Network calculus, deterministic effective bandwidth and VBR trunks

We use network calculus results to study some properties of lossless multiplexing. We define a general form of the deterministic effective bandwidth and equivalent capacity. We find that call acceptance regions based on deterministic criteria (loss or delay) are convex, in contrast to statistical cases where it is the complement of the region which is convex. We find that, in general, the limit of the call acceptance region based on statistical multiplexing when the loss probability target tends to 0 is strictly larger than the call acceptance region based on lossless multiplexing. We consider the problem of determining the optimal parameters of a variable bit rate (VBR) ATM connection when it is used as a trunk, or tunnel, given that the input traffic is known. We find that there is an optimal peak rate for the VBR trunk, independent of any optimization function. For a linear cost function, we find an explicit algorithm for the optimal remaining parameters of the VBR trunk. We expect these results to form the basis of a measurement based call admission control method over a VBR trunk