# Extending Wireless Reschargeable Sensor Network Life without Full Knowledge
## 10 Simulation Results and Analysis
### Algorithm Results  
We will show the performance of our algorithms on more than one hundred thousand networks with no knowledge, and how our algorithms compare to a full knowledge algorithm. Using the  
Figure 2: Plotting 10,000 random WRSNs. Each point is a node with residual power \(Y\). For each node, the actual percentage of nodes with power \(\leq Y\) (x-axis) vs. the computed bound (\(y\)-axis) are plotted. parameters in Table 2, we generate a simulated WRSN with different sizes. Then, we run our algorithms on each network created and record the result returned by each algorithm. We report our results as a percentage of the increase obtained when running the optimal full knowledge algorithm on the same network. When presenting performance, we use box plots, where the red line represents the median of the performance values and the blue dotted line represents the mean of the values. Figure 3 shows the performance of all algorithms over four different network sizes, with ten thousand networks of each size. We pick four sizes: 100, 150, 200 and a maximum network size such that a single node can be charged if the network is fully explored. If we consider, for example, the case of a 150-node network, Naive algorithm's median performance is 8.2% of optimal and it has a mean performance of 13.4%, while Minimum Only median performance is 53.8% and a mean performance of 53%, and ANLPP's median performance is 87.5% and has a mean performance of 84%. It can be seen from Figure 3 that ANLPP not only outperforms the other two implementations, but also has a narrower variance and also a median performance higher than its mean performance. Figure 3 shows how the Naive algorithm can only perform up to a smaller percentage of optimal because it uses all its power charging the first nodes it encounters. On the other hand, the Minimum Only algorithm does better, by charging nodes with minimum power. On the other hand, it also includes non-minimum nodes, which leads to wasted power, thereby causing a smaller life-increase in the WRSN. While Naive has no algorithm parameters, both Minimum Only algorithm and ANLPP used the threshold parameters given in Table 2.  
While ANLPP most of the time outperforms the other two algorithms, we wish to observe its exact behaviour to identify when and where it performs well and poorly. To understand how ANLPP behaves, we need to identify the types of nodes in a WRSN, from a charging algorithm perspective. ANLPP divides nodes into two categories. Based on the action it takes regarding a node, ANLPP either adds the node to the charging list \(v\), or not. Each node in the network belongs to one of three different sets:  
* Y, the node should be charged for optimal performance,
* \(k\) low power nodes, dropped for optimal performance,
* high power nodes, need not be charged. Figure 3: The performance of each algorithm over ten thousand networks of fixed size. The upper left image shows the results for a 100-node network, upper right 150-node, lower left 200-node, lower right maximum size to charge a single node (between 233 and 237). Given the above descriptions, Figure 4 shows the charging performance of ANLPP on four networks with the same parameters. Each sub-figure shows the trend in performance as the network size increases. In all cases, the algorithm starts at optimal performance, since the network size is small enough to fully explore. While they all also show a final optimal performance, there is a lot of variation in each network and between different networks. As the network size increases, the performance varies and demonstrates the discrete nature of the charging problem, and how small changes in network size may have a significant and varying impact on the network lifetime increase. We will attempt to analyze this behaviour.