Statistical Service Assurances for Tra c Scheduling Algorithms

| Network services for the most demanding advanced networked applications which require absolute, perow service assurances can be deterministic or statistical. By exploiting statistical properties of tra c, statistical assurances can extract more capacity from a network than deterministic assurances. In this work we consider statistical service assurances for tra c scheduling algorithms. We present functions, so-called e ective envelopes, which are, with high certainty, upper bounds of multiplexed tra c. E ective envelopes can be used to obtain bounds on the amount of tra c 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 e ective envelope approach to those achieved with existing methods.