Solving dimensioning tasks for proportionally fair networks carrying elastic traffic

The paper studies optimal dimensioning problems associated with the notion of “proportional fairness” (PF) considered for packet networks carrying elastic (greedy) traffic, i.e. the traffic streams that can use up, perhaps within certain assumed bounds, any bandwidth that is assigned to them. We give effective, simple and explicit solutions to the introduced optimisation tasks based on the dual optimisation theory, and illustrate them with numerical examples. The explicit solutions can guide a network operator how to proceed when introducing PF into his network.