Energy balance is a critical issue in wireless sensor networks. Several mixed data transmission (MDT) schemes have been proposed to achieve energy balance. However, most existing works are lack of theoretical study, especially understanding the relationship between network-wide energy balancing and lifetime optimization. In this paper, we conduct comprehensive theoretical analysis to the two-level based MDT scheme when applying to network-wide energy balancing, and eventually to maximize the network lifetime. We propose a novel network model, named energy balance area (EBA), and formally analyze its characteristics under the two-level based MDT scheme. To maximize the network lifetime, we convert the transmission probability allocation problem in the MDT scheme into an EBA partitioning (EBA-PT) problem, which is shown to be NP-hard. We then propose a heuristic approximation algorithm to determine the optimal configuration of EBAs, which is proven in this paper to be the key for maximizing the network lifetime. In this way, we obtain a near-optimal result. Our experimental studies show that network lifetime can be further improved as compared the hop-by-hop and the two-level based MDT schemes.
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