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The authors studied a class of Service Overlay Network (SON) capacity allocation problem. By analyzing the problem with two different nonlinear optimization formulations, they show that the prices of offering service guarantees are closely related to a set of Lagrange multipliers. Moreover, if the Grade of Service (GoS) constraints are not hard requirements, the network design resulting from the set of prices is on the Pareto frontier of a bi-objective optimization problem. A scheme was developed to derive the prices for various classes of customers by referring to the Lagrange multipliers.
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