important to evaluate the distribution of nodes in a region. In their findings, they concluded that a high node density is the best way to ensure that all nodes are connected. Log-normal shadowing was used to study a wireless sensor network transmission model by Agrawal and Patwari. A long-standing issue with the network connection between nodes was ultimately resolved by the authors [15]. For wireless sensor networks, Chai et al. developed a power-efficient method [16]. The researchers have come up with a way to keep sensors safe that is 60% more effective than other methods.In [17], Ashutosh and all of us talked about the numerous types of data transmission routing protocols that exist. They illustrate and compare several wireless sensor network routing mechanisms. The authors of this research [18] discussed how to follow a computer network’s fastest and most optimal path while being risk and energy-sensitive. As an alternative to the existing SLA provisioning models, they came up with a risk energy-aware SLA provisioning model (RSEP). TORA, DSR, DSDV, OLSR, and AODV [19, 20] are also compared in a comparative review.Haque and Baroudi devised a dynamic routing protocol for network longevity in the same way as authors are suggested an energy-efficient protected circle directing protocol for load complementary and enhancing network lifespan [21]. A method for improving WSN connection is presented by Renato et al. [22]. In addition, Kim and Kim [23] have provided an IEEE 802.15.4 clustering technique that is effective for the frequency series. Most of the works provided more energy consumption.A lot of work has been done in the definition of coverage region, connection, power efficiency, data communication, and clustering systems, as well as security procedures and MAC-based structure with various elements as can be seen in Section3. All of these limitations must be implemented for a long-term wireless mobile sensor network. As a result, this research proposes a novel probabilistic method for a mobile network together with a mathematical model against energy wastages. The research demonstrates how mobile sensor nodes’ energy consumption may be optimized while their network connection is increased. Section 5 demonstrates simulated charts.


## 3. Mathematical Modeling

An IoT WSN is made up of a collection of “Nd” sensor nodes, each with a unique serial number indicated by X1, 1, 2, …, and Nd [24, 25]. Based on the graph theory, the distance between the nodes “a” and “b” is Dab. The node’s communication range is designated by the letter “r.” The nodes “a” and “b” form a communication channel if Dab>r. There are “M” different paths that can be taken in wireless sensor networks, ranging from zero to a multiple of NdNd−1/2. For the network to be considered full, M must equal NdNd−1/2.A large number of sensor nodes are often installed in a well-defined region by a top node density in static WSNs used to monitor a large area. Poisson’s distribution may be seen in the node distribution. Compared to a static WSN, a node in an IoT mobile WSN (MWSN) can connect with a lower number of other nodes at any given moment. In addition, the surrounding nodes often form and break connections. As a result, the network becomes less reliable and uses more energy. A network model and energy-saving strategies used in a static wireless sensor network may not deliver the necessary service level; thus, this article explains the network model used in a mobile WSN (MWSN). “A” is the detection region employed in this paper’s network model, where A=r2 and the node’s connectivity probability Pq=r2/A=0.2. This factor represents the ratio of the node’s transmission area to its identified region. Figure 1 depicts the general layout of the monitored region.Figure 1
Architecture of IoT WSN-focused region.


### 3.1. Probability Theory for Connectivity

The nodes in the monitoring region are dispersed in a fashion that follows a binomial distribution, as was demonstrated in a previous study. Because the nodes in this network move about, the connectedness of the system follows a binomial distribution, as shown in this study, which is based on the probability theory (CC, Pr). In M trials, only “CC” occurrences are successful in a binomial event like [M, CC]. To link to all M networks, a node in a network will do just that: connect to as many as it can. CC is the number of connections formed, or how many nodes are active and within this node’s communication range. This is the output of the binomial event. CC is one of the M total nodes with an active connection.The greater the network connectivity, the higher the value ofCC. The “Radius” represents the radius of the node coverage. When “Radius” is less, the number of nodes within the communication range is also smaller. As a general rule, the binomial probability theory may be applied to both small and large datasets. Furthermore, because the nodes in the targeted region are dispersed, the binomial distribution is assumed to be invalid because it cannot be applied to a continuously distributed population. There are more than 20 nodes, and the transmission probability is below 0.3; hence, the wireless sensor network follows a binomial distribution. The predicted value of a binomial distribution may be defined as Ak=MNr where Pq=πr2/A, so Ak=Nπr2/A.The sensor’s node connectivity “CC” is based on the binomial theory, and as a result, the network connectivity probability is
(1)Px=CC=∑x=0nnxπr2s1−πr2sn−x,where P is the probability and CC is the connectivity component.For a given value of “CC,” the relationship between “r” and its nearby nodes may be found in Equation (1) [26]. The portability of a wireless node or the nearby nodes affects the value of “n.” As a result, a greater transmit power is required to achieve the specified connection factor value. So that more power can be sent, this raises the node’s energy consumption. It is possible to reduce overall energy usage by increasing the nodes’ transmit power in addition to increasing network connection probability. Nodes around it can run at a reduced energy level, thereby allowing them to share in some of the power. This means that, unless a pair of nodes requires simultaneous bidirectional transmission, all nodes do not have to function at the same communication power or with the same coverage region. Section 4.1 goes into further detail about the suggested algorithm for achieving this network energy optimization.In terms of connection probabilities, we have observed that “Radius” has an influence. As a result, in order to maximize the network’s connectedness, we compute the variation of “Radius” in relation to the probability of connection. The percentage of alteration ofPq in relation to Radius may be calculated by taking the partial derivative of Equation (1) with “Radius.” Using partial derivatives and equating the equations to zero, it is possible to discover the optimal values. In order to arrive at an optimal value, partial derivation of Equation (1) is critical.


## 3.1. Probability Theory for Connectivity

The nodes in the monitoring region are dispersed in a fashion that follows a binomial distribution, as was demonstrated in a previous study. Because the nodes in this network move about, the connectedness of the system follows a binomial distribution, as shown in this study, which is based on the probability theory (CC, Pr). In M trials, only “CC” occurrences are successful in a binomial event like [M, CC]. To link to all M networks, a node in a network will do just that: connect to as many as it can. CC is the number of connections formed, or how many nodes are active and within this node’s communication range. This is the output of the binomial event. CC is one of the M total nodes with an active connection.The greater the network connectivity, the higher the value ofCC. The “Radius” represents the radius of the node coverage. When “Radius” is less, the number of nodes within the communication range is also smaller. As a general rule, the binomial probability theory may be applied to both small and large datasets. Furthermore, because the nodes in the targeted region are dispersed, the binomial distribution is assumed to be invalid because it cannot be applied to a continuously distributed population. There are more than 20 nodes, and the transmission probability is below 0.3; hence, the wireless sensor network follows a binomial distribution. The predicted value of a binomial distribution may be defined as Ak=MNr where Pq=πr2/A, so Ak=Nπr2/A.The sensor’s node connectivity “CC” is based on the binomial theory, and as a result, the network connectivity probability is
(1)Px=CC=∑x=0nnxπr2s1−πr2sn−x,where P is the probability and CC is the connectivity component.For a given value of “CC,” the relationship between “r” and its nearby nodes may be found in Equation (1) [26]. The portability of a wireless node or the nearby nodes affects the value of “n.” As a result, a greater transmit power is required to achieve the specified connection factor value. So that more power can be sent, this raises the node’s energy consumption. It is possible to reduce overall energy usage by increasing the nodes’ transmit power in addition to increasing network connection probability. Nodes around it can run at a reduced energy level, thereby allowing them to share in some of the power. This means that, unless a pair of nodes requires simultaneous bidirectional transmission, all nodes do not have to function at the same communication power or with the same coverage region. Section 4.1 goes into further detail about the suggested algorithm for achieving this network energy optimization.In terms of connection probabilities, we have observed that “Radius” has an influence. As a result, in order to maximize the network’s connectedness, we compute the variation of “Radius” in relation to the probability of connection. The percentage of alteration ofPq in relation to Radius may be calculated by taking the partial derivative of Equation (1) with “Radius.” Using partial derivatives and equating the equations to zero, it is possible to discover the optimal values. In order to arrive at an optimal value, partial derivation of Equation (1) is critical.


## 4. Architecture of Network

Sensors, a microcontroller, and scheme software for data computation make up the fundamental paradigm of portable sensor networks [27]. There are three types of nodes in the model of the simple MWSN depicted in Figure 2: organization nodes, sensor nodes, and receiver-node components. These nodes have a transceiver to help with data and control signal transmission. Sensor nodes gather data, which is subsequently sent to a central processing node for further processing. Actuators, motion support, positioning, and power regeneration are all controlled by this system. [27]. Nodes in MWSN are distributed around the monitoring region of space in a random manner. Data is collected by the sensor nodes and transferred to other nodes through one or more hops to the sink. The data is sent to the coordination node over a wide area network from the sink node. In the end, the data is processed and delivered to the end-user through a remote connection.Figure 2
Radius: 20.In an IoT mobile wireless sensor network, it is extremely difficult to uphold connectivity whereas the communication systems are still operational (MWSN). It is difficult to sustain a specific level of power in MWSN since the point of interaction changes constantly, and a fast-moving network demands a lot of energy. Maintaining connection while maximizing energy efficiency requires monitoring the node’s coverage area and transmit power. With these two factors, we can retain connection while optimizing the energy level of the surrounding nodes.The term “completely connected wireless network” refers to a network where all nodes may readily communicate and exchange data over a wireless setup that uses either a single-hop or a multihop configuration. For MWSN, this study provides an energy-efficient network connecting approach that achieves excellent node coverage while conserving energy to the minimum necessary level. It has also been looked into and studied to find the best energy solutions in a probability model.


### 4.1. Proposed Modern Optimization Algorithm

The radius of communication (Radius) and the energy stages of nearby nodes are two elements that have been shown to have a significant impact on mobile wireless sensor network connection in Section4.1. When the network’s connectedness rises to a value of “CC,” the change in communication radius may be calculated using Equations (1) and (2) [26]. MWSN’s redundancy rises when nodes occur outside of the set range or limit of nodes, putting exceptional stress on the communication network [22, 28]. As a result, in addition to optimizing the energy consumption of individual nodes, the network as a whole is also given consideration. One of the most critical aspects of a mobile WSN is the amount of energy used by the sensor devices, which are powered by batteries.The sensor will die if the battery energy falls below a certain onset, defeating the purpose of installing the network. Additionally, this work proposes a method that ensures connection while simultaneously reducing energy use. The network’s communication radius may be determined using Equation if the number of nodes “N” and the identified region “A” are known (2). It follows the binomial distribution B (CC, Pq) where Pq=A/A and Pq is the transmission probability of the wireless sensor network. As more sensors are added to a certain region, the likelihood of network connectivity will rise to “CC.” In addition, as the coverage area expands, the number of nearby nodes becomes more readily available, increasing the connection factor. As a result, the huge transmit power Ptr is supported to sustain connectivity by these surrounding nodes, which share in the energy.The PNC method is designed for sensor nodes that often swap their points of contact in a mobile wireless sensor network.Ei is the name given to the group of nodes that surround a given node I. Due to the nature of sensor nodes being movable, they are linked in a random form [29, 30]. An area’s hub is the final node to receive the data, which is subsequently passed on to the other nodes in the area [31, 32]. Each head node in a specific region transmits data to the base station, where it is further processed. When a cycle is complete, the head node switches to a new position to better utilize the available energy. This occurs when data is sent from a node to the cluster head.The quantity of sensorsN should be set to X1, 2, N. “A” encompasses the whole target region. An identifies the portion of the map that is being focused on outside of the overall area. A node’s communications range is denoted by the letter “r,” while its connectivity is denoted by the number CC: step 1: initialize and compute the values of all parameters. Values for “N” and “A” have been established. There is a fixed value for the numbers “N” and “A,” which are 50 and 50 km2, respectively. As a result of this phase, the energy of adjacent nodes can be used to sustain connectivity if necessary. Increasing the communication radius in step 3 expands the coverage area for nodes in the vicinity. Step 4 justifies the requirement that the network will have the maximum number of nodes linked if the coverage area of nearby nodes increases. If there are a lot of linked nodes, then there is a high possibility of a big net transmitted power that is utilized to maintain connection by minimizing energy consumption. When a node’s energy level is low, the nodes around it donate to the other node, ensuring network communication.


## 4.1. Proposed Modern Optimization Algorithm

The radius of communication (Radius) and the energy stages of nearby nodes are two elements that have been shown to have a significant impact on mobile wireless sensor network connection in Section4.1. When the network’s connectedness rises to a value of “CC,” the change in communication radius may be calculated using Equations (1) and (2) [26]. MWSN’s redundancy rises when nodes occur outside of the set range or limit of nodes, putting exceptional stress on the communication network [22, 28]. As a result, in addition to optimizing the energy consumption of individual nodes, the network as a whole is also given consideration. One of the most critical aspects of a mobile WSN is the amount of energy used by the sensor devices, which are powered by batteries.The sensor will die if the battery energy falls below a certain onset, defeating the purpose of installing the network. Additionally, this work proposes a method that ensures connection while simultaneously reducing energy use. The network’s communication radius may be determined using Equation if the number of nodes “N” and the identified region “A” are known (2). It follows the binomial distribution B (CC, Pq) where Pq=A/A and Pq is the transmission probability of the wireless sensor network. As more sensors are added to a certain region, the likelihood of network connectivity will rise to “CC.” In addition, as the coverage area expands, the number of nearby nodes becomes more readily available, increasing the connection factor. As a result, the huge transmit power Ptr is supported to sustain connectivity by these surrounding nodes, which share in the energy.The PNC method is designed for sensor nodes that often swap their points of contact in a mobile wireless sensor network.Ei is the name given to the group of nodes that surround a given node I. Due to the nature of sensor nodes being movable, they are linked in a random form [29, 30]. An area’s hub is the final node to receive the data, which is subsequently passed on to the other nodes in the area [31, 32]. Each head node in a specific region transmits data to the base station, where it is further processed. When a cycle is complete, the head node switches to a new position to better utilize the available energy. This occurs when data is sent from a node to the cluster head.The quantity of sensorsN should be set to X1, 2, N. “A” encompasses the whole target region. An identifies the portion of the map that is being focused on outside of the overall area. A node’s communications range is denoted by the letter “r,” while its connectivity is denoted by the number CC: step 1: initialize and compute the values of all parameters. Values for “N” and “A” have been established. There is a fixed value for the numbers “N” and “A,” which are 50 and 50 km2, respectively. As a result of this phase, the energy of adjacent nodes can be used to sustain connectivity if necessary. Increasing the communication radius in step 3 expands the coverage area for nodes in the vicinity. Step 4 justifies the requirement that the network will have the maximum number of nodes linked if the coverage area of nearby nodes increases. If there are a lot of linked nodes, then there is a high possibility of a big net transmitted power that is utilized to maintain connection by minimizing energy consumption. When a node’s energy level is low, the nodes around it donate to the other node, ensuring network communication.


## 5. Results and Discussions

### 5.1. Implementation Details

Table1 lists the parameters needed for a simulation-based analysis of performance. There is a maximum of 50 nodes (N) in area “A,” and the communication radius (“Radius”) ranges from 10 meters to 60 meters. At a speed of 25 meters per second and a total area of 50 kilometers squared, this equals 90 kilometers per hour. Due to the difficulties in deploying nodes over a wide region due to the high cost and complexity [33, 34], a solution for a specific area was needed. In addition, this study also includes simulation work along with the suggested technique in order to maximize energy usage while retaining connection. By distributing the energy of neighboring nodes, the procedure ensures the network’s connection and reduces energy usage. In the suggested method, the influence of transmitted power is also illustrated.Table 1
Parameters of simulation for mobile communications.
S. No.FactorsValues1MR (monitoring area)50 km sq.2N (no. of nodes)503Radius (radius of communication)10 meters to 80 meters4Speed (mobility)30 m/secMathematical analysis was used to calculate network probability in the preceding section. The application of equations aids in the identification of the link between the communication radius and the likelihood of network connectivity [35, 36]. To demonstrate the validity of this, we built a scenario using the parameters listed above and ran it through a simulation in the MATLAB tool. The diagrams demonstrate the placement of nodes in the desired location for additional dispensation.Figure1 depicts the sensor nodes’ elementary placement in the targeted region. 0.5 m is equal to one division in the 60 km sq. targeted region in the following graphs [37]. Two different situations are used in the simulation performance. When the communication radius is fixed in the first condition, the link between the connectivity factor and network probability may be seen [38]. When the connection factor is fixed, the fluctuation in communication radius is observed with respect to the network probability in other conditions [39, 40]. Section 5.2 includes graphs to illustrate each of the two scenarios.


### 5.2. Results and Comparison

Parameter numerical values are included in Tables2 and 3, which show the findings of both theoretical and simulation studies. As seen in Figure 3, the numerical values of these graphs are displayed in a graphical form. Figure 4–8 show the simulation outcomes with a constant communication radius. The connection factor of a portable wireless sensor network is shown in all four figures as a function of network probability in each case. To monitor a region, theoretical and simulation findings are compared. When the value of “Radius” 20 is constant, the communication radius is constant and the connectivity characteristic is modified based on its chance of being connected, As shown in Figure 4, when “CC”=2, the Pq is at its highest point A. Figure 4 shows a Radius value of 30 and a maximum CC value of 6. Figure 4 shows “Radius” values of 50 and 60, with “CC” values of 20 and 36.Table 2
Theoretical values of probability and connectivity components: constant radius.
CCTheoretical: probabilityX (Prob)Radius=20Radius=30Radius=40Radius=5010.21830.02130.0003760.00000081320.25810.06280.002450.0000074730.21730.20310.006230.0000540.13580.26120.02310.00018150.07720.21540.0410.00073260.03560.27320.06210.00270.009870.23150.09210.0053280.003860.09430.21360.020590.0008560.06430.22970.0204100.0002140.04820.23180.0412110.0000420.0240.22050.0607120.000008030.007320.09990.08130.000002130.003710.08550.0984140.0000002010.002040.06440.2121150.00000003010.0004230.04260.209Table 3
Simulation values of probability and connectivity components: constant radius.
CCSimulation: probabilityX (Prob)Radius=20Radius=30Radius=40Radius=5010.34210.02110.0005760.00000052320.33210.06320.004650.000074330.31230.21340.005130.000740.24280.24350.0260.00095450.07210.28540.0480.0026560.0420.27430.06320.0009270.009690.23540.09540.0037580.003010.1560.21430.0290.0008480.0620.24320.0275100.0002480.04090.35440.0436110.00004230.0310.25430.0684120.000008090.007540.09960.072130.000003430.003860.08430.0963140.0000002130.002060.06430.2453150.00000003980.0004530.04540.275Figure 3
Radius: 30.Figure 4
Radius: 40.Figure 5
Radius: 50.Figure 6
r=0.2.Figure 7
r=0.5.Figure 8
r=0.9.The calculated values of the network likelihood in relation to node coverage are shown in Tables4–7. A constant value of network connectivity is shown in each table, as well as theoretical and simulated values for that connectivity. Due to a quota on the number of values, only the sample data that achieve a peak value are shown in the corresponding tables. This is true for the full 10-60 m range of node coverage “Radius.”Table 4
Comparison when the Radius constant value is 0.2.
RadiusProbability (Prob) forCC=0.2TheoreticalSimulated100.12530.2023110.14120.2456120.17210.2754130.2130.203140.23450.2324150.3650.321160.3510.3421170.3540.3812180.3810.3812190.3830.3712200.3840.3712210.3760.341220.3420.314230.2040.231240.2840.214Table 5
Comparison when the Radius constant value is 0.5.
RadiusProbability (Prob) forCC=.5TheoreticalSimulated200.07820.0743210.09630.0836220.21430.2087230.2130.231240.15760.2134250.21430.2165260.2150.2674270.2750.2754280.20.2786290.2180.2785300.2860.2728310.2780.274320.210.263330.2540.275340.2170.241Table 6
Comparison when the Radius constant value is 0.9.
Node coverage (r)Network probability (Prob) forCC=0.9TheoreticalSimulated300.06430.0643310.080.075320.09640.0912330.09990.1032340.26540.2432350.25460.2154360.2540.2198370.2430.2654380.2540.2564390.2760.2134400.260.2354410.2540.213420.230.216Table 7
Comparison when the Radius constant value is 0.9.
Node coverage (r)Network probability (Prob) forCC=1.5TheoreticalSimulated350.00670.0054360.009360.00843370.02540.0213380.02980.0245390.03540.0325400.04120.0477410.05120.0562420.06870.0586430.07120.0781440.08430.0833450.09990.0934460.10540.1054470.2080.206480.210.205490.2130.222500.2760.208Simulated results are shown below, with a fixed network connection factor and a variable network probability. In Figure2, the network probability achieves a maximum at a communication radius of “Radius”=18 when CC=2.In Figures3 and 4, the probability reaches a maximum at “Radius”=30and40 when CC=5and9, respectively. A look at Figure 4 shows that the network probability is at its maximum peak when the “Radius” value is 50 and declines to 0.06 when it is 55. At this point, CC has been fixed at 15.According to the preceding sections, adjacent nodes give energy when a specific node processes data and its energy level is depleted, so that the overall energy consumption is minimized. In addition, it has been shown that as the radius of coverage area increases, connection and energy levels remain stable. Calculating the sensor node’s total energy is simple.(2)Tmn=∑i=1NNodei,(3)NodeI=MAi+MBi+MBij,(4)MAi=PQi+Tmj+Kmj+CCj,(5)MBi=PQp+Tmx+Kmx+CCx,(6)MBij=Tmw+Kmw+CCsw.In Equation (2), “Tm” is the time in milliseconds, “CC” means voltage in millivolts, “Km” means current in milliamps, “PQ” means the distance of the packet in bytes, and ESwi, ERi, and ETi are the power consumption in communication, starting, and transferring, correspondingly, in the aforementioned equations [41, 42]. When compared to other current algorithms, the simulation results show that our approach uses less energy while still improving the coverage area, as we had hoped. There are a variety of techniques and a suggested algorithm to choose from when it comes to determining how much energy is needed to cover a certain radius [43, 44].It is shown in Figure9 that a number of algorithms are compared in terms of their graphical representations. The simulation results show that the PNC algorithm uses less energy than the other algorithms currently in use. Because of the neighbour node energy sharing idea introduced in Section 4, the suggested solutions are more suited to energy minimization while still preserving network connection [45]. In addition, it sustains the energy stages in relation to the exposure radius of the beam [46]. To begin, this section compares and contrasts a few current studies in wireless sensor network technology. It is seen in Table 8 how they worked around their restrictions.Figure 9
r=0.15.Table 8
Energy optimization comparison of proposed approaches vs. existing approaches.
No.Radius (meters)LEACHZTRDSRProposed11090100148872201001402108933011016023011544012017026012055013018027012566013518027513077014018327713588014218527814099014518728014110100150190290142As can be seen from the comparison table, some researchers are more concerned with the network connection and improving longevity, while others are more concerned with network energy efficiency. Because working in a mobile context is so difficult, most researchers have focused on static wireless sensor networks. Even though it is a time-consuming operation to analyze a mobile network, we attempted to focus on the most important issues: energy efficiency and connection in a mobile context. Energy optimization algorithms for a mobile wireless sensor network are proposed in this study. In order to verify the accuracy of the model’s output, simulation graphs are included with the source code.Wireless sensor networks have long faced the difficulty of optimizing energy consumption. When there are mobile nodes in the network, maintaining connectivity becomes much more difficult. It is proposed a method to maximize energy by sharing each other’s energy via surrounding nodes while controlling network connectivity, based on the notion of network complexity owing to high mobility nodes. Network routing table (NRT) helps to build flexible connectivity between the nodes. Nodes (X) and the node coverage radius (r) of the proposed technique are optimized such that a minimum number of nodes (X) remain active in order to maintain the network’s complete connectivity while r is minimized to reduce energy consumption.Nodes’ battery and transmit power statuses are constantly being updated in the NRT. IfX is increased, for example, more nodes are made active, and the communication range r is lowered in order to keep the energy usage low when the nodes in a region are running low on battery levels. As a control parameter, the V factor (network connectivity) has been introduced [47, 48].A comparison of the values obtained through mathematical analysis (theoretical) and simulation is shown in Figures4 and 5. These results support our hypothesis about the validity of the binomial distribution. Increasing the number of sensor nodes or the communication range is an easy way to increase network connection. As the radius of communication increases, so too does the possibility of a network reaching its maximum connection level. As a result, the network is expected to be more efficient. According to this study, raising the connectivity factor above a specific number diminishes the network likelihood, as the more active node pathways increase the delay in the network beyond the threshold value of link failure for that particular radius of coverage. When numerous active nodes broadcast redundant data, the network becomes congested.In Figure5, it can be shown that when the value of the communication radius “r” is constantly increased, the network probability decreases once a certain threshold is reached while the connection factor is fixed. As a result, network connectivity and energy conservation are not guaranteed. A greater radius may be used to reduce energy consumption while maintaining connectivity.Figure10 demonstrates that the proposed method consumes much less energy averagely 40% compared to the existing methods, which are LEACH, ZTR, and DSR when the radius is 100. According to this experiment, the proposed works consume limited energy than the existing works. The observations from Figure 10 illustrate the optimal utilization of links and node beacons.Figure 10
Plot representation of energy optimization comparison of proposed approaches vs. existing approaches.


## 5.1. Implementation Details

Table1 lists the parameters needed for a simulation-based analysis of performance. There is a maximum of 50 nodes (N) in area “A,” and the communication radius (“Radius”) ranges from 10 meters to 60 meters. At a speed of 25 meters per second and a total area of 50 kilometers squared, this equals 90 kilometers per hour. Due to the difficulties in deploying nodes over a wide region due to the high cost and complexity [33, 34], a solution for a specific area was needed. In addition, this study also includes simulation work along with the suggested technique in order to maximize energy usage while retaining connection. By distributing the energy of neighboring nodes, the procedure ensures the network’s connection and reduces energy usage. In the suggested method, the influence of transmitted power is also illustrated.Table 1
Parameters of simulation for mobile communications.
S. No.FactorsValues1MR (monitoring area)50 km sq.2N (no. of nodes)503Radius (radius of communication)10 meters to 80 meters4Speed (mobility)30 m/secMathematical analysis was used to calculate network probability in the preceding section. The application of equations aids in the identification of the link between the communication radius and the likelihood of network connectivity [35, 36]. To demonstrate the validity of this, we built a scenario using the parameters listed above and ran it through a simulation in the MATLAB tool. The diagrams demonstrate the placement of nodes in the desired location for additional dispensation.Figure1 depicts the sensor nodes’ elementary placement in the targeted region. 0.5 m is equal to one division in the 60 km sq. targeted region in the following graphs [37]. Two different situations are used in the simulation performance. When the communication radius is fixed in the first condition, the link between the connectivity factor and network probability may be seen [38]. When the connection factor is fixed, the fluctuation in communication radius is observed with respect to the network probability in other conditions [39, 40]. Section 5.2 includes graphs to illustrate each of the two scenarios.


## 5.2. Results and Comparison

Parameter numerical values are included in Tables2 and 3, which show the findings of both theoretical and simulation studies. As seen in Figure 3, the numerical values of these graphs are displayed in a graphical form. Figure 4–8 show the simulation outcomes with a constant communication radius. The connection factor of a portable wireless sensor network is shown in all four figures as a function of network probability in each case. To monitor a region, theoretical and simulation findings are compared. When the value of “Radius” 20 is constant, the communication radius is constant and the connectivity characteristic is modified based on its chance of being connected, As shown in Figure 4, when “CC”=2, the Pq is at its highest point A. Figure 4 shows a Radius value of 30 and a maximum CC value of 6. Figure 4 shows “Radius” values of 50 and 60, with “CC” values of 20 and 36.Table 2
Theoretical values of probability and connectivity components: constant radius.
CCTheoretical: probabilityX (Prob)Radius=20Radius=30Radius=40Radius=5010.21830.02130.0003760.00000081320.25810.06280.002450.0000074730.21730.20310.006230.0000540.13580.26120.02310.00018150.07720.21540.0410.00073260.03560.27320.06210.00270.009870.23150.09210.0053280.003860.09430.21360.020590.0008560.06430.22970.0204100.0002140.04820.23180.0412110.0000420.0240.22050.0607120.000008030.007320.09990.08130.000002130.003710.08550.0984140.0000002010.002040.06440.2121150.00000003010.0004230.04260.209Table 3
Simulation values of probability and connectivity components: constant radius.
CCSimulation: probabilityX (Prob)Radius=20Radius=30Radius=40Radius=5010.34210.02110.0005760.00000052320.33210.06320.004650.000074330.31230.21340.005130.000740.24280.24350.0260.00095450.07210.28540.0480.0026560.0420.27430.06320.0009270.009690.23540.09540.0037580.003010.1560.21430.0290.0008480.0620.24320.0275100.0002480.04090.35440.0436110.00004230.0310.25430.0684120.000008090.007540.09960.072130.000003430.003860.08430.0963140.0000002130.002060.06430.2453150.00000003980.0004530.04540.275Figure 3
Radius: 30.Figure 4
Radius: 40.Figure 5
Radius: 50.Figure 6
r=0.2.Figure 7
r=0.5.Figure 8
r=0.9.The calculated values of the network likelihood in relation to node coverage are shown in Tables4–7. A constant value of network connectivity is shown in each table, as well as theoretical and simulated values for that connectivity. Due to a quota on the number of values, only the sample data that achieve a peak value are shown in the corresponding tables. This is true for the full 10-60 m range of node coverage “Radius.”Table 4
Comparison when the Radius constant value is 0.2.
RadiusProbability (Prob) forCC=0.2TheoreticalSimulated100.12530.2023110.14120.2456120.17210.2754130.2130.203140.23450.2324150.3650.321160.3510.3421170.3540.3812180.3810.3812190.3830.3712200.3840.3712210.3760.341220.3420.314230.2040.231240.2840.214Table 5
Comparison when the Radius constant value is 0.5.
RadiusProbability (Prob) forCC=.5TheoreticalSimulated200.07820.0743210.09630.0836220.21430.2087230.2130.231240.15760.2134250.21430.2165260.2150.2674270.2750.2754280.20.2786290.2180.2785300.2860.2728310.2780.274320.210.263330.2540.275340.2170.241Table 6
Comparison when the Radius constant value is 0.9.
Node coverage (r)Network probability (Prob) forCC=0.9TheoreticalSimulated300.06430.0643310.080.075320.09640.0912330.09990.1032340.26540.2432350.25460.2154360.2540.2198370.2430.2654380.2540.2564390.2760.2134400.260.2354410.2540.213420.230.216Table 7
Comparison when the Radius constant value is 0.9.
Node coverage (r)Network probability (Prob) forCC=1.5TheoreticalSimulated350.00670.0054360.009360.00843370.02540.0213380.02980.0245390.03540.0325400.04120.0477410.05120.0562420.06870.0586430.07120.0781440.08430.0833450.09990.0934460.10540.1054470.2080.206480.210.205490.2130.222500.2760.208Simulated results are shown below, with a fixed network connection factor and a variable network probability. In Figure2, the network probability achieves a maximum at a communication radius of “Radius”=18 when CC=2.In Figures3 and 4, the probability reaches a maximum at “Radius”=30and40 when CC=5and9, respectively. A look at Figure 4 shows that the network probability is at its maximum peak when the “Radius” value is 50 and declines to 0.06 when it is 55. At this point, CC has been fixed at 15.According to the preceding sections, adjacent nodes give energy when a specific node processes data and its energy level is depleted, so that the overall energy consumption is minimized. In addition, it has been shown that as the radius of coverage area increases, connection and energy levels remain stable. Calculating the sensor node’s total energy is simple.(2)Tmn=∑i=1NNodei,(3)NodeI=MAi+MBi+MBij,(4)MAi=PQi+Tmj+Kmj+CCj,(5)MBi=PQp+Tmx+Kmx+CCx,(6)MBij=Tmw+Kmw+CCsw.In Equation (2), “Tm” is the time in milliseconds, “CC” means voltage in millivolts, “Km” means current in milliamps, “PQ” means the distance of the packet in bytes, and ESwi, ERi, and ETi are the power consumption in communication, starting, and transferring, correspondingly, in the aforementioned equations [41, 42]. When compared to other current algorithms, the simulation results show that our approach uses less energy while still improving the coverage area, as we had hoped. There are a variety of techniques and a suggested algorithm to choose from when it comes to determining how much energy is needed to cover a certain radius [43, 44].It is shown in Figure9 that a number of algorithms are compared in terms of their graphical representations. The simulation results show that the PNC algorithm uses less energy than the other algorithms currently in use. Because of the neighbour node energy sharing idea introduced in Section 4, the suggested solutions are more suited to energy minimization while still preserving network connection [45]. In addition, it sustains the energy stages in relation to the exposure radius of the beam [46]. To begin, this section compares and contrasts a few current studies in wireless sensor network technology. It is seen in Table 8 how they worked around their restrictions.Figure 9
r=0.15.Table 8
Energy optimization comparison of proposed approaches vs. existing approaches.
No.Radius (meters)LEACHZTRDSRProposed11090100148872201001402108933011016023011544012017026012055013018027012566013518027513077014018327713588014218527814099014518728014110100150190290142As can be seen from the comparison table, some researchers are more concerned with the network connection and improving longevity, while others are more concerned with network energy efficiency. Because working in a mobile context is so difficult, most researchers have focused on static wireless sensor networks. Even though it is a time-consuming operation to analyze a mobile network, we attempted to focus on the most important issues: energy efficiency and connection in a mobile context. Energy optimization algorithms for a mobile wireless sensor network are proposed in this study. In order to verify the accuracy of the model’s output, simulation graphs are included with the source code.Wireless sensor networks have long faced the difficulty of optimizing energy consumption. When there are mobile nodes in the network, maintaining connectivity becomes much more difficult. It is proposed a method to maximize energy by sharing each other’s energy via surrounding nodes while controlling network connectivity, based on the notion of network complexity owing to high mobility nodes. Network routing table (NRT) helps to build flexible connectivity between the nodes. Nodes (X) and the node coverage radius (r) of the proposed technique are optimized such that a minimum number of nodes (X) remain active in order to maintain the network’s complete connectivity while r is minimized to reduce energy consumption.Nodes’ battery and transmit power statuses are constantly being updated in the NRT. IfX is increased, for example, more nodes are made active, and the communication range r is lowered in order to keep the energy usage low when the nodes in a region are running low on battery levels. As a control parameter, the V factor (network connectivity) has been introduced [47, 48].A comparison of the values obtained through mathematical analysis (theoretical) and simulation is shown in Figures4 and 5. These results support our hypothesis about the validity of the binomial distribution. Increasing the number of sensor nodes or the communication range is an easy way to increase network connection. As the radius of communication increases, so too does the possibility of a network reaching its maximum connection level. As a result, the network is expected to be more efficient. According to this study, raising the connectivity factor above a specific number diminishes the network likelihood, as the more active node pathways increase the delay in the network beyond the threshold value of link failure for that particular radius of coverage. When numerous active nodes broadcast redundant data, the network becomes congested.In Figure5, it can be shown that when the value of the communication radius “r” is constantly increased, the network probability decreases once a certain threshold is reached while the connection factor is fixed. As a result, network connectivity and energy conservation are not guaranteed. A greater radius may be used to reduce energy consumption while maintaining connectivity.Figure10 demonstrates that the proposed method consumes much less energy averagely 40% compared to the existing methods, which are LEACH, ZTR, and DSR when the radius is 100. According to this experiment, the proposed works consume limited energy than the existing works. The observations from Figure 10 illustrate the optimal utilization of links and node beacons.Figure 10
Plot representation of energy optimization comparison of proposed approaches vs. existing approaches.


## 6. Conclusion

Getting the most out of an IoT-based wireless sensor network has always been a problem. Maintaining a stable network connection when nearby nodes’ locations vary at random is becoming increasingly difficult because of the prevalence of mobile devices. According to the findings, IoT-based mobile sensor network connections can only be extended up to a certain point while still retaining optimal energy usage. Mathematical and simulation evidence back up these claims as well as a proposed technique for selecting coverage and connection with surrounding nodes. Updating the information in the list to allow energy sharing among nearby nodes represents the notion of updating the routing table with adjacent node status and calculating optimal transmit power. As a result, we can be sure that the network connection has a binomial distribution.Free-space propagation is the only consideration in this paper’s research. This may be taken a step further by considering the impact of adjacent node interference and multipath fading on the intensity of the received signal. In order to achieve desirable levels of the signal-to-interference noise ratio, more transmit power may be required. It can also be thought of as a battery life consideration. Artificial intelligence techniques such as the convolutional neural network (CNN) could be used in the future to figure out how much energy a vehicle needs based on how fast it moves.



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*Source: 7901587-2022-04-14.xml*