Maximum Profit VS Minimum Cost in Service Overlay Network Design
Dziong, Zbigniew, Lam, Ngok, Mason, Lorne G. · Rare & Special e-Zone (The Hong Kong University of Science and Technology) · 2009
We 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 article we investigate the relationship between the MP and MC formulations. We 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. The 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 the network designers may consider.