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In recent years, due to increasing interest in applications of wireless sensor networks that demand certain quality of service (QoS) guarantees, new routing protocols have been proposed for providing energy-efficient real-time relaying of data. However, none of these protocols considered any possible movement of the sink node for performance purposes. In this paper, we propose possible relocation of sink (gateway) for improving the timeliness of real-time packets. Our approach searches for a location close to the most loaded node. The gateway is then relocated to the new location so that the load of that node is alleviated and the real-time traffic can be split. As long as the gateway stays within the transmission range of all last hop nodes, it can be moved to that location without affecting the current route setup. Otherwise routes are adjusted by introducing new forwarders. Simulation results demonstrate the effectiveness of the proposed approach.