# Relay-Enabled Task Offloading Management for Wireless Body Area Networks
## 5 Results and Discussion
### Performance Evaluation
\begin{table}
\begin{tabular}{c c} \hline
**Parameter** & **Value (Unit)** \\ \hline \(C_{i}\) & 1500 bits \\ \(D_{i}\) & 1000 bits \\ \(c\) & \(3\times 10^{8}\) ms\({}^{-1}\) \\ \(B_{ij}\) & 300 kHz \\ \(A\) & \(10^{-11}\) \\ \(\beta\) & 2 \\ \(E_{amp}\) & 1.97 nJ (bit)\({}^{-1}\) \\ \(E_{sen}\) & \(0.12\times 10^{-9}\) nJ (bit)\({}^{-1}\) \\ \(E_{pro}\) & 0.3064 nJ (bit)\({}^{-1}\) \\ \(E_{Tx,elc}\) & 16.7 nJ (bit)\({}^{-1}\) \\ \(E_{Rx,dec}\) & 36.1 nJ (bit)\({}^{-1}\) \\ \(SNR_{thr}\) & 17 dB \\ \(BER_{thr}\) & \(10^{-3}\) \\ \(\sigma_{dB}\) & 4.15 dB \\ \(PL_{dB}(d_{0})\) & 48.4 dB \\ PL exponent \(n\) & 5.9 \\ Initial power \(p_{i}\) & 0.5 J \\ Number of relays & 5 \\ Bandwidth \(B\) & 300 kHz \\ Boltzmann constant \(v\) & \(1.38\times 10^{-23}\) \\ Environment temperature \(T\) & 290 K \\ Transmission power & \(-12\) dBm \\ \hline \end{tabular}
\end{table} 
Table 2: Selected simulation parameters. Figure 2: Cumulative distribution function (CDF) versus channel capacity per unit under on-body channel under different rates. PL is a significant indicator through which we can explore the signal power reduction when considering data transmission from the transmitter to the receiver. In accordance with Reference [8], we only analyze the on-body NLoS communications. The analysis of the LoS communication can be found in Reference [28]. The PL parameters are given as follows: PL exponent \(n\) of 5.9, standard deviation \(\sigma\) of 4.15 dB, and \(PL_{dB}(d_{0})\) of 48.4 dB. As can be obtained from Equation (14), a longer transmission distance \(d\) leads to higher PL values. It can be seen from Figure 5 that relays in scenarios requiring higher computation resources achieve lower PL values. On the contrary, when relay \(i\) cannot handle task \(C_{i}\) locally (when providing lower CPU cycles), it will trigger the offloading process and then offload the task to others. Therefore, the offloaded task \(C_{i}\) with higher computation resources required suffers a longer transmission distance and leads to higher PL values. Data transmission without offloading leads to the highest PL results because all data packets are transmitted to the C-MEC from the implanted sensors via relays, which results in the longest transmission distance when compared with task offload schemes. Figure 4: Residual energy of all relays versus time under different scenarios. Figure 3: Link quality versus transmission distance under different rates. Figure 6 shows the total number of executed packets by relays under different scenarios. As mentioned in Sections 4.2 and 4.3, the total number of executed packets depends heavily on the relays' computation resources and energy status. It can be seen from Figure 6 that approximately 12,500 packets are executed by the relay when \(f_{i}^{c}=2500\) CPU cycles, while around 4500 packets can be implemented when \(f_{i}^{c}=1500\) CPU cycles. Clearly, the number of executed packets is zero without deploying the task offload scheme. Figure 7 illustrates the total delay performance under different scenarios. As mentioned in Equation (6), a larger value of \(F_{i}\) leads to longer local execution time. As can be seen from Figure 7, the maximum delay is around 60 nanoseconds (ns) when \(f_{i}^{c}=2500\) CPU cycles and about 40 ns when \(f_{i}^{c}=1500\) CPU cycles. Then the network becomes stable after 750 rounds and 1250 rounds when \(f_{i}^{c}=1500\) CPU cycles and \(f_{i}^{c}=1500\) CPU cycles, respectively. The non-offloading scheme achieves the worst performance with a maximum delay at approximate 81 ns. One can observe that the value of \(F_{i}\) should be selected carefully when designing a task offloading-based healthcare monitoring system because the large value of \(f_{i}^{c}\) promises a lower PL and a higher number of locally executed tasks, while also decreasing the network lifetime significantly due to the large energy consumption. Figure 5: Path loss (PL) performance versus time under different scenarios. Figure 6: The number of executed packets by relays versus time under different scenarios.