Wireless local area networks (WLANs) are extremely popular being almost everywhere including business, office and home deployments. The IEEE 802.11 protocol is the dominating standard for WLANs. The essential medium access control (MAC) mechanism of 802.11 is called distributed co-ordination function (DCF). This paper provides a simple and accurate analysis using Markov chain modelling to compute IEEE 802.11 DCF performance, in the absence of hidden stations and transmission errors. This mathematical analysis calculates in addition to the throughput efficiency, the average packet delay, the packet drop probability and the average time to drop a packet for both basic access and RTS/CTS medium access schemes. The derived analysis, which takes into account packet retry limits, is validated by comparison with OPNET simulation results. We demonstrate that a Markov chain model presented in the literature, which also calculates throughput and packet delay by introducing an additional transition state to the Markov chain model, does not appear to model IEEE 802.11 correctly, leading to ambiguous conclusions for its performance. We also carry out an extensive and detailed study on the influence on performance of the initial contention window size (CW), maximum CW size and data rate. Performance results are presented to identify the dependence on the backoff procedure parameters and to give insights on the issues affecting IEEE 802.11 DCF performance.