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This paper presents a novel mechanism for scheduling packet transmissions of real-time video conferencing over the public Internet. By scheduling transmissions of video packets at different priorities in the presence of packet losses and delays, we aim to deliver videos with perceptually pleasing and consistent quality at receivers. Fundamental to this new mechanism is a realization of uneven packet transmission rates (UPTR) in the Internet, which allow an instantaneous packet transmission rate to fluctuate around an average rate, without significantly affecting the average loss rate and delay in transmissions. By exploiting this generic UPTR idea, we propose two application scenarios that provide positive design alternatives for robust realtime video delivery over the lossy Internet. Experimental results clearly show the advantages of our proposed methods over those previous solutions without awareness of UPTR.