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A novel model is developed and investigated for a duty-cycle wireless sensor network (WSN), where each sensor node can stay at one of four statuses (i.e., full-active phase, two semi-active phases each with different functions, and a sleep phase) to make the system more efficient. The explicit result of the joint probability for data packet numbers and the sensor phases is achieved by suitably constructing a multi-dimensional Markov process. Furthermore, various energy consumption measures, such as energy consumption per unit time in each of the three energy consumptions and energy consumption switching from one phase to another, are obtained. System performance measures, such as the average delay time of a data packet in the system, throughput of the system, and the probability of the sensor node staying at any of the phases, are also achieved. The numerical analyses are provided to validate the model and the analytic results. The proposed model and the analysis method are expected to be applied to the design and analysis of WSN models with various phases of the sensor.