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

Weina Wang (), Siva Theja Maguluri (), R. Srikant () and Lei Ying ()
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Weina Wang: Computer Science Department, Carnegie Mellon University, Pittsburgh, Pennsylvania 15213
Siva Theja Maguluri: H. Milton Stewart School of Industrial & Systems Engineering, Georgia Institute of Technology, Atlanta, Georgia 30332
R. Srikant: Department of Electrical and Computer Engineering & Coordinated Science Lab, University of Illinois at Urbana-Champaign, Urbana, Illinois 61801
Lei Ying: Electrical Engineering and Computer Science Department, University of Michigan, Ann Arbor, Michigan 48109

Mathematics of Operations Research, 2022, vol. 47, issue 4, 2691-2720

Abstract: 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 .

Keywords: Primary: 93E20; 60K35; secondary: 60H30; bandwidth sharing; weighted proportionally fair sharing; heavy-traffic analysis; drift method; state-space collapse; phase-type distributions (search for similar items in EconPapers)
Date: 2022
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Persistent link: https://EconPapers.repec.org/RePEc:inm:ormoor:v:47:y:2022:i:4:p:2691-2720

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