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In this paper, we propose an adaptive algorithm called Adaptive REM (AREM) that improves the performance of random exponential marking (REM) in two ways. Firstly, it adaptively controls the parameter alpha to achieve fast response, and secondly, it introduces a new method to evaluate dropping/marking probability with each packet arrival to reduce the queue length jitter. We demonstrate by extensive simulation results that AREM maintains queue length stability independently of traffic loads, round trip propagation delay, and bottleneck capacity. We also demonstrate that AREM is robust to non-responsive UDP traffic and HTTP traffic, and it is effective for networks with multiple bottlenecks. Comparison with REM demonstrates the superiority of AREM in achieving faster convergence to queue length target, smaller queue length jitter, lower packet loss rate, and higher link utilization.