# Design of Edge-IoMT Network Architecture with Weight-Based Scheduling
## 4 Implementation and Performance Evaluation
### Analysis on Experimental Results
#### 4.3.3 Energy Consumption  
This set of experiments explores and compares the energy consumption between the proposed clustering scheme and the direct path scheme (i.e., sensed data are forwarded directly to BS in the single-hop communication). Referring to the energy model in [44], the energy consumptions of transmission and reception are:  
\[E_{T_{x}}=\begin{cases}kE_{elce}+k_{fs}d^{2},\ d\leq d_{0}\\ kE_{elce}+k_{mp}d^{4},\ d>d_{0}\end{cases} \tag{7}\]  
\[E_{R_{x}}=kE_{elce} \tag{8}\]  
\begin{table}
\begin{tabular}{c c c c c c} \hline \hline
**Algorithms/Features** & **LLQ with PQ [21]** & **LLQ with CBWFQ [21]** & **WFQ\_TE** & **WFQ\_TP** & **WFQ\_TP** \\ \hline Jitter (s) & 0.041 & 0.034 & 0.033 & 0.034 & 0.032 \\ \hline Delay (s) & 0.556 & 0.391 & 0.331 & 0.333 & 0.312 \\ \hline \hline \end{tabular}
\end{table}
Table 6: Comparison summery of jitter and average service delay.  
Figure 20: Average delay of the communication.  
\[E_{Fusion}=M\cdot E_{elec} \tag{9}\]  
where \(E_{elec}\) is the energy consumed for sending one bit, and \(\varepsilon_{fs}\) and \(\varepsilon_{mp}\) are, respectively, the amplification coefficients in free space and multipath environments. Given \(E_{elec}=50\) uJ/bit [3.5 mA (on the idle state of the raspberry pi) \(\times\) 5V \(\times\) 29 u (s/bit)], \(\varepsilon_{fs}=100\) pJ/m\({}^{2}\), \(\varepsilon_{mp}=0.0013\) pJ/m\({}^{4}\), \(d_{0}=\sqrt{\varepsilon_{fs}/\varepsilon_{ms}}\), the packet size k = 6350 bytes. Given that the distance between the inter-CH and the CH is two meters and the distance between the inter-CH and relay is one meter, the following results show that the proposed clustering scheme achieves lower energy consumption compared with the direct path scheme (Table 7). As the monitoring time of physiological signals increases, the energy consumption of the transmission also increases. Compared to transmitting all nodes directly to a relay node, the clustering scheme can be more effective in reducing transmission delay and energy consumption for fields with a large number of nodes or a larger amount of data.  
In this work, we investigate the energy consumption of the proposed topology scheme with compressed data, comparing to that of the direct path scenario, as shown in Table 7. Moreover, according to the energy saved by compressing data and the energy consumption for running data compression algorithms in edge devices, the net energy income obtained by running an algorithm to compress given data is further examined. Referring to the analysis in [45], we have  
\[E_{net}=E_{uncmp}^{tx}-E_{cmp}^{total}=E_{uncmp}^{tx}-\left(E_{cmp}^{tx}+E_{cmp }^{alg}\right)=(CR-1)E_{cmp}^{tx}-E_{cmp}^{alg} \tag{10}\]  
where \(E_{net}\) is the net energy income obtained by running a data compression algorithm, which is the difference between \(E_{uncmp}^{tx}\) and \(E_{cmp}^{total}\), \(E_{uncmp}^{tx}\) is the energy consumption for transmitting the raw data, \(E_{cmp}^{total}\) is the total energy consumption for compressing data \(E_{cmp}^{alg}\) and transmitting the compressed data \(E_{cmp}^{tx}\), and CR is the compression rate as described in Equation (4). In the future, we plan to investigate the necessary condition of energy saving, considering the tradeoff among the compression rate CR, the energy consumption for communication and algorithm execution, such that energy conservation can be achieved.