## 4 Simulation and Analysis
### Simulation Results: The Stationary Occasion  
Figure 2 demonstrates the performance of the three routing approaches and their multi-agent framework-based enhanced versions in a stationary WSN. The solid lines denote the performance variation of the three routing approaches, while the dashed lines indicate the performance of their multi-agent framework-based counterparts. \begin{table}
\begin{tabular}{c c c} \hline
**Parameters** & **Values** & **Explanations** \\ \hline \(E_{elec}\) & \(50\;nJ/bit\) & Energy dissipation parameter \\ \(\epsilon_{amp}\) & \(0.1\;nJ/bit/unit\) & Energy dissipation parameter \\ \(\beta\) & \(3\) & Path loss exponent \\ \(S^{(1)}\) & \(0.01\) & Storage coefficient for keeping packets \\ \(S^{(2)}\) & \(0.0015\) & Storage coefficient for keeping neighbours \\ \(\delta\) & \(2.5\) & Path length coefficient \\ \(\zeta\) & \(2.2\) & Energy consumption coefficient \\ \(\alpha_{1}\),\(\alpha_{2}\),\(\tau\) & \(0.1,0.3,0.2\) & Learning rate \\ \(\epsilon\) & \(0.4\) & Action selection distribution probability \\ \(k\) & \(20\) & Learning rounds \\ \(\gamma_{1}\),\(\gamma_{2}\),\(\gamma_{3}\),\(\gamma_{4}\) & \(1.7,8.2,0.013,1.5\) & Benefit coefficients \\ \hline \end{tabular}
\end{table} 
Table 1: Parameter settings. Figure 2: Performance of routing approaches in a stationary WSN. (**a**) Average delivery latency; (**b**) successful delivery ration (%); (**c**) number of live nodes; (**d**) total sensing coverage (%). In Figure 2a, initially, the delivery latency values in gossiping and GEAR are less than that in LEACH-revised. However, as time progresses, LEACH-revised turns out to be better than both gossiping and GEAR. This can be explained as follows. Initially, in LEACH-revised, the cluster heads usually have to wait for a period for their cluster members to send packets to them and then aggregate and condense these packets to save transmission energy consumption. As time progresses, some sensor nodes are depleted. In gossiping and GEAR, some pre-existing routing paths will disappear, but in LEACH-revised, the impact, caused by sensor node failure, is much less than that in gossiping and GEAR, because routing in LEACH-revised is based on only a few nodes, _i.e._, cluster heads, and even if these cluster heads are exhausted, some other nodes can take their roles immediately by taking the measure developed in LEACH. In Figure 2b, LEACH-revised achieved the highest successful delivery ratio. This is due to the fact that packets in LEACH-revised use the fewest hops from a source node to the sink node compared to gossiping and GEAR, because, as described above, routing in LEACH-revised is based only on cluster heads. Thus, it is more reliable for LEACH-revised to successfully transmit a packet to the sink node than both gossiping and GEAR. In Figure 2c,d, it can be found that in gossiping and LEACH-revised, more sensor nodes can be saved than that in gossiping (Figure 2c), but in GEAR, the total sensing coverage is larger than that in both gossiping and LEACH-revised (Figure 2d). This finding confirms the argument in [21] that saving energy consumption can prolong the lifetime of sensors, but does not necessarily achieve better sensing coverage. This can be explained by the fact that GEAR's transmission method can easily deplete the nodes that are closer to the sink node, but gossiping's transmission method, randomly choosing a neighbour for transmission, can distribute the energy consumption over a larger area than GEAR's method does; so, in gossiping, fewer nodes are depleted compared to GEAR in the same time span. Likewise, in LEACH-revised, routing only relies on cluster heads, and the role of a cluster head is rotated among different sensor nodes. Thus, the lifetime of each sensor node in LEACH-revised could be further prolonged.