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The paper studies the packet delay distribution of the IEEE 802.11 distributed coordination function (DCF) protocol. DCF treats packets in an unfair manner. Results indicate that, in large networks, most packets have very low time delays, some packets have delays close to the average value and a small number of packets experience extremely high delays. We study the DCF delay distribution by developing a mathematical model that calculates the important properties of the constituent curves of the delay distribution curve, namely the probability that a packet is successfully transmitted from a particular backoff stage and the average delay of the successfully transmitted packets from this backoff stage. The model is simple, gives an insight into the internal mechanisms of DCF and applies to both basic and RTS/CTS access mechanisms. The accuracy of the analytical model is verified by simulations. Analytical results are presented that explore the effect of network size and of the initial contention window size on the fairness of DCF regarding the distribution of packet delays.