# A Grant-Free Random Access Process for Low-End Distribution System Using Deep Neural Network
## 7 Simulation Results  
Before discussing the simulation results, let us explain the feature extraction and training process of the DNN. Figure 7 shows a screenshot of the features extracted. We see that there are 10 rows with each row representing a station and within each station, there is an infinite number of devices that are represented by columns. For each device, six features are extracted and stored. The first six columns of the first row represent the features of the first device in the first station. The columns from 7 to 12 in the first row represent features of the second devices of the first station and so on. The features extracted are as follows:  
* The channel coefficient;
* The transmitting device;
* The successful device;
* The devices that have coefficients greater than the threshold;
* The last outcome of the channel;
* An indicator whether the previous three transmissions of the device are collisions. A channel coefficient is a random number between zero and one drawn from a normal distribution. The second feature tells us whether the device transmits or remains idle. If its value is one, it means that the device has transmitted whereas zero represents an idle scenario. The third feature tells us which device among all is successful. Since there is only one channel, only one device can be successful, in which case this feature's value is one, otherwise, it is zero. The fourth feature is a flag that has a value of one when the device has a channel coefficient greater than the threshold. If the value of the channel coefficient is less than the threshold, its value is zero. The last outcome of the channel means whether the previous outcome of the channel was a success, a collision, or an idle event. It is an important parameter as it tells us whether there is a large number of devices attempting transmissions or not. The last feature is related to the outcome of individual devices, whether successful, idle or a collision. This feature is different from the previous one, as in the previous feature the outcome of the channel was discussed while in this feature, the outcome of the individual device is considered. With all the features in hand, we needed to accumulate success scenarios such that the features vividly point to the successful device. Once it was done, then the data were fed to the DNN, which extracted the features depending on the success scenario. Then, the fully trained DNN was able to tell us in real-time which device needed to transmit to get maximum success and minimum collisions. Let us discuss the simulation results after we apply Algorithm 1 to our system model. The number of stations for the simulation was taken to be four and an infinite number of devices were allowed to arrive and access the channel. In case of collision or idle event for a device, which can result from the channel being busy, the devices could queue up at the stations. The stations randomly accessed the channel based on a slotted ALOHA protocol; however, the transmission was governed by Algorithm 1. The arrival distribution was assumed to be Poisson with the arrival rate changing for each set of simulations. The output parameters considered were the average access delay, the number of successes, and the number of collisions. The idle, success, and collision events were recorded to form  
Figure 7: Extracted features to train the DNN. a dataset that served as input for training the DNN. The DNN was eventually used in real-time to predict which device needed to transmit to maximize success and minimize access delay. In Figure 8, we plotted the average access delay versus the channel coefficient while the arrival rate was kept constant. The access delays were plotted for two values of arrival rates, i.e., \(\lambda=0.1,0.2\). It is obvious that the lower arrival rate exhibits a lesser access delay as shown in the figure. With an increasing value of channel coefficient, the average access delay decreases because larger values of the channel coefficient represent good channel conditions and vice versa.