# A Failure Risk-Aware Multi-Hop Routing Protocol in LPWANs Using Deep Q-Network
## 6 Simulation Results and Analysis
### Performance Analysis
Specifically, MHR selects relays via pre-stored routing tables guided by minimum hop counts, while DQIR prioritizes relays that minimize distance to the GW and balance residual energy distribution. FRDR  
Figure 5: Simulation experiment scenario diagram of FRDR. \begin{table}
\begin{tabular}{c c c c} \hline \hline
**ID** & **RFRV** & **Distance (m)** & **Residual Energy (J)** \\ \hline
1 & 0.1648 & 499.0684 & 5.9358 \\
78 & 0.3042 & 461.9026 & 5.9358 \\
88 & 0.2711 & 559.5603 & 5.9358 \\
93 & 0.4604 & 534.8417 & 5.9358 \\
167 &  
and PFRD incorporate multi-dimensional neighborhood state characteristics of candidate ENs into routing decisions, effectively avoiding relays that introduce high routing failure risk (e.g., Router1 in MHR and Router3 in DQIR). First, the performance analysis of the proposed PRM and Algorithm 3 is provided. Figure 7a demonstrates that PRM effectively reduces energy consumption. By employing PRM, DENs in FRDR and PRRS adjust transmission power levels according to demand, thereby reducing redundant EN activations. Consequently, the lifetime of individual EN can be extended, which in turn enhances the overall network lifetime and PDR. Figure 7b further illustrates that the PDR curves of PRRS and FRDR decline more slowly than PFRS and PFRD. Specifically, when the PDR of PFRD and PFRS drops to 0.80, FDRR and PRRS maintain values of 0.88 and 0.85, representing improvements of 10.00% and 6.25%, respectively. Additionally, as depicted in Figure 7c, both FRDR and PRRS achieve higher HND than their respective counterparts, which confirms the effectiveness of PRM in extending network lifetime. Table 10 presents a comparison of MTH, MTD, and MECP for delivering the first 1000 packets, during which the PDR of each algorithm remains at a relatively high level. It reveals that PRM introduces a slight increase in transmission delay. Compared to PFRD and PFRS, the MTH of FRDR and PRRS increased by 0.20 and 0.30, respectively. This increase is attributed to the fact that the execution of PRM prevents the single-hop range from consistently reaching its maximum, potentially increasing the number of hops required for data delivery. Nevertheless, through the effective combination with pre-selection rules, PRM further amplifies the benefits of reducing redundant EN activations, thereby significantly decreasing the delay and energy consumption associated with REQ  
Figure 6: Simulation experiment scenario diagram of multi-hop routing: (**a**) FRDR, (**b**) MHR, (**c**) DQIR, (**d**) PFRS, (**e**) PFRD, and (**f**) PRRS. packet reception. As a result, the impact of these additional hops on overall delay is minimal. Specifically, the 0.14 s increase in MTD for FRDR constitutes only 3.26% of its total MTD, while for PRRS, it accounts for 3.13%. Overall, PRM achieves an effective balance between transmission efficiency and other critical performance metrics, including energy consumption, PDR, and network lifetime. As for Algorithm 3, Figure 7b clearly illustrates its superiority in PDR. Specifically, when the PDR of PRRS and PFRS decreases to 0.80, FRDR and PFRD sustain values of 0.96 and 0.94, achieving improvements of 20.00% and 17.5%. These improvements arise from the multi-factor routing strategy of Algorithm 3, where RFRV, distance to the GW, transmission hops, and residual energy are considered in tandem. Therefore, Algorithm 3 effectively reduces transmission disruption and enables faster delivery to the GW while balancing energy consumption. The results presented in Figure 7c and Table 10 further confirm the advantage of Algorithm 3. In terms of HND, FRDR improved by 16.81%, while PFRD achieved a growth rate of 9.46%. Additionally, during the whole network lifetime, FRDR achieves reductions of 21.48%, 25.35%, and 24.64% in MTH, MTD, and MECP, respectively, compared to PRRS, while PFRD demonstrates reductions of 20.75%, 25.45%, and 26.03%. Second, to fully illustrate the superiority of FRDR, a comparison among FRDR, MHR, and DQIR is presented.