Stochastic stability under network utility maximization: General file size distribution

M. Chiang, D. Shah, A. Tang
Proceedings of 44th Allerton Conference on Communication, Control and Computing

We prove the stochastic stability of resource allocation under Network Utility Maximization (NUM) under general arrival process and file size distribution with bounded support, for α-fair utilities with α sufficiently small and possibly different for different sources’ utility functions. In addition, our results imply that the system operating under α-fair utility is 1/(1 + α)-approximate stable for any α ∈ (0,∞) for any file size distribution with bounded support. Our results are in contrast to the recent stability result of Bramson (2005) for max-min fair (i.e. α = ∞) under general arrival process and file size distribution, and that of Massoulie (2006) for proportional fair (i.e. α = 1) under Poisson arrival process and phase-type distributions. To obtain our results, we develop an appropriate Lyapunov function for the fluid model established by Gromoll and Williams (2006)1 .