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The authors studied a class of Service Overlay Network (SON) capacity allocation problem with Grade of Service (GoS) constraints. Similar problems in the literature are typically formulated as either a Maximum Profit (MP) optimization problem or a Minimum Cost (MC) optimization problem. In this paper, the authors investigate the relationship between the MP and MC formulations. When the service charges are zero, the MP and MC formulations are obviously equivalent. By using the set of Lagrange multipliers from the MC formulation as a tool, they investigate the extent that this equivalence holds with respect to the service charges.
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