## 4 Centralized Scheduling Algorithm for the IEEE802.15.4e TSCH Network
### Deepening of the Observed Scheduling Algorithm  
This section explains IRByTSA, FTSA, and FLSA, to make sure that they proceed according to plan when their visualization/animation is displayed by the TLS-VaD. The algorithms were applied to networks with topology as shown in Figure 9.  
As an introduction, Table 1 provides a summary of the three scheduling algorithms to highlight their similarities and differences. It can be seen in item 2 of the table that all three algorithms used the bursty transmission mechanism. As for what is meant by bursty transmission, when a node gets a chance to transmit, the node will send all the data in its queue. Thus, with a scheduling algorithm that uses the principle of bursty transmission, every chance to transmit is an opportunity to empty the queue.  
\begin{table}
\begin{tabular}{c c c c c} \hline \hline
**No** & **Item** & **IRByTSA** & **FTSA** & **FLSA** \\ \hline \multirow{4}{*}{1} & Process of generating & & & \\  & scheduling decisions is done & No & No & No \\  & on/for each timeslot & & & \\
2 & Bursty transmission & Yes & Yes & Yes \\
3 & Transmission priority on the network & From higher-rank & From higher-rank & From leaf node \\  & Transmission priority based & node & node & From leaf node \\
4 & & Transmission priority based & No & No & No \\
5 & & Transmission priority based & No & No & No \\  & on number of child nodes & & Yes & Yes & Yes \\
6 & Resource allocation is only & & & \\  & given to nodes with q\({}_{\mathsf{n}}\
eq 0\) & & & \\  & & & & \\  & & & & \\
7 & child to parent node based & Yes & No & No \\  & on turn & & & \\ \hline \hline \end{tabular}
\end{table}
Table 1: Comparison of Iman–Ramli bursty transmission scheduling algorithm (IRByTSA), first top scheduling algorithm (FTSA), and first leaf scheduling algorithm (FLSA).  
Figure 9: Network topology of 16 nodes.  
Since IRByTSA, FTSA, and FLSA apply the bursty transmission principle, the relationship between \(\lambda\) and the number of cycles (C) is formulated in Equation (3) as follows:  
\[\lambda=\sum_{\mathrm{s}=1}^{\mathrm{C}}\mathrm{TS(s)}, \tag{3}\]  
where TS (s) is the number of timeslots needed for each cycle (s) and variable C states the number of cycles needed to send all data to the master node, so that condition \(\mathrm{q}_{0}=\widetilde{\mathrm{Q}}\) can be achieved. TS(s) is determined by Equation (4), as follows:  
\[\begin{split}\mathrm{TS(s)}&=\max\{\mathrm{ts_{i}( s)|n_{i}\in Active(s)}\}\\ &=\max\{\mathrm{q_{i}(s)|n_{i}\in Active(s)}\}.\end{split} \tag{4}\]  
Equation (4) implies that \(\mathrm{ts_{i}(s)}=\mathrm{q_{i}(s)}\), where \(\mathrm{ts_{i}(s)}\) represents the total timeslot needed by \(\mathrm{n_{i}}\) for transmitting data in step/round (s) and \(\mathrm{q_{i}(s)}\) is the number of packets queued in \(\mathrm{n_{i}}\) in a given round s. This is an applicable formula because: (a) the TSCH network requires one timeslot to send one data packet, and (b) the node that receives a transmit turn will do bursty transmission when sending its data. Thus, the number of timeslots needed by each node will be equal to the number of packets in the node's queue. Active(s) in Equation (4) indicates a set of nodes that are active at a particular cycle(s). Based on Equation (4), TS(s) will take the largest \(\mathrm{q_{i}(s)}\) value from Active(s). This is done to ensure that the number of timeslots allocated at each cycle meets the needs of all nodes that are scheduled to be active (sending or receiving data). If the value of TS(s) is smaller than the number of packets that are queuing at the nodes, even only one node, then not all nodes will be able to do bursty transmission because the number of allocated timeslots is insufficient.