A Proportionally-Fair Algorithm for Loss-Free Rate Allocation to Elastic Users

Proportional fairness criterion, first proposed by Kelly, has outstanding properties in allocating fair rates to network users. For example, it resembles the Jacobson’s AIMD method in rate allocation to users, and there exists a well-established stability analysis relating to the stability of the rate allocation algorithm. Kelly’s algorithm uses a form of the scaled gradient ascent projection method for converging to the equilibrium point. The structure of Kelly’s algorithm is such that in some instants of time, the aggregate flow which is passing through a link may exceed the link capacity. In other words, the algorithm is not loss-free. In this paper, we have proposed a novel time-varying scaled gradient ascent projection method that, under some assumptions about the link penalty function, the rate allocation algorithm is loss-free in some network topologies. Also, it is shown by simulation that in a general network topology, the proposed algorithm does not have any loss event in comparison with the Kelly’s method.