# Time Series Analysis to Predict End-to-End Quality of Wireless Community Networks +
## 3 Experimental Dataset
### Dataset Analysis
#### 3.2.2 ETX Behavior  
To understand the behavior of ETX Path Quality, we made some additional measurements. Notice that, in the dataset introduced above, the corresponding EtEQ is ETX Path Quality.  
Figure 4 shows the evolution of average ETX Path Quality throughout a day, for the five working days included in the dataset. In this figure, it can be seen that average ETX path values are more stable at night, between 00:00 and 08:00. Throughout the day, between 09:00 and 01:00, there are more fluctuations, reaching differences of even 1 ETX. Variation of actual ETX path values can be significantly higher, but this information is hidden by the average value. For non-working days (Figure 5), this behavior is less apparent: the fluctuations and stable periods of working days are no longer seen. Similar patterns are often found in network usage datasets, therefore we can assume that the reasons for the depicted behavior is the variation of network traffic and interference during the day, leading to packet loss. This observation suggests that we possibly have to expect different prediction accuracy depending on the day and time when prediction is applied.  
Figure 3: Persistence of paths.  
Figure 2: Temporal evolution of the number of paths.  
To analyze the relationship between path Hop-count and its corresponding average ETX, Figure 6 plots the frequency of each of these values. We can observe that Hops count and average ETX overlap are between the values of 1 and 4. That means that the quality of short paths is maximum. However, for values 5 or higher, average ETX path values present deviations that can be translated as decreased EtEQ and a large number of needed packet retransmissions needed. Notice that the more frequent values of Hops count and average ETX (more than 10% each) are in the range of 5-9.  
In our last study, we analyzed the dispersion of ETX according to the number of Hops. In this way, Figure 7 contains the box plots of the deviation between average ETX and hops. The values were normalized with the corresponding number of hops to provide a better idea of the scale of the deviation, taking into account that the average ETX deviation is not correlated with the number of hops. We can see that the average ETX deviation is minimal for 1-4 Hops, it is significant for 5-9 hops, and relevant for 10-13 hops. We did not consider paths with 14 or more hops because they are very odd cases and are not representative to show the correlation between ETX and hops. Most of them are paths that contain a sequence of nodes connected in a line with fiber. Therefore, we can conclude that the prediction would be more or less accurate depending on the number of Hops.  
Figure 4: Temporal evolution of the average ETX of paths (working days).  
Figure 5: Temporal evolution of the average ETX of paths (non-working days).  
Figure 6: Frequency of path lengths based on hop count and average ETX.  
From the above preliminary observations and dataset studies, we reached the conclusions that from a node's ego-network point-of-view there is a non-negligible amount of unstable paths for which the average ETX path value shows a significant deviation from the optimal value. To better clarify this issue, Figure 8 provides a histogram of deviation between average ETX and number of hops. Notice that paths with ETX-HOPS of zero are optimal in terms of the routing metric. In this case, just 30% of all paths are included in this category. Moreover, the number of paths (up to 50%) that presents ETX-HOPS within the range [0,1] is quite significant. Finally, 20% of the remaining paths are distributed in the remaining ranges.  
In summary, to investigate the EtEQ behavior as well as to find efficient EtEQ prediction strategies based on time-series analysis would result in valuable information for routing in WMCNs.