# Optimal Routing for Time-Driven EH-WSN under Regular Energy Sources
## 1 Introduction  
Recent advances in wireless sensor networks have led to the development of energy-harvesting capabilities, which are expected to enable very long or even perpetual operation. In parallel, the design focus has progressively been shifted from maximizing network lifetime, usually defined as the time until first node death, towards optimizing network performance, basically delay and throughput [1]. Therefore, despite energy issues in energy-harvesting wireless sensor network (EH-WSN) cannot be disregarded, due to the time-varying nature of ambient energy sources, the new design priorities demand for revising current protocols for battery-powered WSN. Note that such new priorities represent a change in statistical sense too: While the design goal in battery-powered WSN is to maximize a lower bound (time until first node death), the goal in EH-WSN is to maximize an average (average performance). Such a difference obviously conditions the design of protocols. Most contributions on battery-powered WSN have focused on the Medium Access Control (MAC) layer, as this plays a fundamental role in the energy expended by a sensor node. Research activity on EH-WSN is also giving priority to the development of MAC protocols, but relaxing the constraints on energy consumption. Specifically, the new objective at the MAC layer is to increase the duty cycle of nodes as much as possible according to their individual energy harvesting patterns, as opposed to the common system-wide reduced duty cycle of battery-powered WSN. References [2; 3] provide, respectively, comprehensive surveys on MAC protocols for battery-powered and energy-harvesting WSN. The network layer is also under review. In fact, a few routing protocols for EH-WSN have been recently proposed with the aim of optimizing performance metrics, such as delay and throughput, again in contrast to the network lifetime maximization pursued by traditional routing protocols [4; 5]. One of the contributions is [6], which proposes an algorithm rather than a protocol. This algorithm, known as Energy-opportunistic Weighted Minimum Energy (E-WME), calculates the cost of each node as an exponential function of its residual energy, and then uses shortest-path routing on the basis of this metric. In addition, it offers high versatility, as it can be easily incorporated into different routing implementation schemes, like proactive or on-demand. In [7], a modification on the well-known Collection Tree Protocol (CTP) is proposed, namely Loop-aware CTP (La-CTP). This protocol introduces several mechanisms to effectively suppress the occurrence of loops and unlock unavoidable loops in moving packets across an EH-WSN. In general, these loops arise from temporary departures of nodes that stop working to enter a recharging state. In [8], a hierarchical topology is assumed and a centralized routing algorithm containing two parts is proposed. The first part consists of a genetic-based unequal clustering algorithm, which is run by the base station to form clusters of unequal size. Here, information about location, energy level and energy harvesting rate of all nodes is used. After clustering, the base station executes another algorithm to construct an inter-cluster routing among all cluster heads. This algorithm also takes into account the energy harvesting condition of the participant nodes, in this case the cluster heads. Another contribution is [9], which proposes the Energy Harvesting Opportunistic Routing (EHOR) protocol for multi-hop EH-WSN. This kind of opportunistic protocol uses a region-based approach to determine the optimal forwarders for every packet, by taking into account the energy condition of all nodes, and the fact that some of them are in recharging state and thus they are temporally unavailable. In [9], a linear topology is assumed. Then, EHOR is extended to 2D topologies in [10], under the name of Adaptive Opportunistic Routing (AOR).