We consider the problem of link capacity dimensioning and bandwidth allocation in networks that support elastic flows and maintain proportional fairness among these flows. We assume that a certain allocated bandwidth to a user demand generates revenue for the network operator. On the other hand, the operator incurs a capacity dependent cost for each link in the network. The operator's profit is the difference between the revenue and the total link cost. Under this assumption, the problem is to determine the bandwidth of the flows and the link capacities such that the profit is maximized. We first show that under fairly general assumptions, the optimum allocation of flows leads to selecting the lowest cost paths between originator-destination pairs. We also derive explicit formulae for the bandwidth allocated to these flows. We distinguish the case when the operator's capacity budget is fixed ("equality budget constraint", in which case the profit is maximized when the revenue is maximized) and the case when the budget is upper-bounded ("inequality budget constraint", in which case the profit can - in general - be maximized by using some portion of the capacity budget). Finally, we show numerical examples to highlight some of the trade-offs between profit maximization, revenue maximization and fairness.
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