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Recent research on sizing router buffers in high speed networks promises the realization of core network with buffer enough to store just a few packets. However, such networks work well with traffic efficiently paced to reduce both short-term and long-range burstiness. In this work, we propose an efficient pacing scheme at the edge network that works for packets with or without pre-determined deadlines and smoothen the traffic according to the occupancy of the router buffer. The proposed algorithm paces the traffic both according to the delay and queue length constraints. It is thus shown to possess the advantages of both delay-based pacing and queue length-based pacing algorithms in the literature and yet overcome their shortcomings. We demonstrate through simulations that the proposed pacing algorithm significantly reduces the loss rate even when the traffic contains significant UDP traffic compared to the best known pacing schemes in the literature.