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One main TCP congestion control objective is, by dynamically adjusting the source window size according to the router queue level, to stabilize the buffer queue length at a given target, thereby achieving predictable queueing delay, reducing packet loss and maximizing link utilization. One difficulty therein is the TCP acknowledging actions will experience a time delay from the router to the source in a TCP system. In this paper, a time-delay control theory is applied to analyze the mechanism of packet-dropping at router and the window-updating in TCP source in TCP congestion control for a TCP/RED dynamic model. We then derive explicit conditions under which the TCP/RED system is asymptotically stable in terms of the instantaneous queue. We discuss the convergence of the buffer queue lengths in the routers. Our results suggest that, if the network parameters satisfy certain conditions, the TCP/RED system is …