# The SF12 Well in LoRaWAN: Problem and End-Device-Based Solutions
## 4 The Problem
### Global Results  
In this subsection, we present and discuss a set of global network performance results, which are obtained for the whole set of simulation scenarios considered. The two main performance results we focus on are the WFT and the PDR. In order to better analyze network behavior, we also compute the number of collisions and the number of packet losses. Each individual result presented corresponds to the average over the 20 simulations using the same scenario configuration. Finally, Figure 8 presents the instantaneous Packet Delivery Ratio (PDR) over time. Note that the instantaneous PDR corresponds to the ratio of packets received by the NS at the application layer divided by the total number of application-layer packets generated  
Figure 6: Evolution of cumulative collisions at the gateway over time. (**a**) Lowest load: 30 CEDs, using an EDL of 0.9 packets/h. (**b**) Highest load: 100 CEDs, using an EDL of 18 packets/h. Figure 7: Evolution of cumulative packet drops at the EDs due to duty cycle restrictions over time. (**a**) Lowest load: 30 CEDs, using an EDL of 0.9 packets/h. (**b**) Highest load: 100 CEDs, using an EDL of 18 packets/h. by the EDs within a relatively small interval (of 4 h and 0.2 h in Figure 8a,b, respectively) that starts at that given time. After the WFT, this performance parameter reflects the steady-state network performance. As aforementioned, in both scenarios, all the CEDs use SF12 after the WFT. However, for low loads, the PDR value after the WFT is near 100%, while in heavy load conditions the PDR is very low, around 10%. In that case, the SF12 Well problem has a dramatic impact on network performance. Figure 9 shows the WFT as a function of the node load. As the offered traffic decreases, the WFT increases quickly. The greatest WFT value is obtained for 30 CEDs and EDL = 0.9 packets/h, with an average WFT equal to 65.3 days. On the other hand, the lowest WFT value is found for 100 CEDs and the EDL = 18 packets/h, with an average WFT equal to 76.7 min (and a maximum value of 93.9 min). Therefore, the WFT depends greatly on the number of CEDs and on the EDL. As the EDL decreases, the mean WFT increases very quickly (note the logarithmic scale for the vertical axis in Figure 9). The WFT differences for the different numbers of CEDs increase as well. Figure 8: Instantaneous PDR after WFT. (**a**) Lowest load: 30 CEDs, using an EDL of 0.9 packets/h. (**b**) Highest load: 100 CEDs, using an EDL of 18 packets/h. Figure 9: Mean and standard deviation of WFT as a function of EDL, for several numbers of CEDs. We next study the impact of the EDL and the number of CEDs on the PDR (see Figure 10). It can be observed how such an impact is significant. For low EDL values, as the EDL increases, the PDR decreases quickly, especially for a high number of CEDs. However, the decrease slows down as the EDL increases. This behavior can be understood by looking at the PDR results corresponding to the CED and UED transmissions (see Figures 11 and 12, respectively). While in the former the PDR exhibits a steady degradation with the EDL, the latter shows only a slight PDR decrease with the EDL, even for high EDL values. Figure 11 also shows that the EDL has a dramatic effect on the PDR, while the number of CEDs generally has a lower influence on the PDR. However, for medium loads, the number of CEDs becomes more relevant. This result can be attributed to the higher impact of the unconfirmed transmissions at high loads when the number of CEDs is low. On the other hand, the high PDR for unconfirmed transmissions shown in Figure 12 indicates that, in contrast with the CEDs, the UEDs are not affected by network congestion, even under a high UED load. Furthermore, the UEDs' PDR is almost not influenced by the CED transmissions or by the number of CEDs. This behavior is due to the constant use  
Figure 11: PDR for CEDs vs. EDL. Figure 10: PDR vs. EDL, from all EDs. of SF7 (i.e., the initial SF value for all the EDs in our considered scenarios) by the UEDs, which yields the lowest possible frame ToA.