Proportional fairness: more secrets revealed.

In this paper, the resource allocation problem in a general network configuration is addressed. In particular, we will present a distributed solution algorithm in one the hand, followed by the exact set of equations that solves for ( p,1)-proportionally fair allocation in an attempt to express the network optimal rates in a closed form on the other hand. First, the problem is presented as an optimization model that maximizes the social utility of the network. A duality approach is used to solve the network model in a timely synchronized iterative manner. Next, the exact analytical variant of the model is presented showing its equivalence to the numerical solution. The analytical model relies on the pattern of bottlenecks inside the network, which can be found using a weighted progressive filling. Such a pattern will help in finding the exact analytical set of equations that solves for proportionally fair rates for any network configuration. Closed-form solutions are now computed for different networks including well-known configurations such as linear, grid, and cyclic networks. Different simulation experiments are conducted along with the solution of standard optimization solvers. The results of the simulation, the solvers, and the analytical solutions coincide and present the same allocation. Copyright © 2015 John Wiley & Sons, Ltd. [ABSTRACT FROM AUTHOR]