## 4 Performance Evaluation
### Simulation Results  
In MCSS, the WPT slotframe length is determined according to the numbers of required power and data cells, among which the number of overprovisioned cells depends on the \begin{table}
\begin{tabular}{c c c c} \hline \hline
**Parameter** & **Value** & **Parameter** & **Value** \\ \hline PHY/MAC & IEEE 802.15.4 & \(d\) & 0-2 m \\ Number of & 4–40 & Data packets & 1, 2, 4 \\ sensor nodes & & transmitted per second & 1, 2, 4 \\ Packet size & 127 bytes & \(P_{tx}\) & 20.98 mA \\ Data rate & 250 Kbps & \(P_{rx}\) & 17.96 mA \\ Timeslot length & 10 ms & \(P_{idle}\) & 0.001 mA \\ CM slotframe length & 331 & \(P_{sleep}\) & 0.001 mA \\ HAP slotframe length & 5 & \(P_{Tx}\) & 100 mW \\ WPT slotframe length & 2–101 & \(\alpha\) & 2.7 \\ TSCH slotframe & 100 & \(\eta\) & 0.65 \\ length & & & \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Simulation parameters. length of the CM slotframe and HAP slotframe. In the simulation, we first set the CM slotframe length shorter than the EB transmission period to ensure that the EB frame is transmitted at least once within the EB transmission period. Then, we experimentally investigated the HAP slotframe length that maximizes the aggregate throughput. In this experiment, the HAP slotframe length varied from three to 20. Figure 6a-c illustrates the variations in the aggregate throughput of MCSS according to the change of the HAP slotframe length and the number of sensor nodes when the numbers of data packets transmitted per second are one, two, and four, respectively. Commonly in each figure, the aggregate throughput of MCSS increases as the HAP slotframe length decreases from 23 to five and decreases again when it changes from five to three. The shorter the HAP slotframe length, the more frequently data packets can be exchanged between HAPs. However, the priority of a cell in the HAP slotframe is always higher than that of a cell in the WPT slotframe. Accordingly, when the HAP slotframe length is very short (i.e., three), the number of data packets transmitted from the sensor node to the CH in the WPT slotframe decreases, and as a result, the aggregate throughput decreases. In the figure,  
Figure 6: Aggregate throughput of MCSS: (**a**) one, (**b**) two, and (**c**) four packets/s. the color represents the level of the aggregate throughput; the brighter the color, the higher the aggregate throughput. As a result, when the HAP slotframe length is five, the overall aggregate throughput is the highest. Therefore, we set the HAP slotframe length to five in later experiments. Figure 7 illustrates the variations in the average end-to-end delay for various numbers of data packets transmitted per second. The average end-to-end delay indicates the average time taken by a data packet to be transmitted from the sensor node to the root. MCSS exhibits a lower average end-to-end delay than the legacy TSCH MAC and TMSS, regardless of the number of data packets transmitted per second. In MCSS, each HAP transmits data packets received from its cluster members to the root using the HAP slotframe, which is shorter than the TSCH slotframe and TMSS slotframe. In MCSS, when the number of data packets transmitted per second is one, the average end-to-end delay does not increase significantly as the number of sensor nodes increases. This outcome is because, in MCSS, the HAP slotframe can sufficiently accommodate data traffic using the HAP slotframe, and only data transmission delays due to the overlapped cells occur. When the numbers of data packets transmitted per second are two and four, the average end-to-end delay increases until the numbers of sensor nodes are 36 and 20, respectively. This result is because, even if the number of data packets transmitted from the sensor nodes to HAPs (i.e., intra-cluster traffic) increases, the number of cells exchanging data packets between HAPs does not increase. In such a case, if the numbers of sensor nodes are greater than 36 and 20, all cells in the WPT slotframe are occupied.