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We analyse the queuing performance of a radio link level round-robin scheduler for downlink data transmission in a multi-rate TDMA (time division multiple access) wireless network. One broadcast channel in the downlink is shared by multiple mobile users in a time multiplexing fashion and a round-robin scheduler serves each user in exactly one time slot. The finite state Markov channel (FSMC) is used to capture different states of a slow Rayleigh fading channel. Depending on the channel condition, the modulation level at the transmitter is adapted and, therefore, one or multiple packets can be transmitted in one time slot. Using the matrix geometric method (MGM), the system is modeled as a quasi-birth and death (QBD) process and then the queue length and delay distributions are derived. We present typical numerical results and discuss their useful implications on system design.