Heavy-Traffic Insensitive Bounds for Weighted Proportionally Fair Bandwidth Sharing Policies

Weina Wang, Siva Theja Maguluri, R. Srikant, Lei Ying

Research output: Contribution to journalArticlepeer-review


We consider a connection-level model proposed by Massoulié and Roberts for bandwidth sharing among file transfer flows in a communication network. We study weighted proportionally fair sharing policies and establish explicit-form bounds on the weighted sum of the expected numbers of flows on different routes in heavy traffic. The bounds are linear in the number of critically loaded links in the network, and they hold for a class of phase-type file-size distributions; that is, the bounds are heavy-traffic insensitive to the distributions in this class. Our approach is Lyapunov drift based, which is different from the widely used diffusion approximation approach. A key technique we develop is to construct a novel inner product in the state space, which then allows us to obtain a multiplicative type of state-space collapse in steady state. Furthermore, this state-space collapse result implies the interchange of limits as a byproduct for the diffusion approximation of the unweighted proportionally fair sharing policy under phase-type file-size distributions, demonstrating the heavy-traffic insensitivity of the stationary distribution.

Original languageEnglish (US)
Pages (from-to)2691-2720
Number of pages30
JournalMathematics of Operations Research
Issue number4
StatePublished - Nov 2022


  • bandwidth sharing
  • drift method
  • heavy-traffic analysis
  • phase-type distributions
  • state-space collapse
  • weighted proportionally fair sharing

ASJC Scopus subject areas

  • Mathematics(all)
  • Computer Science Applications
  • Management Science and Operations Research


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