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We propose a linear model of the throughput of the IEEE 802.11 distributed coordination function (DCF) protocol at the data link layer in non-saturated traffic conditions. We show that the throughput is a linear function of the packet arrival rate (PAR) lambda with a slope depending on both the number of contending stations and the average payload length. We also derive the interval of validity of the proposed model by showing the presence of a critical lambda, above which the station begins operating in saturated traffic conditions. The analysis is based on the multi-dimensional Markovian state transition model proposed by Liaw et al. with the aim of describing the behaviour of the MAC layer in unsaturated traffic conditions. Simulation results closely match the theoretical derivations, confirming the effectiveness of the proposed linear model.