# 3 MSF: A Multi-Modal Adaptation of the 6 TiSCH Minimal Scheduling Function for the Industrial IoT
## 5 Simulations and Results
### Scenario 3: Four Nodes  
In the third scenario, we compared three configurations of the four-node setup shown in Figure 19, wherein all nodes have (1) only the sub-GHz interface-modes; (2) only interface-modes (2, 1) and (1, 1); or (3) all interface-modes listed in Table 3. We assessed the performance of these configurations (in 80 simulations each) in the face of a common adversity in industrial environments. More specifically, at a given point in time, we blocked interface-mode (2, 1) between #4 and #2 to emulate modulation-specific phenomena such as fading. At the beginning of each simulation run, we briefly blocked all (existing) physical links from #1 to #4, between #2 and #3, and between #3 and #4 to ensure a consistent topology (i.e., following Figure 19). Additionally, we very briefly blocked interface-mode (2, 2) between #3 and #4 (should it exist) to ensure (2, 1) was #4's frozen interface-mode towards #2. After that,  
Figure 17: Setup of the second scenario involving three nodes, i.e., one root (#1) and two non-root nodes (#2, and #3). The black arrows indicate (the intended) child–parent relationships. A single grid square measures 10 m \(\times\) 10 m.  
the network was left to operate under normal conditions for 15 min before interface-mode (2, 1) was permanently broken between #2 and #4 at the 20 min mark (hence the reason we ensured that (2, 1) was #4's frozen interface-mode towards #2). From there, each simulation run lasted 10 more minutes. Figure 19: Setup of the third scenario involving four nodes, i.e., one root (#1) and three non-root nodes (#2, #3, and #4). The black arrows indicate child–parent relationships in a steady state. A single grid square measures 10 m \(\times\) 10 m.  
Figure 18: Cumulative number of used transmit links across all simulations of this scenario (represented as a fraction) by slotframe. Only Tx links of directed node pairs in which the destination could potentially be the preferred parent of the source are displayed. How a network reacts is heavily influenced by the metric normalization weights calculated using (5). As explained in [8] (Section 4.4), attaching an appropriate weight to an interface-mode becoming unavailable involves a trade-off between encouraging physical link redundancy (which discourages parent changes and promotes overall stability) and reducing the path length to the root (which reduces end-to-end latency). For the first and second configurations, we used the same parameters as in [8] (i.e., \(IL_{div}=4\) and \(W_{off}=0\)), as each node in both configurations possessed two interface-modes. The third setup retained the parameters listed in Table 6.  
For each configuration, we visualized the statistics of #4 switching to #3 as the preferred parent at any point after the 20 min mark versus #4 switching its frozen interface-mode towards #2 instead. Before we continue, it must be noted that the rules for computing the rank to advertise (which carry over from the Minimum Rank with Hysteresis OF (MRHOF) [23] (Section 3.3)) have a considerable impact on whether and/or when #4 switches preferred parent from #2 to #3. That is, even though #2 and #3 will have approximately identical path costs towards #1, the ranks they advertise are not exactly equal. Depending on which node first receives a DIO from the other (which is completely random), #3 might end up in #2's parent set, or vice versa. This prompts the node that has the other in its parent set to advertise a rank greater than or equal to the highest rank advertised by any member of its parent set, rounded upward to the next integral rank. In practice, this means that when #3 ends up in #2's parent set, #3 will advertise a rank that is lower than the one #2 advertises by a non-negligible amount, making it more likely that #4 switches preferred parent from #2 to #3. In fact, in many cases where #3 is a member of #2's parent set, the combination with the frozen interface-mode switch hysteresis threshold is enough to trigger a preferred parent switch.