## 3 MPTCP Congestion Control Background
### Linked Increases Algorithm (LIA)
\begin{table}
\begin{tabular}{c c c c c} \hline \hline
**Ref.** & **SDN-** & \begin{tabular}{c} **Energy-** \\ **Saving** \\ **Scheme** \\ \end{tabular} & \
\begin{tabular}{c} **Modified** \\ **MPTCP** \\ **Component** \\ \end{tabular} &
\begin{tabular}{c} **Summary** \\ \end{tabular} \\ \hline
[20] & ✓ & - & - & A WRT MPTCP scheduler controlled by SDN for multipath routing \\ \hline
[21] & ✓ & - & - & A dynamic path control on MPTCP using SDN \\ \hline
[22] & ✓ & - & - & A solution for bandwidth utilization problem in WSN using SDN-based flow management \\ \hline
[23] & ✓ & - & - & A scheme using SDN to manage heterogeneous home networks \\ \hline
[24] & ✓ & - & - & A scheme using SDN to reduce the delay between MPTCF subflows \\ \hline
[25] & ✓ & - & - & An SDN-MPTCP framework in naval battle fields \\ \hline
[26] & ✓ & - & - & An SDN-MPTCP implementation in IED satellite networks \\ \hline
[27] & ✓ & - & - & A study on the benefits of SDN and MPTCP in V2 communication \\ \hline
[28] & - & ✓ & Scheduler & A scheme (MPTCP) for improving MPTCP energy efficiency \\ \hline
[29] & - & ✓ & Scheduler & An MPTCP scheduler to choose energy-efficient network path \\ \hline
[30] & - & ✓ & Scheduler & An MPTCP scheduling algorithm for downlink traffic with energy minimization by load distribution and flow control \\ \hline
[31] & - & ✓ & Scheduler & An energy-aware MPTCP-based content distribution scheme \\ \hline
[11] & - & ✓ & Scheduler & A scheduling system (ES-MPTCP) prioritizing subflows for energy minimization \\ \hline
[12] & - & ✓ & Scheduler & An energy-efficient multipath scheduler for IoT monitoring systems \\ \hline
[22] & - & ✓ & Scheduler & An energy-efficient MPTCP scheduling scheme using stochastic optimization approach \\ \hline
[33] & - & ✓ & Scheduler & Energy-efficient MPTCP scheduling schemes for video transmission over heterogeneous wireless networks \\ \hline
[14] & - & ✓ & Congestion Control & A receiver energy-efficient congestion control scheme based on MPTCP \\ \hline
[13] & - & ✓ & Congestion Control & An energy-aware congestion control mechanism that shifts traffic to low-delay and lower-energy paths \\ \hline
[35] & - & - & - & An energy consumption analysis of MPTCP and power models for streaming data to mobile devices \\ \hline
[36] & - & - & - & An MPTCP energy consumption model for smartphones for different multimedia services \\ \hline
[37] & - & - & - & Energy consumption measurements of a mobile device with handover in different operation modes \\ \hline
[38] & - & - & - & A hardware-based energy consumption comparative analysis of three MPTCP congestion control algorithms \\ \hline This work & ✓ & ✓ & No Modification & Energy consumption management of multiconnectivity devices running MPTCP using SDN and DNN \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Related works comparison table. approach ensures that MPTCP subflows do not exhibit more aggressive behavior than regular TCP flows in the same scenario [39]. \[\alpha=CW_{total}\times\frac{\max_{i}\left(\frac{C_{i}}{RTT_{x}}\right)}{\left( \sum_{j}C_{j}\right)^{2}} \tag{2}\]  
where, for any subflow \(x\),  
\[C_{x}=\frac{CW_{x}}{RTT_{x}}.\]  
The terms \(C_{i}\) and \(C_{j}\) refer to the value of \(C_{x}\) for subflows \(i\) and \(j\), respectively. It is assumed that the congestion window size is maintained in terms of packets and the increase in the congestion is per ACK. In (2), the parameter \(\alpha\) determines how aggressively MPTCP behaves. This calculation ensures that MPTCP's total bandwidth is similar to that of a regular TCP flow on the best path available. Additionally, in the event of packet loss, the congestion window size is reduced by \(\frac{CW_{i}}{2}\)[39].