# An Accuracy-Aware Energy-Efficient Multipath Routing Algorithm for WSNs
## 6 Evaluation
### The Effect of Accuracy Constraints on the Performance of the Algorithm  
In this section, the impact of the accuracy constraint \(\Delta\) on the EMRAR algorithm is analyzed under different values of \(\Delta\) when the data rate is 50 kbps. In line with prior research [11; 41], we set the accuracy constraint \(\Delta\) with 3 distinct values--1%, 3%, and 5%--in each simulation, representing incremental levels of allowable accuracy loss. The AAL, PDR, and NRE performances in different node densities are shown in Figure 3.  
Figure 3a shows the AAL performance under different densities of adjacent nodes. From the figure, we can find 3 patterns:  
1. A larger value of \(\Delta\) corresponds to a larger value of AAL. This correlation can be attributed to the fact that, with a fixed network size, a larger accuracy constraint \(\Delta\) implies a reduced constraint on the paths available for multipath routing. Consequently, the probability of path intersections increases, leading to more data aggregation and ultimately resulting in a higher AAL. 2. An increasing density of adjacent nodes leads to a lower AAL, signifying improved data accuracy. The reason for this is that a higher number of neighbors provides more available next-hop nodes for routing. The algorithm can choose the routes that lead to less aggregation towards the sink, consequently reducing accuracy loss. 3. The reduction in AAL becomes more obvious with a larger value of \(\Delta\). The reason for this is that when there is a greater number of neighbors, a larger value of \(\Delta\) provides a relatively greater number of alternative nodes. Hence, it becomes easier to find better path choices that significantly reduce the accuracy loss. Figure 3b shows the PDR performance under different densities of adjacent nodes. The shapes of all three curves are quite similar. For example, when \(\Delta\) = 3%, the PDR increases by approximately 4.5% for every 5-unit increase in the number of adjacent nodes. This trend occurs because as the density of adjacent nodes increases, there are more available paths that meet the constraints. This results in a greater number of reliable paths for data  
Figure 3: The effect of \(\Delta\) on AAL, PDR, and NRE under different adjacent node densities when the data transmission rate is 50 kbps. (**a**) AAL performance, (**b**) PDR performance, (**c**) NRE performance. transmission, fewer intersection nodes, and reduced congestion in the MAC layer. As a result, the PDR is improved. On the other hand, when the density of adjacent nodes is held constant, increasing \(\Delta\) relaxes the constraint on the path and increases the number of available paths, also resulting in improved PDR. Figure 3c shows the NRE performance under different densities of adjacent nodes after 500 rounds. It can be seen that:  
1. Across various values of density, the energy consumption at \(\Delta=5\%\) consistently demonstrates superior performance compared to other values of \(\Delta\). The reason for this is that when the accuracy constraint is relaxed, more intersection nodes are permitted in the multipath, allowing the establishment of shorter routes (with fewer hops) for data transmission, which can save the energy consumption of the whole network and prolong the lifetime. 2. With the increase in node density, the NRE exhibits a consistent increase across various values of \(\Delta\). The reason for this is that higher density implies a larger number of nodes within the area, and the percentage of active nodes relative to the total number of nodes decreases, resulting in an elevated NRE ratio. The AAL, PDR, and NRE performances in different data transmission rates are shown in Figure 4, with an adjacent node density of 20. Figure 4a shows the AAL performance under different data transmission rates. It can be seen that as the data transmission rate increases from 50 kbps to 100 kbps, the AAL increases consistently across all \(\Delta\) values, signifying a reduction in data accuracy.