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We propose in this paper an analytical model to evaluate the average packet delay and its standard deviation in a saturated IEEE 802.16 network with the binary exponential backoff mechanism. In particular, we develop a simple fixed point analysis to approximate the probability that a bandwidth request is unsuccessful in such a network. A closed form expression for the mean and standard deviation of the delay are then derived from the model as a function of the system parameters. The accuracy of the analytical model is evaluated by comparing with simulation results over a wide range of operating conditions.