Stability Analysis of a Second - Order Proportionally - Fair Rate Allocation Algorithm

In this paper, a delay-difference second-order proportionally-fair rate allocation algorithm has been proposed. As conventional proportionally-fair rate allocation algorithms deploy some form of scaled gradient ascent iterative algorithm for converging to user optimal rates, using fast second-order algorithms, such as Jacobi or approximate Newton methods, can be considered as natural and good candidates for increasing the convergence speed of the rate allocation algorithms. Stability analysis, related to scaled gradient ascent algorithms, in the presence of propagation delays, has been performed by some researchers, such as R. Johari et al., in Cambridge. In the current paper, the stability conditions of a second-order Jacobi method in the presence of propagation delays, with the simplifying premise of equality between all the users'' propagation delays, is derived mathematically. Simulation results show that even in the general case of different propagation delays, stability is maintained.