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Due to its fixed assignment nature, the well-known time division multiple access (TDMA) protocol suffers from poor performance when the offered traffic is bursty. In this paper, an adaptive TDMA protocol, which is capable of operating efficiently under bursty traffic conditions, is introduced. According to the proposed protocol, the station which is granted permission to transmit at each time slot is selected by means of learning automata (LA). The choice probability of the selected station is updated by taking into account the network feedback information. The system which consists of the LA and the network is analyzed and it is proven that the choice probability of each station asymptotically tends to be proportional to the probability that this station is not idle. Although there is no centralized control of the stations and the traffic characteristics are unknown and time-variable, each station tends to take a fraction of the bandwidth proportional to its needs. Furthermore, extensive simulation results are presented, which indicate that the proposed protocol achieves a significantly higher performance than other well-known TDMA protocols when operating under bursty traffic conditions.