TY - JOUR
T1 - Heavy-Traffic Insensitive Bounds for Weighted Proportionally Fair Bandwidth Sharing Policies
AU - Wang, Weina
AU - Maguluri, Siva Theja
AU - Srikant, R.
AU - Ying, Lei
N1 - Funding Information:
Funding: This work was supported by the National Science Foundation, the Division of Computer and Network Systems [Grant CNS-2007733], the Division of Electrical, Communications and Cyber Sys-tems [Grants CIF-1409106, CMMI-1562276, ECCS-1609202, ECCS-1609370, ECCS-1739189, and ECCS-1739344], the Division of Computing and Communication Foundations [Grant CCF-1850439], the Office of Naval Research [Grant N00014-15-1-2169], and the Army Research Office [Grant W911NF-16-1-0259].
Publisher Copyright:
Copyright: © 2022 INFORMS.
PY - 2022/11
Y1 - 2022/11
N2 - 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.
AB - 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.
KW - bandwidth sharing
KW - drift method
KW - heavy-traffic analysis
KW - phase-type distributions
KW - state-space collapse
KW - weighted proportionally fair sharing
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U2 - 10.1287/moor.2021.1225
DO - 10.1287/moor.2021.1225
M3 - Article
AN - SCOPUS:85152147196
SN - 0364-765X
VL - 47
SP - 2691
EP - 2720
JO - Mathematics of Operations Research
JF - Mathematics of Operations Research
IS - 4
ER -