# Power Efficient Random Access for Massive NB-IoT Connectivity
## 5 Performance Evaluations
### Simulation Results
More attempts each with less time would also add up to substantial delay. Thus, it becomes important to check the delay observed by devices in PE-RAP in comparison to existing RAP. We perform simulations for the average delay in PE-RAP and compare it to the existing RAP. We observe the time spent by devices in different CE levels before it is finally successful. Figure 9 shows the mean delay observed by a device for our proposed PE-RAP and existing RAP. The delay  
Figure 8: Power consumption comparison (analytical and simulation) for variations in repetitions (**a**) in CE0, (**b**) in CE1, (**c**) in CE2. obtained by PE-RAP is less than the existing. This is because in existing RAP the device keeps trying in the initially chosen CE level for the configured number of reattempts before moving to the higher one. While in PE-RAP, the device ascertains and moves to the correct CE level sooner, which increases the chances of success in less time. As expected, the delay observed by the device increases with the increase in the number of configured repetitions. Figure 10 presents the confidence interval plot for different simulation results. We considered the confidence interval of 95%. We calculated the mean, standard deviation and margin of error. In Figure 10a, for CE0 when the number of repetitions is 4, the upper confidence level is 570.31 and lower confidence is 567.69. From Figure 9, it can be seen that for CE0 with 4 repetitions, the average of simulations is in the confidence interval range (567.69\(\sim\)570.31). This verifies our simulations. The PE-RAP advantages are based on the correct selection of the number of repetitions, the power level and the CE level. Incorrect selections would lead to more power consumption in power limited  
Figure 10: Confidence interval results for (**a**) CE0; (**b**) CE1; (**c**) CE2. Figure 9: Average delay for different number of repetitions (**a**) in CE0, (**b**) in CE1, (**c**) in CE2 (proposed PE-RAP and existing RAP). NB-IoT devices. The device measures RSRP for CE level selection more often in PE-RAP than the existing system. If the device measures RSRP incorrectly then it may select incorrect CE levels, more often resulting in repeated failures. For instance, if the device in CE2 keeps selecting CE0 incorrectly, it would never increment its power or repetitions and would never succeed. This would impact the performance and power consumption adversely. It would also increase the latency. On the other hand, if the channel condition is good, the device is expected to select CE0. However, if it measures RSRP incorrectly and selects CE2, it would suffer an unnecessary high power consumption, though success would be achieved faster. Furthermore, if the configured repetitions are small and the channel variations limited, then the device would have to perform RSRP measurements more frequently. Since our proposal is aimed at obtaining the effect of repetitions and reattempts on the average power consumption, the methodology for measurement of RSRP for the selection of CE levels is not in the paper and can be considered in future works. Another effect that can be considered is the allocation of preambles to different CE levels. If all users in a cell are located at the same distance with the same RSRP then they may select the same CE level which would increase the collision probability. In such a case more preambles should be allocated to this particular CE level. If the network can allocate preamble resources dynamically based on collision probability, the RAP reattempts and therefore impediments of several repetitions can be reduced.