Topology aggregation for combined additive and restrictive metrics

In a hierarchical network, nodes are aggregated to groups for the purpose of simplifying routing. Each group has a set of ingress–egress nodes, and routing information is conveyed to the outside world in the form of a transition matrix (or other equivalent form) that gives the cost of traversing the network between each ingress–egress node pair. In this paper, we present a transition matrix that has enough descriptive power to support service requirements that have both restrictive (bandwidth) and additive (delay) constraints. We present a solution in the form of a matrix whose elements are functions that map requested bandwidth to minimum delay. These functions describe the efficient frontier of the solution space, and we specify a generic procedure for calculating the efficient frontier for various delay functions. The complexity of this procedure is given for a set of well-known delay functions that are of practical importance.