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The authors studied a class of Service Overlay Network (SON) capacity allocation problem with Grade of Service (GoS) constraints. The problem can be 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. They use a set of Lagrange multipliers to investigate the general conditions for the MP formulation to be equivalent to the MC formulation. The set of multipliers can also be shown to act as a set of thresholds for user service charges so that the SON operator will be happy to provide adequate service level even if he/she is not obligated to do so.
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