Asymptotic Properties of Proportional-Fair Sharing Algorithms

Results are presented for the Proportional Fair Scheduler (PF) scheduler of the CDMA 2000 1X-EVDO system (also known as HDR) as well as related algorithms. The PF scheduler uses exponentially smoothed sums of mobile assigned rates to make scheduling decisions. As the smoothing factor approaches 0, the sample paths of these sums converge to the solution of an ordinary differential equation (ODE). For stationary channels, we show the ODE has a unique equilibrium and that it is characterized as optimizing a concave utility function (sum of logs). Explicit formulas for this equilibrium can be used to derive performance results for the PF scheduler such as transmission delay.