## 1 Introduction  
Recent advances in VLSI, microprocessor and wireless communication technologies, and wireless sensor networks (WSNs) have been deploying for various potential applications in environmental surveillance, military operations, object tracking, and other domains [1, 2, 3]. In WSNs, real-time applications such as fire alert and intruder detection require data collection in a desired time deadline [4]. In order to satisfy the desired time deadline, the real-time routing schemes proposed in [4, 5, 6] utilize a spatiotemporal approach by which data are delivered with a delivery speed obtained from both the distance from a source to a destination and the desired time deadline. When the schemes disseminate data from the source as far as the destination, every immediate node elects a next-hop node that is one of the one-hop neighbor nodes closer to the destination than itself and has a relay speed larger than the delivery speed. Hence, by relaying data with a faster speed than the delivery speed per every hop, data collection in the desired time deadline with respect to the distance can be achieved [5]. Typically, the existing schemes [4; 5; 6] assume the distance between the source and the destination is static, i.e., a constant value. In many practical applications, mobile sinks such as soldiers and firefighters tend to move around within the sensor fields and receive data during their movements [7; 8; 9]. Accordingly, when a source disseminates data to a mobile sink in a desired time deadline, the distance between the source and the mobile sink may also be dynamically altered because the mobile sink randomly changes its own locations in a sensor field. This means that the delivery speed should be recalculated by the immediate reflection of the distance alteration during real-time data dissemination to the mobile sink. In order to immediately reflect the new distances, we may take into account three methods: (1) the source-based, (2) the intermediate-node-based, and (3) the sink-based method. First, in the source-based method, the source obtains the current location of the mobile sink by sink location services [10; 11; 12] and then recalculates the new delivery speed to retransmit data to the current location on the desired time deadline. In the second method, an intermediate node currently forwarding data performs the location service to get the current location of the sink. Then, it disseminates the data to the current location with the recalculated new delivery speed. Finally, the sink-based method employs a backward location notification to the intermediate node from the sink when the sink moves to a new location [9]; thus, the intermediate node reflects the new distance for the new delivery speed. However, these three immediate reflection methods might have considerable problems with respect to real-time data transmission. The current methods of location obtainment used by the sink location services may lead to long term delays, shortening the time interval until the desired time deadline. Because the mobile sink frequently alters its own location, this represents a serious problem. The backward location notification means that the reflection of new distances is away from the destination; thus, it also causes high latency. In addition, in existing schemes, because immediate nodes select the nondeterministic next-hop node, the forwarding path for data transmission from the source to the destination might be altered every instance of transmission. Namely, the sink cannot determine the currently forwarding intermediate node to reflect the new distances. Consequently, in terms of real-time routing to the mobile sink, it is hard to immediately reflect new distances due to high latency and nondeterministic forwarding. Thus, we proposed a real-time routing protocol, called EAR2 (expected area-based real-time routing) [13] for mobile sinks in wireless sensor networks.