## 1 Introduction
### Related Work  
Much research effort has already been spent for improving the lifetime of WSNs, based for instance on routing protocols, transmission power control, network coding, MAC layer design, and autonomic approaches. Below, we provide a non-exhaustive list of the efforts and their main characteristics. In [9], a framework for maximizing the network lifetime of a WSN is proposed exploring the sink node mobility under three constraints: prescribed delay tolerance regarding the transmission of the sensor information to the sink node, node energy consumption and data flow conservation. Nodes can temporarily store data until the mobile sink is in a better position for data exchange. The lifetime is a variable of the optimization problem that, when maximized, acts on minimizing the energy required per unit of time to transmit data at a certain bit rate in a multi-hop network topology. Comparisons with the static sink node scenario are also presented in [9]. The work in [10] focuses on finding the optimal sink node position with respect to relay nodes in order to prolong the WSN lifetime. An algorithm based on particle swarm optimization (PSO) is used to find the best position. The authors of [11] propose a unified framework to analyze the network lifetime maximization problem in WSNs. A linear programming model jointly covers sink mobility and routing problems by constraining the sink to a finite number of locations. The authors apply the framework to a set of typical topological graphs, including linear, ring, grid and arbitrary topology. The paper reports lifetime improvements for mobile sinks when compared to static ones for different network sizes. In [12], the authors introduce two linear programming models for data collection in a WSN with a controlled mobile base station and limited buffer capacity. The first model does not consider packet buffering, while the second model does. The paper is focused on comparing both scenarios considering static sensor nodes and a mobile sink. Sensors are randomly deployed, and the sink node can move according to a set of locations. Every sensor sends its data towards the sink either through multi-hop, or via direct communication if the sink is in the sensor's vicinity. In [13], a comparative study of WSN protocols is provided based on various network lifetime definitions, discussing the implications and applicability of the lifetime metrics. Several protocols are grouped into three classes according to similarities regarding lifetime definitions. Analyses are made based on the protocols that are representative to each class. Network-level simulation results are provided, showing numbers associated with the lifetime achieved by each protocol. The authors of [14] deal with clustering algorithms where a number of sensors are distributed in a given area and a number of clusters with single cluster heads are formed. The positions of energy-harvesting nodes are adjusted for optimized network lifetime. The paper thus presents network lifetime improvements for clustered sensor networks. The authors of [15] propose to exploit sensor spatial redundancy by defining subsets of sensors active in different time periods, allowing sensors to save energy when inactive. Two linear programming problems are presented to maximize network lifetime, which is defined in terms of the required coverage level: the first one, based on column generation, must run in a centralized way, whereas the second one is based on a heuristic algorithm aiming at a distributed implementation. The paper reports results to validate the model and to compare the adopted linear optimization problems. A heterogeneous sensor network deployment strategy is proposed in [16]. Simulation is performed, primarily to measure to what extent memory and computation limiting can enhance network lifetime while attaining energy balancing.