# A Poisson Process-Based Random Access Channel for 5G and Beyond Networks +
## 5 Performance Evaluation  
The proposed 2 PRACH approach decreases the collision incidence and improves the performance rate of the existing RA of the UE association without altering the 3 GPP recommended RA procedure. We conducted simulations in a discrete-event network simulator release 3.30.1 (ns-3.30.1) [23] to evaluate the performance of the 2 PRACH approach. The network topology used in simulations includes a radio access network part of a typical UE communication, as shown in Figure 1. The proposed approach's efficiency is measured in terms of network stability (reliability) and end-to-end latency. These two evaluation parameters are tested for three different scenarios. First, we conducted simulations with increasing number of UEs in the network, that is \(N=\{2,4,8,16,32,64\}\). Later, we assess the efficiency with varying data packet sizes and interarrival packet speeds. The objective of conducting simulations of various packet sizes and rates of interarrival is to evaluate the impact on the proposed mechanism's real data transmissions. We observe from Figure 2 that the users' distribution tends towards the similar density function as of a uniform distribution. Therefore, one can choose the average rate parameter (\(\lambda\)) according to the conditions and requirements. In this paper, we use \(\lambda=8\) as our rate parameter, which distributes the users near the initial channel access slots. Detailed simulation parameters and their used values are described in Table 1. \begin{table}
\begin{tabular}{l l} \hline \hline
**Parameter** & **Value(s)** \\ \hline Simulation time & 100 s \\ Simulation model & LTE-EPC model \\ Number of eNBs & 2 \\ Number of UEs & \(2,4,8,16,32,64\) \\ Distance between UE and eNB & 60 m \\ Data payload (packet) sizes & \(32,64,128,256,512,1024\) Bytes \\ Packet Interarrival rates & \(5,10,20,40,80,160,1000\) ms \\ Total number of RA preambles & 64 \\ CB-RA preambles & 52 \\ Rate parameter (\(\lambda\)) & 8 \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Simulation parameters and their values. Figure 4 compares the efficiency of our proposed 2 PRACH mechanism with the existing uniform distribution-based RACH procedure, and the CRB-RACH mechanism [18], where the number of contending UEs varies. In Figure 4a, we show that the 2 PRACH mechanism achieves higher reliability than existing RACH and CRB-RACH procedures, also in dense UEs deployments, which is 64 UEs. Similarly, the network's end-to-end latency is also reduced for the proposed 2 PRACH mechanism, as shown in Figure 4b. In the 2 PRACH scheme, improved reliability and reduced latency are evident that for a denser UE environment, choosing earlier RA preambles with a constant parametric rate decreases collision among the UEs. The improved efficiency is because a Poisson process-based distribution manages the number of events in a fixed time frame and the time between occurrences of those successive events. It fits our RACH scheme's settings because it is one of the distributions with the \"lack-of-memory\" property. It means that, after waiting to access the channel without successful transmission, the probability of a UE to access the channel in the next contention is the same as was the probability (in previous transmission attempt) of accessing the channel in the following two transmission attempts. Thus, as a UE in the system continues to wait, the chance of successful transmission neither increases nor decreases based on the parameter selected. Although the CRB-RACH procedure improves the efficiency compared to the existing RACH with the use of dynamic backoff adjustment, due to the use of uniformly distributed backoff parameters, it achieves lesser reliability and higher latency as compared to 2 PRACH. The efficiency of the proposed 2 PRACH mechanism is also measured with various data packet sizes. The motivation to evaluate an RA process with different data frame sizes is that the UEs' channel capital occupancy time very much depends upon the data frame size to transmit.