## d Comparison of Different Protocols with Node Mobility
### Experiment
#### 4.3.2 Determination of Protocol Parameter Values for Experiment  
When the MAC frame was forwarded from MCU to the radio chip in CC2630, 6 bytes were added to the MAC frame for transmission preamble and frame delimiter when the message was transmitted over the medium to the destination, in order to be compatible with the IEEE 802.15.4 PHY standard [19]. In our implementation, the address information field in MPDU was removed since a command message was broadcasted; other elements were kept in order to keep compatible with the IEEE 802.15.4 standard. We assumed that the MAC payload \(p\) was 100 bytes long. On the sender side, a MAC frame of (3+\(p\)) bytes, i.e., size(MHR) + \(p\), was transferred from MCU into the radio chip, while on the receiver side, a MAC frame of (5+\(p\)) bytes, i.e., size(MHR) + size(MFR) + \(p\), was transferred from the radio chip into MCU (MHR: MAC header, MFR: MAC footer). The total size of a frame when it is transmitted over the medium is size(SHR) + size(PHR) + size(MHR) + \(p\) + size(MFR) (SHR: synchronization header, PHR: Physical layer header). The message transfer times, \(t_{mr}\) and \(t_{rm}\), were determined by the speed of serial peripheral interface (SPI), whereas transmit time \(t_{tx}\) was determined by the transmission speed of the radio chip. The typical Internal Digitally Controlled Oscillator (\(DCOLK\)) clock frequency of the ARM CorTex M3 with the default configuration of the ContikiOS was 3.2 MHz. Therefore, the maximum SPI rate was half of the \(DCOLK\) clock frequency (=1.6 MHz). Based on our ContikiOS interface experiment, the SPI interface on _usens_ achieved a rate of 4 Mbps (\(\approx\)0.25 \(\upmu\)s per bit). Additionally, \(t_{\text{turnon}}\approx\) 100 \(\upmu\)s, \(t_{\text{CCA}}\) = 128 \(\upmu\)s, and \(t_{\text{ppd}}\) = 192 \(\upmu\)s. Based on the size of the frame format at each layer, the processing delay, and the SPI speed, the practical values of \(t_{mr}\), \(t_{rm}\), and \(t_{tx}\) were computed as follows (FCH: Frame control header). \[t_{mr}=(size(MHR)+p)\times 8\times 0.25\mu s=(3+p)\times 2\times 10^{-3}(ms)\] \[t_{rm}=(size(MHR+MFR)+p)\times 8\times 0.25\mu s=(5+p)\times 2 \times 10^{-3}(ms)\] \[t_{tx}=(size(MHR+SHR+PHR+FCH)+p)\times 8\times 4\mu s=(11+p)\times 3 2\times 10^{-3}(ms)\] \begin{table}
\begin{tabular}{c c} \hline \hline
**Parameters** & **Values** \\ \hline Number of nodes & 25 nodes and 1 sink \\ \(N\) & 3 \\ CW & 3 \\ Transmission power & \(-\)12 dBm (\(\approx\) 10 m) \\ Number of mobile nodes & 1 to 3 \\ Dimension & About 2.5 m \(\times\) 70 m \\ Payload, \(p\) & 100 bytes \\ \hline \hline \end{tabular}
\end{table} 
Table 6: Key experimental parameters and values for experiment. Figure 13: Tree network topology with the traces of mobile nodes for both simulation and experiment (H = 6, average speed of 1 m per second, and pause time of 5 s at each stop). By applying these values to Equation (10), we get \(len(BS)\) as follows:  
\[len(BS)=CW\times 0.32+0.788+36\times p\times 10^{-3}(\text{ms}) \tag{21}\]  
Using \(len(BS)\) and the parameter values given in Table 6, we obtained the following values from Equations (10), (11), and (14): \(len(BS)\approx 5.35\) ms, \(len(BSS)\approx 16.1\) ms, \(len(BP)\approx 64.4\) ms.  
As for the values of \(H\) and \(N\), \(H\) depends on the dimension of a target network and the transmission range of a node, and \(N\) depends on the number of neighbors that varies according to the node density of a target network and the transmission range of a node. In case of the tree topology in Figure 13 that is deployed artificially where \(H\) is six, \(N\) is set to three since the number of competing nodes at the same level is equal to three. Consider a tree of a randomly deployed network as in scenario S2 in Table 4, where \(H\) = 5. In this network, \(N\) is set to 4 (BSs) by analysis and simulation. However, in real situations, \(H\) can be used as any value greater than or equal to 5, the real depth of a tree. For example, suppose that \(H\) is set to six conservatively.