## 4 Simulation Evaluation
### Simulation Result
This is because each point on the curve represents the average of 200 nodes, many of which did not participate in packet relaying as much as the nodes in the chain topology. Finally, we evaluate how the variation of _sleep_factor_ in P-MAC integrated with routing affects the network performance. The value of _sleep_factor_ determines the length of the _SLEEP_ period (see Equation 2). Increasing _sleep_factor_ increases the length of the _SLEEP_ period time and the whole cycle time. Increasing the sleeping time of sensor nodes can save more energy. However, when a packet is not generated at the start of the _SEND DATA_ period in the current cycle, a longer cycle time makes the packet wait longer for the next cycle. For the chain topology, it is still the case that \(n=24\). The input interval of a CBR flow in node 0 varies from 10-1 seconds. Each simulation runs for 1,200 seconds. Table 4 shows the different values of _sleep_factor_ we used in our simulation, as well as their corresponding _SLEEP_ period time and cycle time. The average packet delivery latency, the average power consumption per sensor node and the data throughput are observed, and the simulation results are shown in Figure 12. \begin{table}
\begin{tabular}{|c|c|c|c|} \hline _sleep\_factor_ & \(\mathbf{T_{S/R}}\) (ms) & \(\mathbf{T_{SLEEP}}\) (ms) & \(\mathbf{T_{cycle}}\) (ms) \\ \hline
2 & 234 & 468 & 936 \\
5 & 234 & 1,170 & 1,638 \\
8 & 234 & 1,872 & 2,340 \\
11 & 234 & 2,574 & 3,042 \\
14 & 234 & 3,276 & 3,744 \\
17 & 234 & 3,987 & 4,446 \\ \hline \end{tabular}
\end{table} 
Table 4: Cycle duration with different _sleep_factor_. Figure 11: **(a)** Throughput in the random topology. **(b)** Average power consumption per sensor node in the random topology. Note that Figure 12(a) shows the delivery latency that only varies with respect to the input interval from 10-5 seconds. This is because when the input interval is less than 5 seconds, the latency in the network with \(\textit{sleep\_factor}=17\) will be too large to be displayed. Figure 12(a) implies that the packet delivery latency increases as the \(\textit{sleep\_factor}\) increases for the reason stated above. But a greater \(\textit{sleep\_factor}\) ensures that nodes save more energy, as shown in Figure 12(b). When the network throughput is considered, a small \(\textit{sleep\_factor}\) is expected if the network traffic load is high, as shown in Figure 12(c). Figure 12(c) also shows that the cycle time is almost equal to the lowest input interval, which can still ensure that the output rate follows the input rate. For example, when \(\textit{sleep\_factor}=17\), the cycle duration is about 5 seconds, which is the lowest input interval ensuring that the network has 100% throughput, as shown in Figure 12(c). Figure 13 shows the impact evaluation of \(\textit{sleep\_factor}\) in the random topology. The result is in accord with that in the chain topology. Note the evaluation doesn't include a delivery latency  
Figure 12: The impact evaluation of \(\textit{sleep\_factor}\) in the chain topology, **(a)** Packet delivery latency. **(b)** Average power consumption. **(c)** Output rate. evaluation, which is not convenient to be given for the random topology. Designers can select the value of _sleep_factor_ according to the network traffic load. For example, if the network input rate doesn't exceed 0.2 packets/second (the input interval is not less than 5 seconds), _sleep_factor_ = 17 should be chosen, since the throughput can reach 100% with the lowest energy consumption. But if the input rate reaches 1 packet/second or higher, the minimum value of _sleep_factor_ = 2 should be chosen.