# PDTR: Probabilistic and Deterministic Tree-based Routing for Wireless Sensor Networks
## 6 Simulation Results
### Impact of Loss of Energy \(\ell_{e}\) Parameter  
#### 6.1.1 On the Energy Consumption  
Ensuring longer network lifetime when minimizing the energy consumption at the same time is the goal of the best WSN routing protocol. In this paper, we proposed a new tree-based strategy that has an update phase each time any node loses \(\ell_{e}\) of its energy.  
For this, we considered three scenarios; in each scenario, each source node sends one packet every 0.1 s, for the parameters defined in Table 1 and their values given by Table 2.  
The communication range \(R=80\) m, while \(\ell_{e}=\{2\%,4\%,6\%,8\%,10\%,12\%,14\%,16\%,18\%,\)\(20\%,22\%,24\%,26\%\}\). In the first scenario, the number of nodes is fixed, such that \(\mathrm{N}=100\). Figure 3, first scenario shows the simulation results of sending, in each t = 0.1 s, one packet from one random node towards the sink for a period of 300 s. The results show that to minimize the network energy consumption, the value of \(\ell_{e}\) parameter should belong to \(\ell_{e}=[20\%,26\%]\). (see Figure 3, first scenario).  
In the second scenario, the number of nodes is fixed such that \(\mathrm{N}=120\). Figure 3, second scenario shows the simulation results of sending, in each t = 0.1s, one packet from one random node towards the sink for a period of 300 s. The results show that to minimize the network energy consumption, the value of \(\ell_{e}\) parameter should belong to \([16\%,26\%]\) (see Figure 3, second scenario).  
\begin{table}
\begin{tabular}{c c} \hline \hline
**Parameter** & **Value** \\ \hline Network Topology & Tree Topology \\ Network Size & \(100\times 100\) m\({}^{2}\) \\ Number of Nodes & 100 (Static nodes) \\ Sink & 1 Static sink (fixed at the center) \\ Communication Radius & 25–50 m \\ Initial Energy for all nodes & 0.5 Joule/ except when other assumption. \\ Sink Initial Energy & 500 Joule \\ Radio Propagation Model & First Radio model \\ MAC & BOX-MAC \\ Packet Size & 1024 bits \\ \(\alpha\) & 3 by assumption/except if other assumption. \\ \(\beta\) & 1.8 by assumption/except if other assumption. \\ \(\gamma\) & 1 by assumption/except if other assumption. \\ \hline \hline \end{tabular}
\end{table}
Table 2: Parameters values.  
Figure 3: Impact of \(\ell_{e}\) parameter on the total energy consumption varying number of nodes for the first scenario, the second scenario and the third scenario.  
In the third scenario, the number of nodes is fixed such that \(\mathrm{N}=140\). Figure 3, third scenario shows the simulation results of sending, in each \(\mathrm{t}=0.1\) s, one packet from one random node towards the sink for a period of 300 s. The results show that to minimize the network energy consumption, the value of \(\ell_{e}\) parameter should belong to \([14\%,26\%]\) (see Figure 3, third scenario).  
From the above three scenarios, we can conclude that minimize the total energy consumption, the selection of \(\ell_{e}\) value depends on the number of nodes. For the network size \(\mathrm{N}=100\), The value of \(\ell_{e}\) parameter should belong to \(\ell_{e}=[20\%,26\%]\) for the network size \(\mathrm{N}=120\), The value of \(\ell_{e}\) parameter should belong to \(\ell_{e}=[16\%,26\%]\) for the network size \(\mathrm{N}=140\), The value of \(\ell_{e}\) parameter should belong to \(\ell_{e}=[14\%,26\%]\) for the parameter values given by Table 2, and the communication range \(R=80\) m.