## 5 Performance Evaluation
### Energy Efficiency of Nodes and PC
 \tag{19}\]  
In this case, a node may receive only one packet or nothing from a PC in d-TP, so the energy consumption of a PC in this period could be presented as below. \[ \begin{array}{ll}E_{d-TP}^{N}&=\lambda_{d}(P_{Tx}T_{ACK}+P_{Rx}T_{Data})\\ &+P_{idle}(\lambda_{d}T_{IFS}+(\lambda_{d}+k_{d}-2\lambda_{d}k_{d})(T_{Data}+T_ {ACK}))\end{array}  \tag{20}\]  
In u-TP, all nodes possibly have variable transmission event to the corresponding PC. The probability of an uplink event from a node can be affected by the cumulated transmissions that were not sent during the last u-TP and the last CP. Additionally, the number of uplink transmissions from a node could be limited by the number of assigned time slot. For simplification, the analysis of the energy consumption could be calculated under the assumptions that all slots are fairly distributed to all nodes but that all nodes have different number of uplink transmissions, as below equation. Note that the maximum slot number per a node could be presented as \([K_{u}/N]\) with the Gauss function, with the number of data presented as \(\pi\). \[ \begin{array}{ll}E_{u-TP}^{N}=\sum\limits_{l=0}^{[\frac{K_{u}}{N}]}P(\pi=l) \Big{\{}E_{Data}+\Big{(}\Big{[}\frac{K_{u}}{N}\Big{]}-l\Big{)}E_{idle}\Big{\}} \\ E_{Data}=P_{idle}T_{IFS}+P_{Tx}T_{Data}+P_{Rx}T_{ACK}\\ E_{idle}=P_{idle}(T_{IFS}+T_{Data}+T_{ACK})\end{array}  \tag{21}\]  
In CP, all nodes should perform pseudo random back-off delay after IFS whenever any data would be transmitted, but this would not affect the given time duration. Hence, we do not have to consider the random seed value for back-off delay when calculating the energy consumption described below. \[E_{CP}^{N}=\lambda_{e}\bigg{\{}P_{Tx}T_{Data}+P_{Rx}T_{ACK}+P_{idle}\bigg{(} \frac{D_{CP}}{\lambda_{e}}-(T_{Data}+T_{ACK})\bigg{)}\bigg{\}} \tag{22}\]  
A node generally keeps deep sleep mode in overall SP. However, when any emergency data is incurred, a node has to attach long preamble prior to the emergency data for successful reception from the PC which operates LPL mechanism in SP. Therefore, the energy consumption of a node in Sleep frame could be presented below. \[ \begin{array}{ll}E_{Sleep}^{N}&=\lambda_{e}\bigg{\{}P_{Tx}(\varphi+T_{Data })+P_{idle}\Big{(}D_{sleep}-\varphi-T_{Data}\Big{)}\bigg{\}}\\ &\qquad+(1-\lambda_{e})P_{idle}D_{sleep}\\ &=\lambda_{e}(P_{Tx}-P_{idle})(\varphi+T_{Data})+P_{idle}D_{sleep}\end{array}  \tag{23}\]  
Furthermore, we achieved simulation-based experiments to obtain realistic results compared with IEEE 802.15.6 protocol as shown in Figures 12 and 13 under the same scenario described in the previous subsection and Table 2. In this experiment, we operated a given network composed of one coordinator and several nodes during 100,000 s, and then we individually measured the total energy consumption of them. Figures 12 and 13 show the cumulated energy consumption of the coordinator and the node employed in this simulation, according to the variable number of nodes and variable traffic amount. They also show the results of IEEE 802.15.6 protocol with the same conditions. In these figures, the proposed aSymMAC could not show the enhanced performance in PC compared with IEEE 802.15.6 protocol. However, it is not conclusively important in the real environment because a PC generally has the function of energy recharging and also has more powerful energy resource than the micro-sized on-body nodes. Meanwhile, these figures present outstanding energy efficiency of the node side on the aSymMAC protocol compared with IEEE 802.15.6, and this is the key contribution of this research. In real environment, WBAN needs the extreme energy efficiency of the node side, but not PC. Figures 12 and 13 consequently prove that aSymMAC gives higher energy efficiency of the node than IEEE 802.15.6 and that the differentiation of energy efficiency between the coordinator and each node is not  
Figure 12: Cumulated energy consumption amount of both coordinator and node according to the increment of the number of nodes compared with IEEE 802.15.6 protocol.