## 4 Performance Evaluation
### Simulation Results
We observed that the value of \(\rho_{avg}^{100}\) and \(\theta_{1}\) increased as \(N_{RAW}\) increased, which is consistent with our intuition. The values of the \(\rho_{avg}^{100}\) and \(\theta_{1}\) were quite similar when \(N_{s}\) was set to 2 and 4 in our simulation, and, therefore, the table only shows the change of the values when \(N_{s}\) was set to 1. Moreover, it is easy to find the network real-time performance (average delay and packet loss ratio) under each value of \(\rho_{avg}^{100}\) and \(\theta_{1}\) by analyzing Figures 6 and 7. For example, when \(N_{RAW}\) equaled to 20, \(\rho_{avg}^{100}\) and \(\theta_{1}\) were 89% and 0.82, respectively, and the corresponding delay and packet loss ratio were 7.2 ms and 0, respectively. Figures 6 and 7 show the average delay and packet loss ratio of the different backoff algorithms under different RAW parameter settings. We observed that the objective values associated with each algorithm increased as the number of RAW stations increased. This is intuitively expected because the network is more congested if there are more stations transmitting their data. Comparing Figure 6a-c, we observed that the number of the RAW slots (\(N_{s}\)) can influence the delay performance slightly. For example, when the network was not congested (\(N_{RAW}<15\)), the average delay increased if the number of the RAW slots \(N_{s}\) increased. When \(N_{RAW}=15\), the average delay shown in Figure 6a-c was 1.2 ms, 2.24 ms and 7 ms, respectively. The reason is that the RAW mechanism only allows stations to transmit its data in its assigned slot. A station will wait for a longer time to transmit if there are \begin{table}
\begin{tabular}{c c c c c c c c c c c} \hline \hline \(N_{RAW}\) & **1** & **5** & **10** & **15** & **20** & **25** & **30** & **35** & **40** & **45** & **50** \\ \hline \(\rho_{avg}^{100}\) & 2\% & 14\% & 35\% & 53\% & 89\% & 92\% & 94\% & 95\% & 98\% & 98\% & 98\% \\ \hline \(\theta_{1}\) & 0.02 & 0.14 & 0.35 & 0.53 & 0.82 & 0.82 & 0.82 & 0.82 & 0.82 & 0.82 \\ \hline \hline \end{tabular}
\end{table} 
Table 3: The calculated core algorithm value in the first scenario (\(N_{s}=1\)). more slots in a RAW. On the other hand, when the network is heavily loaded, adopting RAW can slightly alleviate network congestion, and obtain a lower average delay (although it is not obvious). The similar analysis result can be obtained for packet loss ratio when comparing Figure 7a-c. Figures 6 and 7 further show that the CA-CWA algorithm has better performance on average delay and packet loss ratio than the other two algorithms, regardless of the different number of RAW slots. We take the results in Figure 6a as an example; when \(N_{RAW}\) was less than 15, all the three backoff algorithms performed well due to the non-congested channel condition. However, when \(N_{RAW}\) was more than 20, the average delay of the network rose rapidly. In BEB, each station blindly reset its contention window to \(CW_{min}\) after a successful transmission, which further aggravates the degree of channel congestion. Thus, BEB has the worst performance on average delay among the three algorithms. CCCW algorithm aims to optimize the network throughput by adaptive usage of contention window size. It significantly reduces collisions of the stations, and the average delay was up to 40% lower than the performance in BEB. However, CCCW does not consider the collisions caused by interference, which results in the adjusted CW value not matching the real channel condition. Thus, the average delay in CCCW was at most 30% higher comparing with the average delay in CA-CWA. On the other hand, Figure 7a shows the packet loss performance of the three backoff algorithms. The packet loss ratio of BEB increased dramatically from 5% to 23% when \(N_{RAW}\) was 40. Compared with BEB, the packet loss ratio decreased up to 37.5% and 62.3% in CCCW and CA-CWA, respectively, when the network was congested (\(N_{RAW}>=35\)).