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The definition of TCP friendliness has been evolved over time from the traditional one for congestion control protocols to the recent ones for admission control protocols. All of them can effectively prevent the Internet from congestion collapse and TCP starvation, while enabling a wide variety of traffic control protocols other than TCP. However, the current TCP-friendly admission control protocols are designed to be TCP friendly only on fairly long time scales. That is, it is likely that a group of TCP users all experience persistent poor performance during their transmission, which then leads to dissatisfaction of TCP users. In this paper, we first present a new definition of TCP friendliness, called Stochastic TCP Friendliness, with which we study the time scale of TCP-friendly admission control protocols. Second, we develop a new traffic control protocol, called Stochastically TCP- Friendly Admission Control (STFAC), which is stochastically TCP friendly not only on a long time scale but also on a short time scale. Finally, we present very encouraging simulation results showing that STFAC can considerably improve the performance of UDP users and TCP users on both a long time scale and a short time scale, when compared with the traditional TCP- friendly congestion control protocols.