## 1 Introduction
Thus, this research first experimentally analyzes and compares the energy consumption of devices running MPTCP using the aforementioned congestion control algorithms available as Linux kernel implementations. Since the MPTCP scheduler and congestion control algorithm are the main contributors to the MPTCP operation, various researchers propose modifying the implementation of one, such as in [11; 12], or both of them, as in [13; 14], to reduce the energy consumption of MPTCP. However, the proposed modification may impact the throughput performance compared to other congestion control algorithms and affect the compatibility with other nodes operating the Linux kernel implementation of single-path TCP or MPTCP. Therefore, this paper proposes the usage of SDN accompanied by a deep neural network (DNN) to reduce the energy consumption for devices with dual or multiconnectivity. SDN [15] is an evolutionary paradigm with great potential in controlling network traffic flows. It has recently enabled a significant leap forward in the networking industry as it allows networks to become faster, more flexible, automated, and less complicated [16]. In this paradigm, the network data plane and control plane are physically separated, where the control plane manages several devices. The SDN controller generates the forwarding tables and pushes them into the data plane [17]. It provides the necessary commands to configure the network based on an overall network view and software programs written over the controller. Moreover, it paves the way for the control of the network by software functions from a central controller, by avoiding the difficulty of the manual reconfiguration of network devices [18]. The integration of SDN with MPTCP can minimize the energy consumption of wireless devices without modifying the MPTCP implementation [19]. Thus, we propose a scheme employing the SDN concept to control the traffic flows received by each node wireless network interface to minimize the downlink energy consumption. In this scheme, the SDN controller decides on steering the flow of data packets to the receiving nodes based on a lightweight interface selection algorithm relying on the measured achievable throughputs of each node's wireless interfaces. Moreover, the proposed scheme offers another algorithm that also runs on the SDN controller to fine-tune its interface selection based on energy consumption information provided by a trained DNN. This paper offers two main contributions. Firstly, it provides a comparative experimental study of the data transfer throughput and energy consumption of different MPTCP congestion control algorithms, namely LIA, OLIA, BALIA, Cubic, and wVegas, which are all available as Linux kernel implementations. Secondly, it presents two algorithms that select which wireless interface should operate in each network node to minimize the overall network energy consumption. These algorithms are implemented using a Ryu-based SDN controller, which manages an Open vSwitch-based switch via the OpenFlow protocol. Based on the comparative study results, the first algorithm selects the operating radio interfaces of each node mainly based on their probed achievable throughput. The second algorithm uses a trained DNN to make an informed decision about whether the interfaces selected by the first algorithm are the best selection in terms of energy consumption or need further tuning. Both algorithms are tested on a real hardware testbed that fully implements a single-cell LTE network (with a real eNodeB and a fully fledged evolved packet core) and a WiFi network using dual-homed single-board computers as sending/receiving nodes. The rest of the paper is organized as follows. Section 2 reviews the most relevant research works in the literature. The background regarding different MPTCP congestion control algorithms available as Linux kernel implementations is introduced in Section 3. Section 4 outlines the system model. The details of the used experimental setups and procedures are described in Section 5.