# A Failure Risk-Aware Multi-Hop Routing Protocol in LPWANs Using Deep Q-Network
## 6 Simulation Results and Analysis
### Performance Analysis
The comparisons of PDR and residual energy of the network among different EN densities are depicted in Figures 8 and 9. It is evident that FRDR significantly outperforms MHR and DQIR by maintaining a higher PDR and reducing energy consumption. Moreover, Table 11 provides a comparison of network lifetime, while a more detailed comparison of MTH, MTD, and MECP across different EN densities is presented in Table 12. They demonstrate that FRDR achieves the longest network lifetime while maintaining comparable transmission delay. These improvements are attributed to the integration of PRM and the DQN-based multi-factor routing strategy, which dynamically adjusts activation range to reduce redundant activation and optimizes routing decisions based on RFRV, residual energy, transmission hops, and the distance to the GW. \begin{table}
\begin{tabular}{c c c c c} \hline \hline  & **PFRS** & **PRRS** & **PFRD** & **FRDR** \\ \hline MTH & 4.82 & 5.12 & 3.82 & 4.02 \\ MTD (s) & 5.58 & 5.76 & 4.16 & 4.30 \\ MECP (J) & 0.73 & 0.69 & 0.54 & 0.52 \\ \hline \hline \end{tabular}
\end{table} 
Table 10: MTH, MTD, and MECP for delivering the first 1000 packets. Figure 7: Comparisons between FRDR, PRRS, PFRD, and PFRS in terms of the residual energy of the network, PDR, and HND: **(a)** residual energy of the network, **(b)** PDR, and **(c)** HND. MHR focuses solely on minimizing transmission hops, which contributes to its superiority in MTH, as shown in Table 12. However, to achieve this goal, the maximum transmission power is fixed in MHR, which leads to higher redundant activation than FDRR, particularly as EN density increases. This increased redundancy diminishes the delay and energy efficiency advantages gained by minimizing transmission hops, as higher reception delay and energy consumption occur during REQ reception. Table 12 further reveals that MHR results in a higher MECP than FDRR, while achieving a marginal reduction in MTD. Moreover, the exclusive consideration of hop count in MHR inevitably leads to hotspot issues due to the overutilization of partial ENs, which in turn leads to a higher transmission power. \begin{table}
\begin{tabular}{c c c c} \hline  & **FRDR** & **MHR** & **DQIR** \\ \hline
300 & 2516 & 2249 & 2205 \\
350 & 2651 & 2298 & 2445 \\
400 & 2736 & 2420 & 2452 \\ \hline \end{tabular}
\end{table} 
Table 11: HND under different densities. \begin{table}
\begin{tabular}{c c c c c} \hline  & **FRDR** & **MHR** & **DQIR** \\ \hline
300 & MTH & 4.02 & 3.76 & 4.06 \\
300 & MTD (s) & 4.30 & 4.14 & 5.94 \\  & MECP (J) & 0.52 & 0.54 & 0.70 \\ \hline
350 & MTH & 3.88 & 3.57 & 3.60 \\
350 & MTD (s) & 4.30 & 4.07 & 5.47 \\  & MECP (J) & 0.54 & 0.56 & 0.67 \\ \hline
400 & MTH & 3.65 & 3.39 & 3.52 \\
400 & MTD (s) & 4.21 & 4.04 & 5.72 \\  & MECP (J) & 0.55 & 0.58 & 0.72 \\ \hline \end{tabular}
\end{table} 
Table 12: MTH, MTD, and MECP for delivering the first 1000 packets under different densities. Figure 8: Residual energy of the network under different densities: (a) 300, (b) 350, and (c) 400. Figure 9: PDR under different densities: (a) 300, (b) 350, and (c) 400.  
shorter network lifetime and lower PDR. Conversely, by integrating RFRV and residual energy into routing decisions, FRDR effectively avoids routers that will introduce high routing failure risk and realizes a more balanced energy distribution. As a result, FRDR achieves a higher network lifetime and PDR. Specifically, when the PDR of MHR drops to 0.80, FRDR maintains a higher PDR, achieving improvements of 14.71%, 15.69%, and 18.90% at EN densities of 300, 350, and 400, respectively. Consequently, compared to MHR, FRDR effectively improves the PDR and network lifetime while maintaining a comparable transmission delay. As for DQIR, multiple factors, including residual energy and distance to the GW, are considered when selecting the next-hop router from candidate ENs to minimize delay and balance energy distribution. Table 12 indicates that DQIR achieves lower MTH at EN densities of 350 and 400 compared to FDRR.