# Adaptive TCP Transmission Adjustment for UAV Network Infrastructure
## 4. \(AsRAN\) throughput Model  
This section shows the throughput model of \(ASRAN\). \(ASRAN\) modeling has two purposes. The first purpose is to verify the result of real experiment. Under environment of wireless multi-hop network, packet arrival period and segment loss event are unstable and aperiodic. Therefore, it is difficult to figure out whether experiment result is affected by \(ASRAN\) or just an accidental result caused by unstable environment. To decide whether the experiment result is credible or not, modeling the algorithm and calculating the expected throughput gain of \(ASRAN\) are necessary. The second purpose is to prove mathematically that \(ASRAN\) outperforms TCP-CUBIC. Please note that TCP-CUBIC is faster than TCP-NewReno and TCP-Reno to recover communication when segment loss occurred, which is shown in Section 5. TCP-CUBIC is developed in consideration of the wireless communication environment with both high bandwidth and high latency [22]. The congestion avoidance of TCP-CUBIC increases CWND size as cubic [23]. We confirmed through modeling that the \(ASRAN\) can show better throughput than the TCP-CUBIC. As shown in Figure 3, CWND size of the \(ASRAN\) reaches to the \(last\_max\_cvnd\) faster than TCP-CUBIC. After that, even if \(ASRAN\) increases with cubic curve as the same as TCP-CUBIC, difference of CWND size between \(ASRAN\) and TCP-CUBIC is getting larger. Because of CWND size of \(ASRAN\) reaches \(last\_max\_cvnd\) faster than TCP-CUBIC, \(ASRAN\) obtains more time to increase CWND with a cubic curve, compared to TCP-CUBIC. In the subsequent modeling, these effects are proved by calculating total throughput gain of \(ASRAN\). To obtain the expected throughput gain of \(ASRAN\), simplified modeling was used to calculate the throughput ratio between throughput of TCP-CUBIC and throughput of \(ASRAN\). Total throughput can be calculated by integrating graph of CWND size fluctuation shown in Figure 3. Predicted total throughput of \(ASRAN\) in Figure 3 will be the following equation:  
\[ASRAN\_total\_throughput=\int_{0}^{K}{(x+i)^{2}dx}+\int_{K}^{T}{\{(x-k)^{3}+last \_max\_CWND\}dx}. \tag{1}\]  
In Equation (1), \(x\) indicates the time variable, \(i\) indicates the initial CWND size, \(T\) indicates the time until the next segment loss occurs, and \(K\) represents the time that CWND reaches the \(last\_max\_cvnd\). In \(ASRAN\), before \(x\) reaches \(K\), CWND will be increased in Slow-Start phase. After that, CWND is increased by the congestion avoidance algorithm of TCP-CUBIC in probing phase which is cubic curve. For calculating \(K\) value, CWND size will be recovered with quadratic curve of slow-start until CWND reaches the \(last\_max\_cvnd\). At this moment, \(x\) value will be \(K\) value. Part of the quadratic CWND increase equation is shown in the front part of Equation (1). Calculating \(K\) value is:  
\[last\_max\_CWND={(K+i)^{2}} \tag{2}\] \[K=\sqrt{last\_max\_CWND}-i.\]  
Since CWND goes up every time an ACK arrives, the rise of CWND is discrete event. Therefore, the total throughput should be calculated by summing CWND value at each discrete time, instead of calculating predicted total throughput obtained by integrating graph of modeling. Figure 3 shows discrete time at regular interval. Sum of each CWND size at each discrete \(x\) value represents the total throughput. The gain of \(ASRAN\) compared to TCP-CUBIC ratio value can be calculated by dividing total throughput obtained from \(ASRAN\) by the total throughput of TCP-CUBIC. To show the difference of throughput between \(ASRAN\) and TCP-CUBIC, we set the example model to calculate the gain value. \(i=1\), \(last\_max\_cvnd=2\), \(T=2.5\) were arbitrarily assigned in example model, and Figure 3 is drawn  
Figure 3: Discrete time division of \(ASRAN\) and TCP-CUBIC. based on the example model. Based on example model, the throughput gain of \(ASRAN\) is calculated as follows:  
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