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Advanced Infrared (AIr) is a proposed standard of the Infrared Data Association (IrDA) for indoor infrared LANs. AIr Medium Access Control (MAC) employs Carrier Sense Multiple Access with Collision Avoidance (CSMA/CA) techniques with Request To Send/Clear To Send (RTS/CTS) frame exchange to address the hidden station problem. A long Collision Avoidance Slot (CAS) duration, that includes the beginning of the CTS frame, is defined to cope with collisions caused from hidden stations. AIr MAC employs linear adjustment of the Contention Window (CW) size to minimize delays emerging from the long CAS duration. This paper provides a simple and accurate analytical model for the linear CW adjustment that calculates AIr throughput assuming a finite number of stations and error free channel transmissions. Validity of the model is verified by comparing analysis with simulation results. By examining the first derivative of the throughput equation, we derive the optimum CW size that maximizes throughput as a function of the network size. In the case of the AIr protocol, where a collision lasts exactly one CAS, different conclusions result for maximum throughput as compared with the corresponding conclusions for the similar IEEE 802.11 protocol. Using the proposed model, we present an extensive AIr throughput performance evaluation. The effectiveness of physical and link layer parameters on throughput performance is explored. The proposed long CAS duration combined with CW linear adjustment are proven quite effective. Linear CW adjustment combined with the long CAS duration offer an efficient collision avoidance scheme that does not suffer from collisions caused from hidden stations.