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The Berkeley-medium access control (B-MAC) is a lightweight, configurable and asynchronous duty cycle medium access control (MAC) protocol in wireless sensor networks. This article presents an analytic modelling of single-hop B-MAC protocol under a Poisson traffic assumption. Our model considers important B-MAC parameters such as the sleep cycle, the two stage backoff mechanism, and the extended preamble. The service delay of an arriving packet and the energy consumption are calculated by an iterative method. The simulation results verify that the proposed analytic model can accurately estimate the performance of single-hop B-MAC with different operating environments.