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Over the last decade a large number of routing protocols has been designed for achieving energy efficiency in data collecting wireless sensor networks. The drawbacks of using a static sink are well known. It has been argued in the literature that a mobile sink may improve the energy dissipation compared to a static one. Some authors focus on minimizing Emax , the maximum energy dissipation of any single node in the network, while others aim at minimizing Ebar , the average energy dissipation over all nodes. In our paper we take a more holistic view, considering both Emax and Ebar . The main contribution of this paper is to provide a simulation-based analysis of the energy efficiency of WSNs with static and mobile sinks. The focus is on two important configuration parameters: mobility path of the sink and duty cycling value of the nodes. On the one hand, it is well known that in the case of a mobile sink with fixed trajectory the choice of the mobility path influences energy efficiency. On the other hand, in some types of applications sensor nodes spend a rather large fraction of their total lifetime in idle mode, and therefore higher energy efficiency can be achieved by using the concept of reduced duty cycles. In particular, we quantitatively analyze the influence of duty cycling and the mobility radius of the sink as well as their interrelationship in terms of energy consumption for a well-defined model scenario. The analysis starts from general load considerations and is refined into a geometrical model. This model is validated by simulations which are more realistic in terms of duty cycling than previous work. It is illustrated that over all possible configuration scenarios in terms of duty cycle and mobility radius of the sink the energy dissipation in the WSN can vary up to a factor of nine in terms of Emax and up to a factor of 17 in terms of Ebar. It turns out that in general the choice of the duty cycle value is more important for achieving energy efficiency than the choice of the mobility radius of the sink. Moreover, for small values of the duty cycle, a static sink turns out to be optimal in terms of both Emax and Ebar . For larger values of the duty cycle, a mobile sink has advantages over a static sink, especially in terms of Emax . These insights into the basic interrelationship between duty cycle value and mobility radius of a mobile sink are relevant for energy efficient operation of homogeneous WSNs beyond our model scenario.