The rapid increase of multimedia traffic has to be accounted for when designing IP networks. A key characteristic of multimedia traffic is that it has strict Quality of Service (QoS) requirements in a heterogeneous manner. In such a setting, scheduling by service curves is a useful method as it allows for assigning each flow exactly the service it requires. When hosting heterogeneous multimedia traffic, the utilization of packet-switched networks can be increased by using bandwidth/delay decoupled scheduling disciplines. It has been shown in previous work how optimal network service curves are obtained with them. A basic result from Network Calculus is that the network service curve is obtained by the min--plus convolution of the node service curves. We state a theorem on the min--plus convolution in this work, which simplifies the computation of the min--plus convolution of service curves. The theorem follows from the continuous ΓΔ-transform, which we develop. With this theorem, we derive the optimal service curves for the nodes along a path. Further, we show how the admission control can be improved when networks are designed based on service curves. Considering one node, reallocating the service curves leads to admitting more flows. Then we point out scenarios where sub-optimal allocation of service curves in a node can increase the number of admitted flows to the network.
The key results are accompanied by numerical examples. On a broader scale, this paper advances the research in analytically modeling packet-switched networks by pointing out novel properties and a new application of Network Calculus.