# A Power Planning Algorithm Based on RPL for AMI Wireless Sensor Networks
## 5 Evaluation  
In this section, we compare our planning strategy with two other approaches commonly used in the RPL experiments: fixed-power and vertex-based power assignment. The fixed-power strategy consists of assigning the same power to all nodes in the network. This simplistic approach is indeed the most used in the RPL experiments published in the literature. The vertex-based approach consists of adjusting the transmission power to assure that each node can communicate with a certain number of neighbors through links that satisfy an ETX-based quality constraint. Because our algorithm aims to improve RPL behaviour through transmission power planning, we identify it as DODAG-based. In order to provide a fair comparison between methods, we assigned the same average power to the nodes on every evaluated method. The average power obtained with the DODAG-based planning is assigned to all nodes in the fixed approach. In the vertex-based approach, the number of neighbors is increased until the average power is the same as that obtained with the DODAG-based method. In some cases, imposing the power obtained with the DODAG-based planning may result in disconnected graphs for the fixed method and vertex-based method. We find the minimum increase of power that permits the connection of all nodes, by adjusting the power of the nearest nodes between unconnected sub-graphs. The wireless channel conditions have been modeled using the Nakagami-\(m\) distribution and a log-distance path model. We assume that radios operate in the 914 MHz band. We have considered two distinct channel conditions: rural and urban areas. The path loss exponent (\(\alpha\)) and the Nakagami fading severity (\(m\)) have been adjusted to match different channel conditions. In the scenario for rural areas, nodes were randomly placed within a disk of 1 km radius, and we have assumed \(\alpha=2.5\) and \(m=2\). The radio power could range from -10 dBm to 10 dBm in steps of 2 dBm. For the  
Figure 3: Centralized operation of the transmission power planning algorithm. urban area scenario, nodes have been distributed in a disk of radius 100 m, with \(\alpha=3\) and \(m=1\). The transmission power could be adjusted from \(-12\) dBm to 0 dBm in steps of 1 dBm. The root was placed in the mean position of all nodes, and all nodes are connected to the root using a single DODAG. To show that the proposed algorithm is capable of planning the transmission powers so that the ETX is low in both directions (i.e., the quality of the link is good), the maximum ETX imposed for links in rural and urban area conditions is 1.2. We pre-configure the ETX between each node and its neighbors by using the values calculated with Equation (3). Table 2 summarizes the evaluation parameters. The proposed algorithm has two objectives. The first is to assure that the parent set satisfies a minimum predefined size, which allows for designing networks with a desired degree of resilience. The second is to assure that the links connecting nodes to their parents all have similar quality. This allows all nodes in the parent set to offer connectivity through paths of similar quality. Accordingly, we selected two metrics to evaluate the proposed algorithm: parent set size and the quality of the path through the preferred parent. The first is to evaluate if the power setting is able to achieve the resilience objective, and the second is to assess if, in addition to improving RPL resilience, the method does not worsen the quality of the preferred parent path. The performance of the method is evaluated by observing the two metrics jointly. In the following, the vertical bars represent the 0.95 confidence level of the average parent set size obtained with 30 random topologies. First, we show how the size of the network (number of nodes) affects the size of parent sets and the cost of paths through the preferred parent (Figures 4-7). For these cases, the DODAG-based power planning algorithm was executed with a target parent set size \(k=3\).