Fluid model for a network operating under a fair bandwidth-sharing policy.

DOI10.1214/105051604000000224zbMath1066.60093arXivmath/0407057OpenAlexW2106896172MaRDI QIDQ1879902

F. P. Kelly, Ruth J. Williams

Publication date: 15 September 2004

Published in: The Annals of Applied Probability (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/math/0407057

zbMATH Keywords

invariant manifoldfluid limitexponential networkBrownian modelfair resource sharing

Mathematics Subject Classification ID

Stochastic network models in operations research (90B15) Queueing theory (aspects of probability theory) (60K25) Applications of queueing theory (congestion, allocation, storage, traffic, etc.) (60K30)

Related Items (28)

Bandwidth-sharing networks under a diffusion scaling ⋮ Asymptotic behavior of a critical fluid model for bandwidth sharing with general file size distributions ⋮ A stability conjecture on bandwidth sharing networks ⋮ Log-weight scheduling in switched networks ⋮ Designs of optimal switching feedback decentralized control policies for fluid queueing networks ⋮ Monotonicity properties for multi-class queueing systems ⋮ Switched networks with maximum weight policies: fluid approximation and multiplicative state space collapse ⋮ Stability of a Subcritical Fluid Model for Fair Bandwidth Sharing with General File Size Distributions ⋮ Qualitative properties of \(\alpha\)-fair policies in bandwidth-sharing networks ⋮ Resource sharing networks: Overview and an open problem ⋮ Fluid models of congestion collapse in overloaded switched networks ⋮ Structural properties of proportional fairness: stability and insensitivity ⋮ The heavy traffic limit of an unbalanced generalized processor sharing model ⋮ A queueing analysis of max-min fairness, proportional fairness and balanced fairness ⋮ Fluid models of integrated traffic and multipath routing ⋮ Resource pooling in congested networks: Proportional fairness and product form ⋮ State space collapse and diffusion approximation for a network operating under a fair bandwidth sharing policy ⋮ Stability of Processor Sharing Networks with Simultaneous Resource Requirements ⋮ Decentralized Proportional Load Balancing ⋮ Fluid limits for networks with bandwidth sharing and general document size distributions ⋮ Concave switching in single-hop and multihop networks ⋮ Diffusion Limit of Fair Resource Control—Stationarity and Interchange of Limits ⋮ Flow level convergence and insensitivity for multi-class queueing networks ⋮ Fluid Limits for Bandwidth-Sharing Networks with Rate Constraints ⋮ Proportional fairness and its relationship with multi-class queueing networks ⋮ Interacting multi-class transmissions in large stochastic networks ⋮ Improved queue-size scaling for input-queued switches via graph factorization ⋮ Minimal and Locally Edge Minimal Fluid Models for Resource-Sharing Networks

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Diffusion approximations for open multiclass queueing networks: Sufficient conditions involving state space collapse
• State space collapse with application to heavy traffic limits for multiclass queueing networks
• Convergence to equilibria for fluid models of head-of-the-line proportional processor sharing queueing networks
• A broader view of Brownian networks
• Brownian models of open processing networks: Canonical representation of workload.
• Bandwidth sharing and admission control for elastic traffic
• Heavy traffic limits for some queueing networks
• Convergence to equilibria for fluid models of FIFO queueing networks
• An approach to service level agreements for IP networks with differentiated services

This page was built for publication: Fluid model for a network operating under a fair bandwidth-sharing policy.