Scaling of the most likely traffic patterns of hose- and cost-constrained ring and mesh networks

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We consider ring and mesh networks of arbitrary size, whose traffic matrix is unknown apart from the fact that the total traffic entering and leaving each node is known, and there is an upper bound on the total network cost to service the traffic. We formulate approximate analytical expressions for the elements of the traffic matrix that have maximum entropy subject to these constraints, i.e., the matrix most likely to be realized. The analytical solution is found to be in good agreement with numerical solutions, over wide ranges of the cost constraint and randomly selected hose constraints, for a graph corresponding to the core of a real-world IP backbone network. The model is scalable in several parameters and in effect identifies a spectrum of nonuniform, distance-dependent demand, for which the expected values of link and node capacities, and the corresponding costs, may be estimated analytically for classes of networks.