In hierarchical sensor networks, higher powered relay nodes can be deployed to act as cluster heads. The lifetime of such a network is primarily determined by the lifetime of the relay nodes. Recently, it has been shown that the use of a Mobile Data Collector (MDC), which moves through the sensor network to collect data, can improve the performance of the network in a number of ways. We propose a model for hierarchical networks using a MDC, where the MDC travels along a pre-determined trajectory at a known speed, and collects data from each relay node. In this model, the relay nodes need to buffer their data until they can be uploaded to the MDC. To reduce the buffer size, as well as the delay for the data communication, it is desirable to minimize the length of the trajectory. In our model the MDC "visits" a relay node, to collect data, at any point within the permitted transmission distance of the relay node. There is a trade-off in this approach, as a large permitted transmission distance means that the relay node will expend higher energy, and hence, have a reduced lifetime. In this paper, we present two formulations for computing the minimal trajectory of the MDC. Our approaches allow us to control the transmission distances of the relay nodes and hence, achieve the lifetime objectives. Minimizing the length of the trajectory reduces the buffer size requirements at each node as well as the delay between successive visits.
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