# Time Series Analysis to Predict End-to-End Quality of Wireless Community Networks +
## 5 Use Case Analysis
### Analysis of Results  
To evaluate the impact of the prediction on the network messages, we first studied the Packet Delivery Ratio (PDR). Table 2 shows the results obtained simulating diverse network load conditions. We can observe that both EtEQ prediction and ETX + Dijkstra presented a similar delivery rate. When links were not overloaded, the behavior was equal, showing that the few prediction errors did not produce path changes. On the other hand, when links were overloaded due to data traffic, our approach detected earlier this situation. In this last case, EtEQ prediction achieved 22.7% better delivery rates.  
We also analyzed the PDR behavior under link failures, as shown in Table 3. Both strategies showed very similar behavior, with differences below 1%, which we considered insignificant. Therefore, we argue that the predictor is not able to foresee link failures.  
In our next set of simulations, we measured the quality of links for the compared routing strategies, using ETX of links and EtED. We first studied the ETX, as computed when the network was overloaded. In Figure 22, we can observe the frequency of the diverse ETX values (ETX values close to 1 are better, because they are less overloaded). From the results in this figure, we can argue that, using EtEQ prediction, the average ETX of links is higher, thus the observed link quality is increased. Additionally, the deviation of the quality of the proposed strategy is lower than the one using ETX + Dijkstra, resulting to a better behavior. Finally, when the quality of a link deteriorates, EtEQ prediction allows the routing algorithm to adapt earlier than ETX + Dijkstra. Therefore, we argue that the former reacts earlier upon an overloaded link.  
The second metric we used to evaluate both prediction approaches was EtED, where lower values are better. Figure 23 shows the histogram of EtED normalized values. Overall, EtEQ presents similar EtED values to ETX + Dijkstra. Nevertheless, when the network was overloaded, EtEQ values were slightly higher (worse) than ETX + Dijkstra. As observed in the figure, when the quality of a link declines, the EtEQ routing algorithm changes earlier to a new path. This implies an earlier reaction before link overloading. Moreover, under the proposed approach, the new paths used are less overloaded, resulting in an improved Packet Delivery Ratio (PDR, as previously shown in Tables 2 and 3). On the contrary, the new chosen paths are equal or slightly larger (in HOPS), thus the delivery times are higher (worse). Finally, for the cases of EtEQ prediction failures, i.e., changes in the used path, the new paths are equal or slightly larger (in HOPS), contributing to higher delivery times without achieving a higher PDR.  
\begin{table}
\begin{tabular}{c c c c} \hline \hline  & **1 Packet Every 100 Slots** & **1 Packet Every 10 Slots** & **1 Packet Every 1 Slots** \\ \hline ETX + Dijkstra & 1.0 & 0.98 & 0.44 \\ End-to-End Quality Prediction & 1.0 & 0.98 & 0.54 \\ \hline \hline \end{tabular}
\end{table}
Table 2: Packet delivery ratio (PDR) under diverse load conditions.  
\begin{table}
\begin{tabular}{c c c c c c} \hline \hline  & **None** & **Uniform 10** & **Uniform 2** & **Pareto 10** & **Pareto 2** \\ \hline ETX + Dijkstra & 1.0 & 0.99 & 0.91 & 1.0 & 0.89 \\ End-to-End Quality Prediction & 1.0 & 0.98 & 0.90 & 1.0 & 0.89 \\ \hline \hline \end{tabular}
\end{table}
Table 3: Packet delivery ratio (PDR) with link failures.  
Our simulations were very small compared to real WMCN such as Funkfeuer network. Therefore, it is difficult to generalize the simulation results to Funkfeuer network. Nevertheless, we believe that dealing with EtEQ prediction may be useful with paths that present the most overloaded links.