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With the rapid development of the Internet, the control of traffic congestion has become one of the most critical issues that must be confronted by the users. It is also a major challenge to researchers in the field of performance modelling. The paper presents a discrete-time stochastic queueing model for the performance evaluation of the active queue management (AQM) based congestion control mechanism called random early detection (RED) using a two-state Markov-modulated Bernoulli arrival process (MMBP-2) as the traffic source. A new analytical framework is proposed and a two-dimensional discrete-time Markov chain is introduced to model the RED mechanism. This mechanism takes into account the reduction of the incoming traffic arrival rate due to packets dropped probabilistically with the drop probability increasing linearly with the system contents. The analytical evaluation of the queue considered could be of interest for modelling the performance of the RED mechanism for the Internet traffic with short range dependent (SRD) traffic characteristics. The mean system occupancy, mean packet delay, probability of packet loss and system throughput are computed from the analytical model for a dropping policy, which is a function of the thresholds and maximum drop probability. The numerical results clearly demonstrate how different threshold settings can provide different tradeoffs between loss probability and delay to suit different service requirements. The effects of input parameters on a selected set of performance metrics, burstiness and correlations for the arrival process are also studied.