Stochastic stability under fair bandwidth allocation: General file size distribution

Mung Chiang, Devavrat Shah, Ao Tang

Research output: Chapter in Book/Report/Conference proceedingConference contribution

10 Scopus citations

Abstract

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 ε (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.We obtain our results by developing an appropriate Lyapunov function for the fluid model of Gromoll and Williams (2006)1.

Original languageEnglish (US)
Title of host publication44th Annual Allerton Conference on Communication, Control, and Computing 2006
PublisherUniversity of Illinois at Urbana-Champaign, Coordinated Science Laboratory and Department of Computer and Electrical Engineering
Pages899-908
Number of pages10
ISBN (Electronic)9781604237924
StatePublished - Jan 1 2006
Event44th Annual Allerton Conference on Communication, Control, and Computing 2006 - Monticello, United States
Duration: Sep 27 2006Sep 29 2006

Publication series

Name44th Annual Allerton Conference on Communication, Control, and Computing 2006
Volume2

Other

Other44th Annual Allerton Conference on Communication, Control, and Computing 2006
CountryUnited States
CityMonticello
Period9/27/069/29/06

All Science Journal Classification (ASJC) codes

  • Computer Science Applications
  • Computer Networks and Communications

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    Chiang, M., Shah, D., & Tang, A. (2006). Stochastic stability under fair bandwidth allocation: General file size distribution. In 44th Annual Allerton Conference on Communication, Control, and Computing 2006 (pp. 899-908). (44th Annual Allerton Conference on Communication, Control, and Computing 2006; Vol. 2). University of Illinois at Urbana-Champaign, Coordinated Science Laboratory and Department of Computer and Electrical Engineering.