Network services for the most demanding advanced networked applications which require absolute, per-flow service assurances can be deterministic or statistical. By exploiting statistical properties of traffic, statistical assurances can extract more capacity from a network than deterministic assurances. In this work we consider statistical service assurances for traffic scheduling algorithms. We present functions, so-called effective envelopes, which are, with high 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 provisioned with statistical service assurances. We show that our bounds can be applied to a variety of packet scheduling algorithms. In fact, one can reuse existing admission control functions for scheduling algorithms with deterministic assurances. We present numerical examples which compare the number of ows with statistical assurances that can be admitted with our effective envelope approach to those achieved with existing methods
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