## 4 Description of MRP
### Phase II: Constructing Multipath
The process of route maintenance will be initiated when there comes out these conditions as follows:

* When the residual energy of the current CH is lower than 50% the average energy of all nodes in the cluster, a new CH will be selected according to (24). If there are more than two paths to sink, the new CH will send the packets via these paths. Otherwise, the new CH will initiate a new route discovery process. * When the number of multiple paths is less than two, that means the reliability of path decreased seriously. The current CH will initiate a new route discovery process. ## 5 Performance Evaluation

Various performance metrics are used for comparing different routing strategies in WSNs. We have used the following:

* _Average Energy_: The metric gives the average of energy of all nodes at the end of simulation. * _Energy consumption_: The metric gives the energy consumption of nodes in the event area for transmitting a data packet to sink. * _The standard deviation of energy_: The metric gives the average variance between energy levels on all nodes. * _Network lifetime_: This metric gives the time of the first node running out of its energy. By using a simulator developed by MATLAB, the proposed scheme was compared with the TEEN [29] dynamic clustering algorithm and the other two kinds of multipath algorithms in [14] (MP) and [25] (MACS), respectively. We evaluated these four algorithms over a set of sensor networks with the number of nodes ranging from 100 to 500. For the same number of nodes, we randomly generated ten network topologies and ran these algorithms over them to obtain the average results. In each network, the sensor nodes are randomly distributed on a \({}_{M\times M}\) region with M = 200 m. For radio power consumption setting, we adopt the first-order model [11] and set \(E_{\text{elec}}\) = 50 nJ/bit, \(E_{\text{amp}}\) = 10 pJ/bit/m\({}^{2}\). The energy for data aggregation is set to EDA = 5 nJ/bit. The parameters (\(k_{1}\), \(k_{2}\), \(k_{3}\), \(k_{4}\), \(k_{5}\), \(k_{6}\), \(k_{7}\), \(k_{8}\), \(k_{9}\), \(k_{10}\), \(k_{11}\), \(k_{12}\)) are set to (0.5, 0.1, 0.4, 2, 1, 1, 0.4, 0.2, 0.4, 0.5, 0.3, 0.2). Table 2 lists the other simulation settings. \({}_{\tau_{\omega}(i,j)}\) is the initial pheromone value at a link (i, j). \[k= \begin{cases}0.01,\text{if node $i$ and node $j$ are neighbors}\\ 0\qquad\text{otherwise}\end{cases} .\]

We designed two scenarios to compare the performance of the different algorithms. The first scenario (Figure 4) simulates a homogeneous WSN, where the sensor nodes were randomly deployed with the same initial energy. The initial energy of each node is 2 joules. The second scenario (Figure 5) \begin{table}
\begin{tabular}{l c} \hline  & **Parameter** & **Value** \\ \hline \(\alpha\) & 2 \\ \(\beta\) & 2 \\ \(\rho\) & 0.2 \\ \(\tau_{\omega}(i,j)\) & \(k\) \\ the number of event & 1 \\ packet size & 512 bytes \\ broadcast packet size & 20 bytes \\ the coordinate of sink & (0,200) \\ event radius & 20 m \\ \hline \end{tabular}
\end{table} 
Table 2: List of Many Parameters Used. simulates a heterogeneous WSN where the network is composed of many nodes with different initial energy. The energy level changes between 1 joule and 2 joules, which are uniformly distributed over the nodes. Figure 4 presents the results of the simulation for the studied metrics to different network scale in scenario one. It can be seen that MRP performed better than the other algorithms. In Figure 4a, the average energy of the MRP is higher than the other algorithms. This indicates that there exists more residual energy of the nodes in MRP, which implied MRP needs less energy for transmitting data. Figure 4b shows a linear increase of energy consumption as the network becomes denser, as more sensor nodes become involved for all the algorithms. This brings more traffic into the network. It is obvious that MRP and MP consume less energy than the others. However, MRP outperforms the MP algorithm.