# Improved Cell Allocation Strategies Using K-Means Clustering in Congested 6 TiSCH Environments
## 8 Results  
### Objective Function Zero (OF0) Routing Protocol  
We initially conducted a performance test using the Objective Function Zero (OF0) routing protocol. This test compared our proposed clustering method with other methods and the MSF, as shown in Figure 9. Our method maintained a consistent delivery ratio across varying node counts. However, ECRP clustering slightly surpassed it at 150 nodes due to its cluster head selection based on node energy, as this value may be slightly higher due to the previously described clustering process affecting the scheduling process for each  
\begin{table}
\begin{tabular}{c c} \hline \hline
**Parameter** & **Value** \\ \hline Simulation area (grid size) & 2 km \(\times\) 2 km \\ Simulation platform & 6 TiSCH \\ Battery level & 2821.5 mAh \\ Number of nodes & 100, 150, 200, 300 \\ RPL extensions & Unicast \\ RPL DAO interval & 60 s \\ RPL objective function & OF0, MRHOF \\ Traffic period & Periodic \\ Node distribution & Random \\ TSCH number of channels & 16 \\ TSCH TX queue size & 12 frames \\ TSCH timestamp length & 10 ms \\ K maximum value & 10 \\ K-means maximum iterations & 120 \\ K-means features & 3 \\ Slot frame per run & 4800 \\ Packet size & 1016 \\ Silhouette score & \(-1\) \\ Silhouette cluster & 3 \\ \hline \hline \end{tabular}
\end{table}
Table 1: Simulation parameters.  
frame slot. The minimum hop count process in OF0 also affects inter-cluster communication. Despite this, our method's iterative clustering and scheduling processes effectively predicted packet arrival, outperforming the grid-based clustering method. Overall, our clustering process yielded positive results. Figure 9 also demonstrates that the end-to-end latency with the OF0 routing protocol remained under 100 s even with 300 nodes, which can be attributed to the effective distribution of slot frames and time slots. The end-to-end latency for clustering on cell allocation also showed critical improvements compared to grid-based K-means. Noteworthy here is that slot frame distribution slightly affects latency, as the node coordinates used in slot frame distribution are divided appropriately for slot frames and individual time slots.  
Figure 9 highlights the consistent joining time across different node counts, with K-means clustering reducing the time needed for new nodes to receive advertisements from the sink node. Energy efficiency in clustering remains high, mainly due to residual energy considerations for each node group. This allows our method to optimize how the sink node manages packet delivery for reserved nodes. The energy efficiency of clustering tends to be high in the following moments, as it heavily relies on the residual energy of each group of nodes; thus, our proposed method could determine how the sink node might accept and deliver some packets for reserved nodes. Figure 9 shows favorable throughput results, with each packet's transmission speed enhanced by OF0's low-overhead path selection. We believe that the throughput value will still be high through packet sending, as it might barge the transmission cells. Energy efficiency clustering reduces the throughput margin to 8.89 kbps at 300 nodes, yet overall throughput stays high due to effective packet transmission. In summary, our proposed method excels in packet delivery ratio and throughput, showing an 8% increase in delivery ratio, a 30.01% reduction in latency, a 15.95% decrease in joining time, and a 13.82% increase in throughput compared to the MSF under the OF0 routing protocol.  
Figure 9: Graphs showing results for the Objective Function Zero (OF0) routing protocol: (**a**) Packet Delivery Ratio (PDR), (**b**) end-to-end latency, (**c**) joining time, and (**d**) throughput.