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In a wireless sensor network, the routing control overhead is prohibitive because mostly many nodes are involved in routing. To overcome the overhead problem, tier based anycast protocol was proposed in (Kulkarni et al., 2006). However, it has a shortcoming of using much more energy compared to other competitors of deterministic routing protocols in transmitting data packets towards the sink node. In this paper, we visited the tier based anycast protocol in depth and presented a new analytic framework by using the concept of sub-tiering. Firstly, we formulated the problem for finding an optimal duty cycle for each tier as a minimax optimization problem, and proved that the solution exists and it is unique. From the analysis results, we found that the network lifetime can be improved very much by allocating a duty cycle adaptively for each tier. Through simulations, we also confirmed that our duty cycle control algorithm increases the network lifetime by approximately 30%.