Capacity Allocation in Service Overlay Networks - Maximum Profit vs Minimum Cost Formulations

We 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 article we 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, we investigate the extent that this equivalence holds with respect to the service charges. The same set of multipliers also acts as thresholds for 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. A key contribution of this paper is the provision of insight into the solution nature of the MP and the MC formulations under different service charge parameters, thereby giving guidelines to the proper formulation should be chosen. The second contribution is the use of the Lagrange multipliers in providing pricing information to the network operators.