## 2 Related Work  
The data collection rate is affected significantly by the energy extracting rate from the environment. Therefore, a large number of researchers pay the utmost attention to the characteristics of R-WSNs [37; 38], especially regarding the features of energy supplement. At present, solar is the main energy source considered firstly for providing clean power in R-WSNs and a solar panel is generally installed on the outside to recharge an energy storage device for a sensor node [39]. On the one hand, considering the cost factors and economic feasibility, the size of the solar panel always is small, which results in limited energy being gained [40]. On the another hand, considering the weather factor and the different angles of the solar panel, each sensor node will obtain distinct power. Thus, it is not realistic the achieve data transmission synchronously in R-WSNs. For maximizing data collection rate, we analyze the techniques provided in traditional WSNs. Numerous works have been done focusing on maximizing data generation rate by saving energy in WSNs; e.g., [41; 42; 43]. A degree-constrained routing tree is introduced by minimizing hop counts with transmission power control to enhance the data collection rate, which can avoid the high-degree  
Figure 2: Components of a energy-powered sensor node. bottleneck effectively [44]. In [45], the authors present the optimal convergecast scheduling algorithms by the maximum degree in the routing tree for which information is collected fast. [PERSON] et al. [46] provide an iterative linear programming solution for finding the maxmin optimal rate assignment in a low-rate sensor network. [PERSON] et al. [47] formulate the optimal rate allocation with data aggregation as a network utility maximization problem and apply duality theory to decompose it into a rate control subproblem, other examples can be found in [48; 49], and references therein. Despite the maximum data generation rate achieved in these algorithms, they encounter critical tradeoffs between data flow and lifetime due to energy constraint. In R-WSNs, the lifetime is less of an issue, which can be maximized by operating in an energy neutral mode for nodes. Regarding the characteristics of R-WSNs, several protocols discuss several aspects of power management or MAC schemes to improve energy efficiency and maximum data collection rate [50; 51]. A centralized algorithm with line programming is proposed to compute the lexicographically maximum data collection rate and routing paths for each node [52]. [PERSON] et al. [53] provide a distribute algorithm for jointly determining the routing structure and amount of flows on each link with flow adjustment to achieve an optimal data collection rate. [PERSON] et al. [54] propose real time adaptive energy management policies based on observed information for optimal throughput. [PERSON] et al. [55] propose four throughput enhancement schemes from a simple naive scheme with low complexity to a probabilistic probing scheme incorporating advanced methods to appropriately use the harvesting energy. However, the ideal energy replenished precondition is used and data aggregation has not been considered in these protocols. Data aggregation is adopted widely in WSNs for improving data collection rate by removing redundant information [56]. The main idea behind data aggregation or data fusion is that, rather than sending individual data items from sensors to sinks, multiple data items are aggregated as they are forwarded by the sensor network [57]. In [44], the authors introduce two strategies to maximize the data collection rate: an aggregation tree is contracted to minimize the number of time slots needed and combine the scheduling with transmission power control to reduce the effects of interference. [PERSON] et al. [58] introduce an algorithm for maximum data collection rate in rechargeable wireless sensor networks with multiple sinks.