In this paper, we consider statistical assurances for traffic scheduling algorithms. We present functions, so-called effective envelopes, which are, with hight certainty, upper bounds of multiplexed traffic. Effective envelopes can be used to obtain bounds on the amount of traffic on a link that can be provided with statistical service assurances. We show that our bounds can be applied to a variety of traffic scheduling algorithms. In fact, one can re-use existing admission control functions for scheduling algorithms with deterministic assurances. We prtesent numerical examples which compare the number of flows that can be admitted with statistical assurances by our effective envelpe approach to those achieved with existing methods.

KEY WORDS: Internet, packet switching, quality-of-service, scheduling, statistical multiplexing, statistical service, traffic control (communication).