## 4 Numerical Results  
Here, the simulation results are presented to display the impacts of the delay exponent and the transmission error probability on NOMA networks with short packet communications. Assuming that there are three non-orthogonal users in the network and the corresponding power allocation factors are allocated to be \(a_{3}=0.2\), \(a_{2}=0.3\) and \(a_{1}=0.5\), the finite blocklength is equal to \(300\), i.e., \(n=300\), and the delay exponents and transmission error probability are set to \(\theta_{1}=\theta_{2}=\theta_{3}=0.01\) and \(\varepsilon=10^{-5}\), respectively. We chose the conventional orthogonal multiple access (OMA) as a generality baseline, and fairness can be guaranteed. Figure 2 plots the effective capacity of the three users vs. the SNR for a simulation setting with \(n=300\), \(\theta_{1}=\theta_{2}=\theta_{3}=0.01\), and \(\varepsilon=10^{-5}\). The effective capacity curves of the user \(m\) (i.e., \(m=1\) and \(m=2\)) for NOMA networks with short packets are plots based on (17). The effective capacity curve of the user \(M\) (i.e., \(M=3\)) is plotted based on (18). Clearly, the simulation results are matched with the theoretical expressions. It can be observed that the effective capacity of NOMA networks is a throughput ceiling, and this is a result of the impacts of transmission error probability. Another observation is that the effective capacity of OMA is worse than that of User 3, as our the capacities of Users 1 and 2.This phenomenon demonstrates that NOMA with low-latency communications can also serve multiple users, and other papers [8; 20; 27] show the same conclusions. Figure 3 shows the effective user capacity vs. SNR with a different blocklength (i.e., \(n=400\), \(300\), and \(200\)). As shown in Figure 3, as the blocklength decreases, the effective capacity of User 3 becomes much greater, while there are almost no changes for Users 1 and 2. The main reason for this is that the distant users suffer serious impacts from the process of decoding. Figure 4 plots the effective capacity of the three users vs. \(\varepsilon\) for a simulation setting with \(n=300\) and \(\theta_{1}=\theta_{2}=\theta_{3}=0.01\). As can be seen in Figure 4, the transmission error probability has a greater influence on NOMA networks under low-latency communications. As the value of \(\rho\) increases, the effective capacity of NOMA networks substantially decreases. This is because that \(\varepsilon\) becomes a major factor relative to the low SNRs. Figure 5 plots the effective capacity vs. \(\theta\). It can be observed that a larger value of the delay exponent leads to a smaller effective capacity. However, the high SNR improves the effective capacity at a given \(\theta\), and the effective capacities of Users 1 and 2 seem to be more stable than that of User 3. Figure 6 plots the effective capacities of the three users vs. the SNR and blocklength for a simulation setting with \(\theta_{1}=\theta_{2}=\theta_{3}=0.01\) and \(\varepsilon=10^{-5}\). As can be seen in Figure 6, the effective capacity of User 1 is mainly affected by the SNR, and the blocklength has little effect. With respect to User 2, the effective capacity is affected by the SNR and the blocklength. The effective capacity of User 3 increases with the increase in SNR and the decrease in blocklength. This can be explained by the fact that, in the NOMA system, the blocklength of User 2 is not shorter than the blocklength of User 1; otherwise, the detection of User 2 will not succeed. The blocklength of User 3 is not shorter than those of the other two users at the same time. Figure 7 shows the influences of blocklength and SNR on the user's effective capacity. The effective capacity of non-orthogonal users increases with SNR and eventually tends to be stable in the high SNR region. In the low SNR region, the change of blocklength has little impact on the effective capacity. The asymptotic effective capacities of non-orthogonal users are convergent in the high SNR region.