## 5 Experimental Results
This may be because the Markov chain model relies on certain assumptions (e.g., busy channel probability does not depend on backoff stages), which is prone to slight estimation errors. On the other hand, while the proposed algorithm also makes use of such models, the real-time CCA feedbacks can help to correct the modeling error and lead to a more accurate operating point with respect to the throughput demand. Moreover, due to its distributed nature, the proposed algorithm is easier to implement and requires local channel sensing information only while the Markov chain method is more computationally expensive and requires certain network-wide information. Lastly, the proposed method employs a real-time traffic estimation method and is able to adapt to possible traffic changes while in the case of the Markov chain method, a new model will need to be solved when there is a traffic change. Figures 8 and 9 show the experimental results for a network with changes on the number of nodes. Initially Node 1, Node 2 and Node 3 are in the network with throughput demands of 1/100, 1/150, 1/200, respectively. At the second update, Node 4 is injected with a throughput demand of 1/100, followed by injection of Node 5 with a throughput demand of 1/200 at the 4 th update. Node 4 and Node 5 become inactive at the 6 th update. The update time is set to be 120 s and the threshold \(\upbeta_{THR}\) is set to 0.02. \begin{table}
\begin{tabular}{c c c c} \hline \hline  & **Method** & **Proposed Method** & **Markov Chain-Based Methods** \\ \hline \multirow{2}{*}{Errors} & Homogeneous & 0.43\% & 3.2\% \\  & Heterogeneous & 0.524\% & 4.7\% \\ \hline \multirow{2}{*}{Complexity} & easy to implement; able to & \multirow{2}{*}{computationally intensive; requires solving} \\  & be stored in a look-up table & & of multi-dimension Markov chain \\ \hline \multirow{2}{*}{Required Information} & local information only, e.g., & \multirow{2}{*}{needs network-wide information,} \\  & channel sensing result & & e.g., the number of active nodes \\ \multirow{2}{*}{Flexibility} & able to adapt traffic changes & & requires the traffics to be constant \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Comparisons of the proposed method and the Markov-chain based Methods. Figure 8: Busy channel probability in a heterogeneous network with changes on the number of nodes. Figure 8 shows the results of busy channel probability (BCP). The BCPs of Node 1-3 changes significantly when Node 4 is injected, with an increment of 0.06, 0.05, 0.02, respectively. According to Section 4, the change of BCP due to the injection of Node 4 is 0.0598 and the maximal fluctuations of the BCPs of the three without any traffic changes are 0.0234, 0.0287 and 0.0331, respectively. Node 3 with the lowest transmission rate suffers most from the noisy measurement of BCP. Nevertheless, as 0.0598 is greater than the maximal fluctuations and all nodes are able to detect the injection of Node 4. However, the detection of Node 5 is difficult as it brings a lower traffic. The BCPs do not change significantly. When Node 4 and Node 5 become inactive, the BCPs of the remaining nodes change significantly, with decrement of 0.02, 0.04 and 0.06. Despite the fluctuations on BCP, each node is able to adjust the transmission rate to meet the throughput demand. The actual throughput is plotted in Figure 9. It is observed that the average throughput of each node is very close to the demand, with an average percentage error of 0.875% at the optimal point.