# Multi-Tier Heterogeneous Beam Management for Future Indoor FSO Networks
## 5 Results and Analysis  
To observe the relative impact of the parameters, we evaluate the search time for a few scenarios where the switching time of the Tier 3 FSO link is faster than, equivalent to, or slower than the switching time of the Tier 2 mmWave link. To provide a more general analysis, all results are depicted in time relative to the switching time of the mmWave link (i.e., \(t_{2}\)). Without loss of generality, we also assume \(T_{d}=0\) since the Tier 1 discovery time is a constant offset independent of the other parameters. The first results, depicted in Figure 6, illustrate the search time when the FSO tier can switch between configurations much faster than the mmWave tier (i.e., \(t_{2}=100t_{3}\)). The plot on the left shows the search time versus \(\alpha_{2}\) and the plot on the right shows the corresponding results as a function of \(\beta_{3}\). In each plot, results are shown for combinations of \(\beta_{2}\in\{9,25\}\) and \(\alpha_{3}\in\{625,2500,10,000\}\). These Tier 3 resolution values represent FSO links with instantaneous coverage of 16, 4, and 1 cm\({}^{2}\), respectively. When the Tier 2 resolution is low, we can see that the search time is heavily influenced by the Tier 3 resolution (i.e., the third component of Equation (2)). This implies that the Tier 2 scan completes quickly and most of the time is spent searching within Tier 3. Conversely, as the resolution increases there are more Tier 2 configurations in a given space and fewer Tier 3 configurations within the instantaneous coverage of a single Tier 2 configuration; therefore, the scan spends most of its time in Tier 2. Accordingly, the search time is heavily influenced by the Tier 2 range (i.e., the second component of Equation (2)). This is similarly seen in the right plot where search time is heavily influenced by Tier 2 range when Tier 3 range is small and heavily influenced by Tier 3 resolution when Tier 3 range is large. In Figure 7, we demonstrate the impact of relative switching times--specifically, we show results for scenarios where: (a) switching between FSO configurations is 10\(\times\) faster than switching between mmWave configurations; (b) FSO and mmWave switching times are equivalent; and (c) switching between FSO configurations is 10\(\times\) slower than switching between mmWave configurations. The key observation here is that the trends are similar; however, increasing the time to switch between FSO configurations or reducing the time to switch between mmWave configurations shifts the optimal Tier 2 resolution to the right and, accordingly, reduces the optimal Tier 3 range. Intuitively, this makes sense since reducing the relative performance of Tier 3 implies that the system should increase the utilization of Tier 2. Figure 6: Maximum search time for MTH protocol as a function of Tier 2 resolution (i.e., \(\alpha_{2}\)) and Tier 3 range (i.e., \(\beta_{3}\)) when \(t_{2}/t_{3}=100\). Figure 7: Maximum search time for MTH protocol as a function of Tier 2 resolution (i.e., \(\alpha_{2}\)) and Tier 3 range (i.e., \(\beta_{3}\)). Results are shown for: \(t_{2}/t_{3}=10\) (**top**); \(t_{2}=t_{3}\) (**middle**); and \(t_{2}/t_{3}=0.1\) (**bottom**). The legend in the bottom right plot is common to all plots. Lastly, Figure 8 highlights the impact that Tier 2 range, Tier 3 resolution, and relative switching times have on the optimal Tier 2 resolution (or, similarly, Tier 3 coverage). The obvious observation is that the three sets of figures appear similar; however, the color bar range shows that relative switching time has an impact on magnitude of the outcomes. As FSO switching becomes faster, Tier 3 can explore a larger space in a similar time, therefore the optimal Tier 2 resolution (i.e., \(\alpha_{2}\)) decreases and the optimal Tier 3 range (i.e., \(\beta_{3}\)) increases. Observing the impact of \(\beta_{2}\) and \(\alpha_{3}\), we can see that larger spaces (i.e., larger \(\beta_{2}\) values) increase the optimal Tier 3 range in order to distribute the additional required search time across both tiers.