# A Grant-Free Random Access Process for Low-End Distribution System Using Deep Neural Network
## 7 Simulation Results
In Figure 9, we plotted the average access delay versus the arrival rate when the arrival rate varied from 0.1 to 0.3. The devices transmitted according to the scenario mentioned in Algorithm 1. We see that the access delay is small when the arrival rate is small and keeps on increasing with the increase of the arrival rate. This is understandable as more and more devices try to transmit to the channel when the arrival rate is large and hence, they need to wait more in the queues, which results in an increased access delay. Figure 8: Delay vs. channel coefficient. Figure 9: Delay vs. arrival rate. The plots in Figure 9 are shown for the scenarios where the thresholds on the channel coefficient are 0.3, 0.5, and the optimal \(T\) are represented in back, red, and blue colors, respectively. We see that when the threshold on the channel coefficient for transmission is 0.3 or 0.5, the average delay is large. This is because when the threshold is 0.3 and 0.5, too many devices transmit and this results in collisions, which increase the access delay. Similarly, when the threshold is optimal, a relatively fewer number of devices transmit, resulting in successful events. Moreover, it also reduces the number of idle events, and we see that when it is optimal, the delay is less as compared to 0.3 and 0.5. In Figure 10, we plotted the number of successes versus the channel coefficient threshold for the arrival rate of 0.2. We see that the number of successes is small when the threshold is low. It is because a large number of devices qualify for the transmission and it results in collisions. As the threshold increases, a smaller number of devices transmit, thus increasing the chance of success. At the thresholds of zero and one, there is no success because the channel coefficients are generated in (0, 1), so no device qualifies for transmission, hence zero success. Moreover, we also plotted the number of successes in a scenario where the transmitting device was predicted through the DNN. The graph in blue color represents the actual number of successes whereas the estimated one in red color closely follows the actual ones. This shows that our algorithm works fine and that the DNN predicts the transmitting device such that success is maximized. In Figure 11, we plotted the backlog of each station in actual and DNN-applied scenarios. The backlog at each station is the number of IoT devices waiting for transmission. In the actual scenario, the devices transmitted based on the Algorithm defined above for learning purposes. In the applied DNN scenario, the devices transmitted based on the prediction by the DNN. Please note that the DNN predicted which device needed to transmit to have maximum chances of success. We see that the backlogs of both scenarios are close to each other. Moreover, the backlog in the applied DNN scenario follows the actual backlog, which determines that the prediction is quite good and the actual scenario coincides with the applied DNN scenario. Figure 10: Number of successes vs. channel coefficient. Along the same lines as Figure 11, Figure 12 represents how the DNN erroneously selected a different device other than the actual one. In this figure, we present whether the DNN successfully predicts the transmitting device not. Since in each time slot, only one device transmits, the graph is either one or zero with one representing the transmission of a device and zero representing the idle scenario. We see that our DNN model performs correctly as we advance in time because we do not have a match in only some instances. We also observe that the DNN estimated graph closely follows the actual one which states that the DNN is performing well. Figure 11: Backlog vs. time. Figure 12: Number of successes vs. channel coefficient.