## 4 Communication Architecture
### Network Energy Consumption Model  
We consider our LS-WSN architecture to be made up of \(N\) sensors generating periodic and constant size traffic. Each period, each sensor generates an \(m\)-bit size message to the sink. The sensors have a limited common transmission range (\(R\)), they can be solicited for routing messages from neighboring sensors. Only sensors located at a distance less than \(R\) can communicate directly with the sink. Therefore, sensors positioned at a distance of \(d\in 2[ktimesR;(k+1)timesR]\) must use a path of at least \(k\) jumps to route messages to the sink. We then defined a circular geographic model based on the different levels of our architecture. We partitioned the different levels of our architecture into eccentric rings centered on the position of the CH. Each crown has \(R\) as width and models one level of the routing tree. We call each crown, level. Let \(L\) be the number of levels in the network and \(l_{0}\) the level of the sink. A sensor positioned at the first level of the architecture, furthest from the sink (\(l_{L}\)) will be responsible for collecting its own data and will generally not be asked to transmit data from other sensors. A sensor positioned at the second level of the architecture \(l_{L-1}\) will have to collect its own data, receive data from some sensors at the lower level \(l_{L}\), and retransmit it to the next hop. Based on this finding, we consider the energy dissipated for each data sending or receiving operation and give an estimate of the overall energy dissipated by a level taking into account the number of transmitting or receiving operations performed by its sensors. It is important to stress that we do not pretend to calculate the energy consumed with accuracy but we present a possible approximate case with the aim of better distributing the energy consumption in a network of sensors. Moreover, adopting the energy dissipation model of [PERSON] et al. (2016) and considering our assumptions, we assume that all sensors dissipate the same amount of energy for a basic operation, either receiving or transmitting. We note, respectively, by \(T_{x}\) and \(R_{x}\), the energy dissipated by a sensor for sending data and receiving data. Figure 8: Sink Activity Sequence Diagram. Figure 10: Instant of the first sensors having exhausted their energy following the SEP.  
Figure 9: Instant of the first sensors having exhausted their energy following the LEACH. Figure 11: Number of sensors having exhausted their energies at the end of the simulation according to LEACH. Figure 12: Number of sensors having exhausted their energies at the end of the simulation according to SEP.  
Figure 14: Average residual energy rate according to SEP.  
Figure 13: Average residual energy rate according to LEACH. Figure 15 shows the average energy consumption (in Joule) of the sensors of the three levels of the architecture as a function of the transmission time (at a constant step of 10 s). Obviously, energy consumption varies according to the nature and types of sensors. We can clearly see that the well is the type of sensor that is gluttonous for energy: 0.36% of the well's energy is consumed for a transmission time interval of 10 s (compared to the initial energy of 16200 Joules) and 0.34% for the interval of 30 s. The main reason for this consumption is the well's operating mode. Due to its nature, the well is the sensor of the model whose radio component must remain in reception mode as long as possible in relation to the sensors (to receive the _msg_ wake-up message). It can also be noted that the consumption of the other sensors (CH), (N1) and (N2) has remained close.