## 5 Performance Evaluation
### Latency Analysis of Emergency Transmission
Since it has smaller IFS denoted as \(T_{SIFS}\) than the other case(\(T_{IFS}\)) to preempt the opportunity to transmit with high priority in d-TP and CP, the emergency data should be accepted to transmit only when the condition of the given time slot is idle in u-TP. Hence, in each time slot, we have considered the number of nodes and have seen the probability of whether other normal data transmission is incurred or not, denoted as \(\rho\). By these cases, the expected value of each period could be presented as follows. \[L_{d-TP}^{\epsilon}=T_{SIFS}+T_{Data}+T_{Ack} \tag{7}\]  
\[ \begin{array}{ll}L_{u-TP}^{\epsilon}&=(\rho_{1}+\rho_{2}+\rho_{3}\cdots \rho_{k_{u}})(T_{IFS}+T_{Data}+T_{Ack})\\ &=\frac{k_{u}}{\xi}\left\{1-\big{(}1-\lambda_{u}\big{)}^{n}\right\}^{\delta-1 }\cdot(1-\lambda_{u})(T_{IFS}+T_{Data}+T_{Ack})\\ &=\Big{[}1-\big{\{}1-(1-\lambda_{u})^{n}\big{\}}^{k_{u}}\Big{]}(T_{IFS}+T_{ Data}+T_{Ack})\end{array}  \tag{8}\]  
As mentioned in Section 4.2, the PC just performs the duty cycle mechanism in Sleep frame, and the node which has emergency data has to transmit a fixed long preamble that should be larger than the interval of the duty cycle that the PC performs. In the nodes, the latency in CP has the same value in d-TP because the nodes get always prioritized transmission opportunity in d-TP, compared with PC. Therefore, the latency of emergency data transmission in Sleep frame could be the following Equation (9) and the latency of that in CP also could be Equation (10). \[L_{sleep}^{\epsilon}=\varphi+T_{Data} \tag{9}\]  
\[L_{CP}^{\epsilon}=L_{d-TP}^{\epsilon} \tag{10}\]  
With the above equations from Equations (1)-(10), we performed an experiment with the environmental parameters shown in Table 2. We found that the latency of emergency data transmission showed outstanding results compared with the normal data transmission. In this experiment, we employed one coordinator and variable nodes. Figures 7 and 8 show the comparison results according to the number of nodes and traffic amount in each transmission rate. Figure 7 shows the results of average latency according to the number of nodes where they have same traffic. In this case, we fixed the traffic amount from all nodes as 1 packet/s per node and increased the number of the node to verify the latency of normal data transmission. Figure 8 shows the average latency from all nodes according to the variable traffic. Even though the latency of normal data transmission could not show the enhanced latency compared with IEEE 802.15.6, it could not say that the proposed MAC has more weakness because the amount of differentiation is too small and this  
could be changed by adjusting the parameters related to time schedule. Moreover, we could find that aSymMAC showed better performance than IEEE 802.15.6 beyond 0.4 of traffic interval in Figure 8. Therefore, the proposed scheme would show enhanced latency at high traffic environment. To consider the different speed on the PHY layer, we simulate 128 kbps and 32 kbps of transmission rates and present the results in Figures 7 and 8. Both results similarly show the pattern of differentiation of delivery time on IEEE 802.15.6 and normal transmission on the proposed scheme; higher transmission rate induces lower delivery time. However, it cannot easily say that the differentiation of two transmission rates is high, because both mechanisms are depending on slot assignment structure. Meanwhile, in high traffic environment, high transmission rate can mitigate congested competition during contention period (RAP in IEEE 802.15.6 and CP in aSymMAC). Moreover, this condition can provide more opportunities to transmit normal data during  
Figure 8: Average delivery time of normal data transmissions according to the traffic amount compared with the IEEE 802.15.6 protocol. Figure 7: Average delivery time of normal and emergency data transmissions according to the increment of the number of nodes compared with the IEEE 802.15.6 protocol. contention-less period (Type I/II in IEEE 802.15.6 and u-TP in aSymMAC).