Routing to minimize the maximum congestion in a communication network

Abstract : Some new results in the area of routing algorithms for communication networks are presented. The aim has been to take as much advantage as possible of the inherent structure of the routing problem, as given by the graph supporting the network. It seems reasonable to believe that new insights in topological design can be developed as one gains new understanding of how performance varies with routing policy when topology is held fixed. For the purpose of making the topological structure of the network to explicitly appear in the routing policy, an optimization criteria that divides into a hierarchy of linear programs with a natural hierarchical partition of the network, has been chosen. The power of the criteria lies in the fact that, given the network state, it identifies the 'worst' congestion problem and alleviates it with maximum resources. Furthermore the linear programming formulation allows one to express all results in terms of graph related matrices. This fact contributes, not only to reduce the amount of computation needed for finding, and dynamic tracking, the optimal solution, but it also provides with properties and simplifications that can be used for gaining a better understanding of the routing policy, or optimal routing policies in general if one assumes that optimal policies do not differ much from one another.