## 5 Performance Evaluation
### Latency Analysis of Emergency Transmission  
Meanwhile, the transmission latency of normal data does not need minimized delay, emergency data must be delivered to PC as immediate as possible. For the evaluations, we analyzed the numerical results of the transmission delay from both normal data and emergency data transmissions. The overall time duration at the viewpoint of the whole superframe expressed as \(D_{super}\) could be presented as Equation (1). \[ \begin{array}{ll}D_{super}&=\Big{(}D_{active}+D_{sleep}\Big{)}\eta+D_{ beacon}\\ &=\Big{(}D_{sync}+D_{d-TP}+D_{u-TP}+D_{CP}+D_{sleep}\Big{)}k+D_{ beacon}\end{array}  \tag{1}\]  
defined by the following equation. The opportunity of nodes to send normal data should exist in u-TP and CP. Hence, the equation employed \(L\) variable in these periods, compared with the constant time duration denoted as \(D\). \[L_{total}^{n}=\frac{1}{2}\bigg{(}L_{u-TP}^{n}+L_{CP}^{n}+D_{sync}+D_{d-TP}+D_{ sleep}+\frac{D_{bacon}}{\eta}\bigg{)} \tag{2}\]  
Moreover, at the viewpoint of the respective time period, the latency of \(L_{u-TP}\) at a given node denoted as \(m\) could be described as Equation (3), considering that the probability of opportunity to transmit at \(k\)th time slot might be \(k/n\). \[L_{u-TP(m)}^{n}=\frac{k_{u}}{n}(T_{IFS}+T_{Data}+T_{Ack}) \tag{3}\]  
Hence, the average latency of each node during both u-TP and CP denoted as respective \(L_{u-TP}\) and \(L_{CP}\) could be presented as follows, where the deviation of time drift of nodes and PC are denoted \begin{table}
\begin{tabular}{c c c} \hline \hline
**Layer** & **Parameters** & **Value** \\ \hline \multirow{5}{*}{PHY} & Data Rate & 64/256 kbps \\  & Tx Power & 2.428 (0 dBm) mW \\  & Rx Power & 1.814 mW \\  & Sleep Power & 0.027 mW \\ \hline \multirow{5}{*}{MAC} & Number of PC & 1 \\  & Number of nodes & 1 to 5 \\  & Topology & Star \\  & Traffic Pattern & 128 byte/Given Interval \\  & Communication Range & 5 to 10 m \\  & Beacon Interval & 1 s \\  & Period of a Sub-Frame & 20 ms \\  & Active/Sleep ratio & 1:4 (200 ms:800 ms) \\  & Duration of u-TP & 120 ms \\  & Duration of d-TP & 40 ms if only required \\  & Duration of CP & 40 ms \\  & Number of time slots in u-TP & 6 \\  & Number of time slots in d-TP & 2 \\  & Number of Active frames & 10 \\  & Duty cycle interval of PC & 1 ms \\  & Length of long preamble & 950 μs \\  & Clock drift for PC and nodes & 40 ppm \\  & Occurrence of control frame in CP & less than 1\% \\  & Length of IFS & 150 μs \\  & Length of SIFS & 50 μs \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Simulation parameters. as \(\varepsilon_{n}\) and \(\varepsilon_{c}\), respectively. In Equation (5), we needed to consider the occurrence ratio of each control frame in CP, such as slot request or registration request denoted as \(\lambda_{slot}\) and \(\lambda_{rgs}\) variables, respectively. \[ \begin{array}{ll}L_{u-TP}^{n}&=\frac{k_{u}}{n^{2}}\underset{\delta}{\sum}^{n} (T_{IFS}+T_{Data}+T_{Ack})\cdot 2(\varepsilon_{n}+\varepsilon_{c})\cdot\delta\\ &=n^{-1}k_{u}(n+1)(T_{IFS}+T_{Data}+T_{Ack})(\varepsilon_{n}+\varepsilon_{c}) \end{array}  \tag{4}\]  
\[ \begin{array}{ll}L_{CP}^{n}&=O_{avr}+\Big{(}1-\big{(}\gamma+\lambda_{rgs}+ \lambda_{slot}\big{)}^{-1}\Big{)}(T_{Data}+T_{Ack})\\ &=T_{IFS}+\frac{1}{2}\big{(}O_{MAX}+O_{\min}\big{)}+\Big{(}1-\big{(}\gamma+ \lambda_{rgs}+\lambda_{slot}\big{)}^{-1}\Big{)}(T_{Data}+T_{Ack})\end{array}  \tag{5}\]  
Meanwhile, the emergency data could be transmitted in d-TP, u-TP, CP, and Sleep frame if each condition is satisfied, so the expected latency of the emergency data transmission should be differently described as below Equation (6) by Equation (1). \[L_{total}^{\epsilon}=\frac{1}{2}\bigg{(}L_{d-TP}^{\epsilon}+L_{u-TP}^{\epsilon }+D_{sync}+L_{CP}^{\epsilon}+L_{sleep}^{\epsilon}+\frac{D_{beacon}}{\eta}\bigg{)} \tag{6}\]  
Contrary to normal data transmission, emergency data can be sent at any time if allowed.