# 3 MSF: A Multi-Modal Adaptation of the 6 TiSCH Minimal Scheduling Function for the Industrial IoT
## 4 The Multi-Modal Minimal Scheduling Function
### Sloframe Structure  
For 3 MSF, we maintained (in spirit) the three slotframes of [PERSON] et al. [16] (and MSF) and added two more. The minimal slotframe is virtually identical. As shown in Figure 5, it contains a minimal supercell for every unique interface-mode. The string of minimal supercells starts at a slot offset of zero and spans exactly as many consecutive subcells (see Section 2.2) as needed to accommodate one supercell per unique interface-mode without the minimal supercells overlapping with one another. When a new slotframe comes around \begin{table}
\begin{tabular}{l l l} \hline \hline _m.ii_ & **Value** & **Description** \\ \hline
0.00 & 0b000 (0\({}_{10}\)) & Legacy mode (reserved) \\ \hline
1.00 & 0b100 (4\({}_{10}\)) & Alternating mode \\ \hline
0.01 & 0b001 (1\({}_{10}\)) & Communication mode with index 0 of interface with index 0 \\ \hline
1.01 & 0b101 (5\({}_{10}\)) & Communication mode with index 1 of interface with index 0 \\ \hline
0.10 & 0b010 (2\({}_{10}\)) & Communication mode with index 0 of interface with index 1 \\ \hline
1.10 & 0b110 (6\({}_{10}\)) & Communication mode with index 1 of interface with index 1 \\ \hline
0.11 & 0b011 (3\({}_{10}\)) & Communication mode with index 0 of all interfaces \\ \hline
1.11 & 0b111 (7\({}_{10}\)) & Communication mode with index 1 of all interfaces \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Three-bit encoding of the TSCH mode abstraction. and it is time to advertise the TSCH network, an identical EB must be broadcast on each consecutive minimal supercell of said slotframe, with no retransmissions allowed. This could be achieved by, for example, having a separate buffer (i.e., from the broadcast buffer) for EBs, giving absolute priority to EBs in minimal supercells, and simply adding as many EBs to the EB buffer as there are minimal supercells. At first glance, the negotiated slotframe also incurs minimal changes from [PERSON] et al. (2016) (and MSF) in the sense that, e.g., adding at least one negotiated Tx supercell towards an RPL parent when it becomes preferred remains mandatory. However, we consider devices, and not individual communication modes, to be independent RPL neighbors. Therefore, the cost associated with each communication mode is no longer automatically accounted for through routing layer operations alone. Negotiated supercells can only overlap with autonomous Tx supercells and certain so-called \"shadow\" supercells (more about that later). All negotiated supercells towards a given neighbor can only be tagged with a single non-simultaneous TSCH mode at a time. Our autonomous slotframe uses the alternating TSCH mode (see Section 4.1), mostly to maintain up-to-date inferred metrics for all interface-modes of each neighbor towards whom a node can (still) use an autonomous Tx supercell. Since autonomous supercells always occupy the same number of subcells, we slightly modified the hashing function to ensure they fall within predetermined bins, meaning overlapping autonomous supercells start and end at the same slot offsets. With MSF, a node cannot use an autonomous Tx cell towards a neighbor to which it already has a negotiated Tx cell. However, in our case, if we have negotiated Tx supercells towards a given neighbor, we also require at least one Tx supercell tagged with the alternating TSCH mode towards the same neighbor. Otherwise, we could not maintain fresh inferred metrics towards it. The only way to maintain fresh inferred metrics and consistent MAC sequence numbers is to allow non-probe (see Section 4.6) unicast packets on both kinds of supercells. That is, once we have attempted transmission of a unicast packet with a given MAC sequence number towards a given neighbor, we cannot send it a unicast packet with a lower sequence number before a certain (typically quite long) lifetime expires to maintain sequence number consistency.