# An Efficient Model-Based Clustering via Joint Multiple Sink Placement for WSNs
## 2 Related Works
### Sink Placement  
Single-sink solutions are not highly efficient in applications requiring large-scale deployment, such as environmental monitoring, industrial networks, surveillance, and agricultural scenarios.  
In an early study by [23], the authors used an iterative clustering technique with multiple sinks in the agricultural field to find the optimal location for each sink while maximizing the network's lifetime. To ensure the network's scalability, they used the k-means method to divide the whole network into clusters, where each sink is situated in the middle of each cluster in terms of energy. The number of sinks increases until a necessary lifetime is reached. However, due to the vast number of SNs and the deterministic static number of sinks at constant positions in the network, the technique is unsuited to large-scale networks. In addition, the route from sensors to sinks needs to be considered.  
Another work [47] modelled the problem of optimal sink position and sensor-to-sink communication as a mixed integer linear programming (MILP) model that attempts to prolong the network's lifetime and simplify the routing to the sink to gather data using the PSO algorithm. The model indeed prolonged the network's lifetime, but it may choose the longest path. An analytical model [32] proposed to deal with the energy hole issue by allocating k-sinks in the network based on the k-median problem, hence marking a more extended network lifetime. However, the model did not mention the type of applications used, since in cognitive WSN the sinks are not qualified for processing the data of every sensor.  
Other studies [48] combined sink position, sensor position, scheduling, and routing with the linked coverage (SPSRC) model in a single model that deals with the design problems mentioned. The SPSRC model allows the deployment of sink and sensor locations, as well as scheduling/monitoring the activity of the located sensors, and the data travels from each energized node to its associated sink for network coverage across a restricted zone area. Meanwhile, ref. [49] introduced a model for heterogeneous-WSN using a clustering technique founded on the energy forecast (CTEF). This model considered quality and packet loss rate to decrease SN's energy consumption. Unfortunately, coverage time has not been considered in this model. As a result, it impacts the lifetime performance of sensor networks.  
The use of a mobile sink trajectory, where the moving sink traverses all SNs and gathers data by means of single-hop communication based on the Hilbert curve, was initiated in [35]. However, this method suffers from a high transmission time, since data is only conveyed to the sink by traveling near to the boundary and in a single hop. Similarly, efficiency, scalability, and availability are factors to be achieved with a single sink. The authors of [50] gathered sensor data using several sinks around the observation field. The sensors have three-sector antennas and send data to BS directly or via intermediary nodes, depending on which sector they use.  
In [51], they developed mixed-integer linear programming (MILP), in addition to referencing the hot-spot or energy-hole problem by proposing the utilization of \"optimal mobility patterns\" on three representations for multiple sinks (random, grid, and spiral patterns). As a result, it extended the WSN lifetime as long as possible. A mobile sink can be suggested as a solution to the energy hole problem, but it remains challenging to design a dynamic path sink.  
Some research [52] has combined the moth flame optimization (MFO) algorithm and differential evolution (DE) algorithm to construct an optimal mobile sink route by clustering the wireless sensor networks. This technique reduced energy usage and maximized the network's lifetime. Nevertheless, it failed to calculate the data transmission delay and throughput. Table 1 summarizes relevant research papers studying sink placement.