Mobile sinks can significantly extend the lifetime of a sensor network by eliminating the need for expensive hop-by-hop routing. However, a sensor node might not always have a mobile sink in transmission range, or the mobile sink might be so far that the data transmission would be very expensive. In the latter case, the sensor node needs to make a decision whether it should send the data now, or take the risk to wait for a more favorable occasion. Making the right decisions in this transmission scheduling problem has significant impact on the performance and lifetime of the node. In this paper, we investigate the fundamentals of the transmission scheduling problem for sensor networks with mobile sinks. We first develop a dynamic programming-based optimal algorithm for the case when the mobility of the sinks is known in advance. Then, we describe two decision theoretic algorithms which use only probabilistic models learned from the history of interaction with the mobile sinks, and do not require knowledge about their future mobility patterns. The first algorithm uses Markov Decision Processes with states without history information, while the second algorithm encodes some elements of the history into the state. Through a series of experiments, we show that the decision theoretic approaches significantly outperform naive heuristics, and can have a performance close to that of the optimal approach, without requiring an advance knowledge of the mobility
