# A Joint Strategy for Fair and Efficient Energy Usage in WLANs in the Presence of Capture Effect
## 5 PHY Capture Induced Unfairness in WLAN and Proposed Solutions Based on Joint Strategy
### Adaptive Transmission Power Control (ATXPR)
#### 5.2.2 Extensive Simulations  
In the remaining paper we choose AIMD+ and compared its performance with the baseline in various settings. We compared the energy efficiency obtained by nodes in Zone 1, Zone 2, and aggregate network energy efficiency for the baseline and AIMD+, shown in Figure 11. In this experiment, the total number of nodes in the network remained constant, i.e., \(N_{total}\) = 20 and the number of nodes in Zone 1 and Zone 2, denoted as \(N_{1}\) and \(N_{2}\), respectively, varied from 2\(\sim\)18. At first, this comparison shows that the aggregate network efficiency, for both baseline and AIMD+, overlap each other and that our proposed solution does not compromise on the aggregate energy efficiency. Secondly, energy efficiency of nodes in Zone 2 when using AIMD+ always remains higher than the baseline method for any value of \(N_{2}\). Thirdly, when using the AIMD+ mechanism energy efficiencies for both Zone 1 nodes \begin{table}
\begin{tabular}{c c c} \hline \hline
**Strategy** & \(\mu_{fair}\) & \(\eta\) \\ \hline Baseline & 0.81 & 1.51 \\ CWADJ & 0.91 & 1.51 \\ AIAD+ & 0.98 & 1.53 \\ MIAD+ & 0.96 & 1.54 \\ AIMD+ & 0.99 & 1.54 \\ MIMD+ & 0.97 & 1.55 \\ \hline \hline \end{tabular}
\end{table} 
Table 4: Result comparisons. Figure 10: Collision probability comparison between four transmission control algorithms. and Zone 2 nodes approach convergence when \(N_{1}=N_{2}=10\), indicating AIMD+ is substantially fairer than the baseline. Figure 12 compares energy efficiencies obtained using AIMD+ and baseline with varying inter-zone distances. Similar to Figure 11, \(N_{total}=20\) whereas \(N_{1}\) and \(N_{2}\) are fixed to 10. At first, we see the overlap between the aggregate energy efficiency obtained using AIMD+ and baseline. It means our proposed solution is effective in maintaining the overall aggregate energy efficiency. Secondly, we see that when the inter-zone distance was initially 20 m, there was no difference between the energy efficiencies obtained via baseline and AIMD+ for both zones. The reason is that at 20 m difference there are very few successful captures. Most simultaneous transmissions turn into collisions, hence, AIMD+ is rarely invoked. Moreover, as the inter-zone distance starts increasing capture starts happening frequently that causes unfairness between the energy efficiency of Zone 1 and Zone 2 using the baseline. At 40 m inter-zone distance this unfairness reaches its peak. In contrast to baseline our proposed solution improves efficiency of Zone 2 nodes in addition to keeping unfairness to minimum unlike baseline. Even though energy efficiency of the group of nodes in Zone 1 decreases using AIMD+, overall energy efficiency remains same and fairness improves to the maximum level for all values of inter-zone distance. We also compare the throughput performance obtained by baseline and AIMD+ in Figure 13. Similar to Figure 11 the total number of nodes in network is \(N_{total}=20\) and \(N_{1}\) and \(N_{2}\) vary from 2\(\sim\)18. At that can be seen in Figure 13 that the total network throughput when using AIMD+ either remains equal or higher than the case when using baseline. Secondly, throughput for the nodes in Zone 2 always remained higher for all the values of \(N_{2}\). Thirdly, we can see that throughputs of Zone 1 and Zone 2 nodes coincide when approaching the case \(N_{1}=N_{2}=10\), again indicating that AIMD+ is more fair than the baseline in which the convergence of throughputs of Zone 1 and Zone 2 nodes happen when \(N_{1}=3\) and \(N_{2}=17\). Finally, it can be seen that throughput for the nodes in Zone 1 when using AIMD+ is always lower than when using baseline. It shows that AIMD+ effectively controls Zone 1 node's access to the channel in order to maintain channel access fairness among the nodes of two Zones as well as the total network throughput. Figure 11: Comparison of additive increase, multiplicative decrease (AIMD+) with baseline.