## 4 Experiments and Results
### Coverage and Network Life  
Deployment and self-healing results can be evaluated in terms of the parameters proposed in Section 3.1.  
The most relevant parameter is coverage. As the number of dead nodes in the MWSN increases, coverage decreases. Figure 13a shows how nodes die in time during the simulations in Figures 7, 8, 10 and 11. Nodes run out of battery mostly depending on the number of packets they route and also on transmission distance (Figure 6). As commented in Section 3, in our closest neighbor routing implementation, all nodes transmit with constant power, specifically at \(-12\) dBm to reach \(25\) m. In hierarchical routing, packets are sent to the sink node via L1 nodes, and transmission power is adapted to reach the destination node depending on the distance between transmitter and receiver. Nodes usually die in small groups that have been routing similar traffic since the network reached balance.  
Figure 13a shows the evolution of dead nodes in time for all simulations in Section 4.1. As commented, results in real conditions would most likely change (e.g., robot battery life, localization errors, etc.), so coverage and network lifetimes would probably be significantly lower. Nevertheless, conclusions extracted from these simulations as a whole are consistent and coherent with theoretical expectations. Closest neighbor routing provokes partial flooding. Hence, the number of packets in the network is much larger in this mode than in hierarchical routing, where an L0 packet is just one hop away from the sink node. Consequently, nodes start to die earlier and faster in geographic routing simulations: around \(120\) days after initial deployment, \(70\%\) of the nodes are dead. In hierarchical routing simulations, nodes do not start to die until approximately Day \(250\), and their dying rate is  
Figure 11: Network configuration when: (**a**) \(0\%\); (**b**) \(12.5\%\); (**c**) \(25\%\); (**d**) \(50\%\) and (**e**) \(70\%\) of the nodes are dead (figures are scaled 1:10 m).  
Figure 12: Deployment with hierarchical routing: area difference with and without obstacles: (**a**) initial; (**b**) final.  
lower. Indeed, the network life is extended to almost 600 days. On the other hand, as observed in Section 4.1, coverage in geographic routing scenarios is initially higher. Figure 13b shows how coverage is higher than 90% in these scenarios, both with and without obstacles, whereas it is slightly over 50% for hierarchical routing scenarios. However, coverage decreases much faster in geographic routing simulations: after approximately 60 days, hierarchical networks present a better coverage than non-hierarchical ones. Indeed, they preserve the same coverage until nodes start to die (around Day 250), and afterwards, coverage decreases significantly slower. This effect can be better appreciated in Figure 14, where coverage is plotted against the number of living nodes instead of against time. This was to be expected, since nodes live longer when hierarchical routing is used.  
It is important to note that if we changed our routing algorithms, we could improve the performance of geographic routing deployment in our simulations. Similarly, if we change algorithm parameters, like attraction forces, we could improve coverage in hierarchical routing. However, the general conclusions would remain the same: geographic routing deployment with our algorithm provides better coverage, and the hierarchical one provides a longer network life. In this sense, non-hierarchical networks are probably more suited for emergency deployment of MWSN, whereas hierarchical networks are more adequate for long-term deployment.  
Figure 14: Coverage vs. number of nodes alive in an MWSN deployed with the proposed algorithm.  
Figure 13: Network evolution in time: (**a**) dead nodes; (**b**) coverage.