# On the Benefits of Listen before Talk Scheme for NB-Fi Networks
## 7 Numerical Results
### Results for a Circle with Radius of 0.4 km
#### 7.1.2 Delay  
Figure 5 shows the dependencies of the average delay on the load for six sensor operating modes.  
Figure 5a,b show the average delay for the 25.6 kbps and 3.2 kbps rates, respectively. The results for the Aloha and CSMA modes are almost the same at low load. This happens because of the low probability of collision and the small time interval needed for carrier sensing in CSMA modes. At a load of about 2-100 packets/s, the average delay in the CSMA modes is much less than in the Aloha mode because a sensor in the Aloha mode wastes much time on retransmissions, while with CSMA, it has to wait for the channel to become idle but makes fewer retransmissions. At higher loads, the average delay in the Aloha mode is less than in the CSMA modes because packets are either transmitted successfully during the first attempt or are replaced by new ones, while in the CSMA modes, a sensor defers transmissions and avoids collisions. At a load below 100 packets/s, among different CSMA modes, non-persistent CSMA with and without frequency hopping obtain the lowest delay. With a higher load, the \(p\)-persistent CSMA with \(p=0.01\), and non-persistent CSMA with and without frequency hopping have the highest average delay, while the persistent and \(p\)-persistent with \(p=0.1\) ones have a lower average delay. Such a result contradicts [12] but is explained by the peculiarities of the buffering model because frames that wait too long in the buffer are preempted by the newer frames and are not taken into account in the statistics of the average delay (but are accounted for in the PLR).  
Figure 5c,d show the average delay for the 400 bps and 50 bps rates, respectively. At low loads, the average delay is also almost the same for all the modes. At higher loads, the results differ from the rates of 25.6 and 3.2 kbps. With loads up to \(\approx\)40 packets/s for 50 bps and up to \(\approx\)100 packets/s for 400 bps, the average delay in the Aloha mode is higher than in CSMA modes. It happens because, in the Aloha mode, the sensors waste much time retransmitting packets after collisions, while in the CSMA mode, the sensors spend less time listening to the channel to avoid retransmissions. These results align with the classic studies of Aloha and CSMA, e.g., [12]. At higher loads, when PLR becomes almost the same in all modes, we see the opposite situation: in the CSMA modes, the sensor delays the transmission for a long time, while in the Aloha mode, the sensor transmits packets immediately after generation. Moreover, a notable difference between the CSMA modes can be explained by specific implementation features of each mode, such as the immediate start of the transmission in persistent CSMA or delaying the transmission in p-persistent CSMA and non-persistent CSMA. At high loads, in all modes, the average delay decreases because packets are frequently replaced by new ones, and successful packets are transmitted with few retries or without them at all. This result contradicts [12] but is explained by the peculiarities of the buffering model, i.e., that the packets are lost if new packets arrive before their transmission.  
From the obtained results, we can conclude that the lowest delay is obtained with the data rate of 25,600 bps and non-persistent CSMA for loads up to 100 packets/s, and with p-persistent CSMA for loads greater than 100 packets/s. However, the loads above 100 packets/s are unfeasible for NB-Fi because the PLR becomes close to one at such loads.