## 6 Numerical and Simulation Results
### System Performance versus Packet Size  
In this and the next subsections, we will validate the analysis of system capacity and system equilibrium for the pure S-ALOHA protocol and pure TDMA protocol. For this purpose, we assume that the arrival rate of new packets follows a Poisson distribution and the evaluation time is set to 500 cycles.  
Shown in Figure 5, the system performance of S-ALOHA and TDMA protocols with different packet size are derived by the iterative method. For small packet size \(\delta\) = 0.5, as shown in Figure 5a,b, when the available resource blocks are insufficient, both the average success probability and resource utilization ratio of S-ALOHA protocol is higher than that of TDMA protocol. At the same time, as shown in Figure 5c, the average request number of S-ALOHA protocol is lower than that of TDMA protocol. When the number of available resource blocks is large enough, the success probability and resource utilization ratio of S-ALOHA protocol are almost the same with that of TDMA protocol while the average request number of S-ALOHA protocol is still lower than that of TDMA protocol. For large packet size \(\delta\) = 2, on the contrary, when the available resource blocks are insufficient, both the average success probability and resource utilization ratio of S-ALOHA protocol is lower than that of TDMA protocol and the average request number of S-ALOHA protocol is higher than that of TDMA protocol. When the number of available resource blocks is large enough, the success probability and resource utilization ratio of S-ALOHA protocol are almost the same with that of TDMA protocol while the average request number of S-ALOHA protocol is still higher than that of TDMA protocol.  
\begin{table}
\begin{tabular}{c c} \hline \hline
**Parameter** & **Settings** \\ \hline Cell bandwidth & 10 MHz (50 RBs in frequency domain) \\ Cycle interval \(\tau\) & 5 ms \\ Reserved RBs for uplink transmission \(L\) & 200 \\ Transmission limit \(Q\) & 5, 10 \\ H2H traffic model & Poisson distribution \\ M2M traffic model & Beta distribution \\ Signaling overhead parameter for H2H traffic \(\gamma\) & 2 \\ Packet size of H2H traffic \(\delta_{1}\) & 2 \\ Packet size of M2M traffic \(\delta_{2}\) & 0.5 \\ Number of M2M devices \(N^{\text{M2M}}\) & 10,000–60,000 \\ Activation time of M2M devices \(T\) & 10 s \\ Beta function parameters \(\alpha\), \(\beta\) & 3, 4 \\ Backoff window size for M2M traffic \(W_{BO}\) & 20 \\ DPBO time control parameter for M2M traffic \(\eta\) & 10 \\ \hline \hline \end{tabular}
\end{table}
Table 1: Performance Evaluation Parameters for Proposed HSTMAC Protocol.  
\begin{table}
\begin{tabular}{c c c c c c c c c c c} \hline \hline \(Q\) & **1** & **2** & **3** & **4** & **5** & **6** & **7** & **8** & **9** & **10** \\ \hline \(P_{S}\) & 0.3679 & 0.6004 & 0.7474 & 0.8403 & 0.8991 & 0.9362 & 0.9597 & 0.9745 & 0.9839 & 0.9898 \\ \hline \hline \end{tabular}
\end{table}
Table 2: Success Probability at the Saturation Threshold under Different Transmission Limit.  
Therefore, we can validate the analysis in Section 3.1 and make a conclusion that the S-ALOHA protocol is superior to the TDMA protocol for small packet transmission while the TDMA protocol is superior to the S-ALOHA protocol for large packet transmission.