# Energy Storage Overflow-Aware Data Delivery Scheme for Energy Harvesting Wireless Sensor Networks
## 4 Performance Evaluation
### Simulation Results  
We compare our OP-ESO and OP-RE with the EHWA [20], the EHARA [15], the uniform allocation scheme (UAS), and inverse proportion allocation scheme (IPAS) in terms of number of bits delivered to the sink, where all paths have the same capacity in the UAS, and each path having capacity inversely proportional to the number of hops in the path in the IPAS. For instance, assume \(k\) paths have \(h_{1}\), \(h_{2}\),..., and \(h_{k}\) numbers of hops. Then, the \(i\)-th path is allocated to capacity of \((1/h_{i})/(1/h_{1}+1/h_{2}+,\ldots,\)\(+1/h_{k})\) out of the total capacity (\(i=1,2,\ldots,k\)). First, we study impact of data sending rate on number of delivered bits. Letting the source send its data for one hour with rates of 10, 20, 30,..., and 90 bytes per second, we obtain Figures 5-7. From the figures, we observe that the proposed OP-ESO and OP-RE outperform the other four schemes in number of delivered bits in the LER, MER, and HER cases. Figure 5 indicates that in the LER case, the number of delivered bits reduces as data sending rate grows. The reason is that a higher data sending rate causes more energy to be consumed in delivering data and thus the node needs to spend more time on harvesting energy, which reduces the number of delivered bits. This phenomenon can be alleviated when energy harvesting rate increases, which is reflected in Figure 6 that illustrates the results of the MER case. From Figure 6, when the sending data rate is no more than 80, a higher data sending rate makes the proposed OP-ESO and OP-RE bring in a higher number of delivered bits. The other four schemes present a similar up-then-down trend, i.e., number of delivered bits gradually grows and then goes down. This trend can be clearly seen from Figure 7, in which the HER case is considered. In summary, from Figures 5-7, we observe that for a given energy-harvesting rate, the numbers of delivered bits in all the schemes exhibit the up-then-down trend when data sending rates increases.  
\begin{table}
\begin{tabular}{c c c} \hline
**Notation** & **Definition** & **Value** \\ \hline \(u\) & The minimum transmission unit & one octet \\ \(B\) & The energy storage capacity & 5 Joule \\ \(\varepsilon_{0}\) & Energy consumption in digital coding, modulation, filtering, and & 50 nJ/bit [20] \\  & spreading of the signal, etc & 10 pJ/bit/m\({}^{2}\)[20] \\ \(\varepsilon_{1}\) & Energy consumption of the transmitter power amplifier & 10 pJ/bit/m\({}^{2}\)[20] \\ \(\gamma\) & Path loss exponent & 2 \\ \(M\) & The number of chromosomes in a population in GA & 400 \\ \hline \end{tabular}
\end{table}
Table 2: Parameter values.  
Figure 5: Number of delivered bits vs. data sending rate in the low energy-harvesting rate (LER) case.  
Figure 6: Number of delivered bits vs. data sending rate in medium energy-harvesting rate (MER) case.  
Figure 7: Number of delivered bits vs. data sending rate in high energy-harvesting rate (HER) case.  
Next, we compare them in terms of residual energy and ESO. We only consider the MER case with a data sending rate of 20 octets per second, which leads to Figure 8. This figure indicates that the OP-RE achieves the maximal residual energy and the OP-ESO achieves the minimal ESO, respectively. That is, the objects of the OP-ESO (i.e., minimizing ESO) and the OP-RE (i.e., maximizing total residual energy) have been realized. Another observation is that the total residual energy fluctuates with time (see Figure 8a) and ESO increases with time (see Figure 8b).  
Last, we study the impact of \(\alpha\) on residual energy and ESO in the proposed EAMP. Setting \(\alpha=0\) (i.e., the OP-RE), \(10^{-4}\), \(10^{-2}\), and \(1\) (i.e., the OP-ESO), we obtain Figure 9. From the figure, we have the observations that: 1) the smaller the \(\alpha\), the higher the residual energy, and the EAMP with \(\alpha=0\) (i.e., the OP-RE) has the highest total residual energy (see Figure 9a), and ESO is slightly affected by variation in \(\alpha\) (see Figure 9b).