# Energy-Saving Traffic Scheduling in Hybrid Software Defined Wireless Reschargeable Sensor Networks  
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However, for node \(n_{2}\), there is \(E_{2}\propto{d_{2}}^{2}\). Supposing that \(d_{2}=2d_{1}\), then \(E_{2}\) is approximately 4 times of \(E_{1}\). Consequently, the energy saving problem in WRSNs is more complicated than normal WSNs. Traditional energy saving schemes in normal WSNs cannot be directly transplanted into WRSNs. At the same time, the combining of Software Defined Networking (SDN) and WRSNs [4], which is an inexorable trend, brings new opportunities to energy saving issues in WRSNs. SDN can schedule the traffic and energy distribution in the perspective of the whole network, so as to achieve more energy gain while satisfying the service requirements. Nevertheless, the evolution of WRSN to Software Defined WRSN (SDWRSN) is a gradual process. Normal WRSNs and SDWRSNs may exist concurrently in a long time, sometimes even in the same area, for the same set of applications. That is to say, in such networks, sensor nodes with SDN capabilities (SDN nodes) and normal sensor nodes (normal nodes) may coexist. We define such networks as hybrid SDWRSNs. In such hybrid SDWRSNs, the SDN controller can only directly control the SDN nodes, but not the normal nodes, leading to a discount on possible energy saving effect. Consequently, in the context of hybrid SDWRSNs, the energy saving problem is quite different comparing to normal WSNs, or even normal WRSNs, as follows:  
1. The lifetime of each node is no longer a key problem. Their energy can be supplemented by the wireless charger in time. On the contrary, the total energy consumption of all nodes, or the burden of the wireless charger turns out to be a key problem. 2. The energy consumption model is different. The geographical distribution of sensor nodes will directly impact the charging efficiency, and thereby change the burden of the wireless charger. 3. Although the SDN controller can only directly control the SDN nodes to optimize the traffic and energy consumption, this will indirectly influence the inlet flow of normal nodes, and thus change the behaviours of normal nodes indirectly. Existing studies, which will be demonstrated particularly in Section 2, usually concentrate on several major aspects. For normal WSNs, a great amount of work has been done focusing on how to extend the lifetime for sensor nodes in the energy-constrained network with a special routing algorithm. In WRSNs, most works try to improve energy efficiency by optimizing the deployment or moving route of the wireless charger. A few studies take the energy limitation of wireless charger into account. To the best of our knowledge, no current work has been done focusing on the energy saving issue in hybrid SDWRSNs. To solve the above problem, in this paper, we put forward an Energy-saving Traffic Scheduling (ETS) algorithm for hybrid SDWRSNs. The ETS algorithm adequately considers the new characters in hybrid SDWRSNs and takes advantage of the SDN controller's direct control ability on SDN nodes and indirect control ability on normal nodes. The simulation results show that ETS can substantially improve the energy efficiency in hybrid SDWRSNs, and therefore ensure the network working more steadily and chronically. We highlight our contributions of this paper as follows:  
Firstly, we derive a mathematical optimization model for the energy efficiency problem in hybrid SDWRSNs. Although it proved to be a non-deterministic polynomial hard (NP-hard) problem, the model provides an outline and paradigm for energy saving problem in hybrid SDWRSNs. Figure 1: An example of wireless recharging. Then, a fast heuristic algorithm known as Energy-saving Traffic Scheduling (ETS) is presented, which takes charging losses and the new energy saving characters into account, and schedules the flows through both SDN nodes (directly) and normal nodes (indirectly). Finally, we evaluate the performance of the ETS algorithm with simulations.