## 4 Results
### Protocol Evaluation
The corresponding network topology is shown in Figure 11, where three traffic sources send traffic to three potential gateways, with several available routing alternatives. A simulation of 120 s has been performed where each source sends one traffic flow, with a rate of 120 Kbps, to any gateway. In addition, we establish the time windows to assess the accumulated exposure to 5 s.  
Figure 12 shows the rhythm at which the accumulated exposure grows for the three potential intermediate nodes (\(I_{5}\), \(I_{6}\), and \(I_{7}\)) over time, and for different \(\omega\) values. The results show that for high \(\omega\) values (\(\omega=1\) or \(\omega=5\)), the proposed protocol is actually able to modulate this corresponding rhythm, and so the \(\xi^{\prime\prime}\) parameter fluctuates during the simulation. However, when the weight given to this cost decreases, the protocol favors the route with the lowest transmission power (minimum \(\mathcal{P}\)), which is maintained throughout all the  
Figure 11: Network topology with three sources and three destinations. Figure 12: Evolution of the second derivative metric. (**a**) Node \(I_{5}\). (**b**) Node \(I_{6}\). (**c**) Node \(I_{7}\). simulation, and so there is no change to the rhythm at which the accumulated exposure grows at the intermediate nodes. Afterwards, we also evaluated the impact of the \(\omega\) parameter over the accumulated transmitted power. Figure 13a shows its standard deviation for different values of \(\omega\). We can see a clear influence of the \(\mathcal{K}\) cost, resulting in a much more homogeneous exposure when the factor \(\omega\) is higher. Besides, Figure 13b also illustrates the power that was transmitted by the entire network. In this setup we can also see a slight improvement for the highest \(\omega\) value, which was not expected, since higher \(\omega\) values usually lead to using routes that are not favoring the minimum power criterion. However, the traffic balancing between the various routes leveraged by this configuration causes fewer collision events and re-transmissions. After assessing the correct behavior of the routing protocol, we have analyzed its performance over more complex scenarios, considering random topologies. We assume a square scenario of \(500\times 500\) m\({}^{2}\), where four arbitrary sources send traffic to any of the four gateways, which are deployed to maximize their coverage. We increase the number of intermediate nodes, and therefore the network density, from 50 to 200, and we modify the value of \(\omega\in 1,3,5\). We run 100 independent simulations for each \(\omega\) value, and for the two different network densities (50 and 200 intermediate nodes). As was done with the algorithm evaluation previously discussed, we discard those network deployments where there is no route from each source to one of the available gateways. We also use the same traffic characteristics and window time (\(T\)) as in the previous analysis. First, Figure 14 shows the Complementary Cumulative Distribution Functions (CCDFs) of the power transmitted by each node during the whole experiment. As can be observed, there is a slight improvement when moderate weight (\(\omega=1\) and \(\omega=3\)) is given to the metric that considers the accumulated exposure, \(\mathcal{K}\), while such an improvement is no longer evinced as we increase the weight (\(\omega=5\)). This enhancement is slightly higher for more dense networks, as can be seen in Figure 14b for 200 intermediate nodes. In any case, the difference with the configuration in which the protocol just seeks the minimization of the transmitted power (\(\omega=0\)) is not very relevant. Afterwards, in Figure 15 we assessed the influence of the \(\mathcal{K}\) metric over the average and overall transmission power. Figure 15a shows the average transmitted power per node. We can observe a monotonic decrease of the average transmission power due to the fact that the denser the network, the more routing alternatives become available.