# Extensive Experiments on Opportunistic Routing in Wireless Sensor Networks
## 5 Testbed Deployment and Experimentations
### Overhead of ODYSSE  
We evaluate the number of beacons sent per data packet per node when varying \(\alpha\). As expected, results depicted in Figure 4 show that the overhead increases with \(\alpha\) (less forwarders are available), and it is almost linear. However, the increase is more noticeable for MED_N_ADAP scenario, because in this scenario, no particular measure is applied to compensate the duty cycle of nodes. This result, actually, confirms the traditional trade-off concerning energy consumption between: (i) the duty cycle that tends to save energy, and (ii) the forwarder discovery that becomes longer and hence more beacons and energy is consumed for high values of \(\alpha\). \begin{table}
\begin{tabular}{c c c c} \hline \hline ACTIVE\_PERIOD & 0.2 s & WAIT\_DATA\_RPERIOD & 3 s \\ MIN\_SLEEP\_PERIOD & 0.05 s & RSSI\_THRESHOLD & \(-\)83 dBm \\ LEVEL\_PERIOD & 8 s & BEACON\_PERIOD & 3 s \\ MAX\_NB\_REPLY & 1 & SHORT\_SLEEP\_COUNT & 3 \\ WAIT\_REPLY\_PERIOD & 0.2 s & & \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Experiment parameters. Now, looking more in details, we can analyse the distribution of the number of beacons for a sample image (Figure 5). The immediate observation is that, with INFR and \(\alpha=0\), each node can immediately find a forwarder as in Figure 4(a), almost after sending one beacon. More interesting, is the result with low duty cycle (high \(\alpha\)) in Figure 4(b): it appears that the distribution is more varied. The number of beacons is expected to be proportional to the waiting time given by the Beta distribution Beta \((1,n)\) presented in Section 4 (where \(n\) is the number of admissible forwarders of a node). We verify the qualitative match between the theory and our practical experiment results as follows:  
* We first translate and rescale our experimental data, so that the random wake-up time of the nodes in the experiment (accounting for \(\alpha\), ACTIVE_PERIOD, etc.) matches best the random uniform distribution \([0,1]\) of the model. * Then we search for the parameter \(n\) which makes the distribution \(B\)\((1,n)\) the best fit against the experimental data. For the example of Figure 4(b), we find that the best fit is for \(n\approx 2.32...\),
* Finally, we plot the theoretically expected histogram (by rescaling back the beta distribution \(B\)\((1,n)\)) in Figure 6.  
Figure 4: Average number of beacons sent per data packet per node. Figure 5: Distribution of the number of sent beacons. We can see that there is a qualitative match. To provide a more sound comparison between distributions from experimentation and model, we represented their q-q plot one against another in Figure 7: the match is satisfying. Notice that differences are expected for a variety of reasons, such as different number of potential forwarders of different nodes, packet collisions and losses, imperfect timings in actual hardware, etc. We also note that the network behaves as if almost 2.32... forwarders are available for each node, which is rather on the low side. However, please note that losses/collisions and high number of neighbors of the sink can only decrease this number. Figure 5c illustrates the adaptiveness of MED_ADAP scenario since the most probable number of beacons necessary to find a forwarder is 1, in stark contrast with MED_N_ADAP scenario. The low efficiency of MED_N_ADAP compared to INFR can be noted (e.g., through the lower probability to find a forwarder with a low number of beacons, closer to 1). The explanation is as follows: in both scenarios, the nodes able to find forwarders faster are nodes with a larger number of neighbors. However, in MED_N_ADAP the network saturation is reached. In consequence, even if forwarders are found faster, forwarders themselves have to actually forward the packet to the next hop, before being available again: the benefits of having a large number of neighbors (favoring low delay) are thus naturally cancelled by congestion. Figure 6: Distribution of the number of sent beacon with the rescaled Beta distribution.