# An Efficient Model-Based Clustering via Joint Multiple Sink Placement for WSNs
## 1 Introduction
In general, sensor nodes can be deployed in different environments with different technologies, such as Wireless Body Sensor Networks [27] that gather and evaluate patients' vital-sign-related data by deploying various bio-medical sensors (body temperature, blood pressure, heartbeat, etc.) in the human body for an extended period, thereby lowering healthcare costs. An essential part of the Intelligent Transport System (ITS), the Vehicular Ad-hoc Network (VANET) [28], connects and allows wireless communication between moving vehicles. It is a particular type of Mobile Ad-hoc Network (MANET). The Flying Ad-hoc Network (FANET) [29] consists of several Unmanned Aerial Vehicle (UAV) nodes that connect wirelessly. UAVs can be controlled remotely or using pre-programmed instructions. Typically, SNs consume a larger amount of energy while transmitting data. Hence, reducing the amount of redundant data transferred to the BS is crucial when the cluster head (CH) nodes in a network are appropriately selected. Additionally, it is essential to examine the routing protocol in the main features and common scenarios to ensure real-world WSN construction and optimum environment simulation for further improvements using a range of optimization methodologies [30]. Previous studies have notably discussed approaches to sensor deployment, sink placement, and data transmission for energy efficiency. These techniques [23; 31; 32; 33; 34] are not suggested in the case of large-scale sensor deployment. Other studies focused only on the issue of routing paths without attaching them to sink placements [31; 34; 35; 36; 37; 38; 39] or addressed only the sink placement [23; 32]. Studies have provided a clustering model for data routing, but there are considerable shortcomings in the clustering methods. In particular, they put a tremendous load on CH and ignore the residual energy and distance between the Cluster Head and the sink, which impacts energy consumption. Therefore, we need a solution that addresses the aforementioned issues in order to reduce energy consumption, increase the network's lifetime, and shorten the data transmission delay in a constrained IoT network. Thus, we have to propose a fully analytical model that considers the most common review limitations: clustering optimization, placement of multiple sinks, and data routing problems in heterogeneous WSNs. In this research, inspired by swarm intelligence methods, especially the ant clustering algorithm, we propose an efficient model based on clustering that determines the ideal position for multiple sinks and routing data pathways in WSNs. The following are some of our research's significant points in terms of the proposed model-based clustering:  
1. We propose a complete model that aims at increasing the network's lifetime. It performs essential tasks like CH selection (higher Cp factor), path construction from sink to CH (less costly path), and sink placement (in the barycenter of the cluster); as a result, it minimizes the load on the sensor nodes. 2. Under the operation of our model, no intermediate node participates or transmits their data packets with less than an energy threshold and more than a distance threshold (long link--discussed in Section 3.1), thereby conserving a significant amount of energy. 3. We compared our proposed technique with others under various simulation settings (varying the number of sensor nodes, CHs, and sinks) to identify areas of limitation and found that it outperformed all of them. We observed that the number of hops is reduced by more than 4% to one hop, and the residual energy is increased by more than 3%. We have adopted the ant clustering algorithm because of its various features [40]: (i) it requires minimal information about the issue at hand; (ii) it can typically complete both broad and parallel searches over the area of potential solutions by having a swarm (population) of candidate solutions.