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Title

Network stability under alpha fair bandwidth allocation with general file size distribution

Author(s)

Paganini, Fernando;  Tang, Ao;  Ferragut, Andres;  Andrew, Lachlan L. H.

Abstract

Rate allocation among a fixed set of end-to-end connections in the Internet is carried out by congestion control, which has a well established model: it optimizes a concave network utility, a particular case of which is the alpha-fair bandwidth allocation. This paper studies the slower dynamics of connections themselves, that arrive randomly in the network and are served at the allocated rate. It has been shown that under the condition that the mean offered load at each link is less than its capacity, the resulting queueing system is stochastically stable, for the case of exponentially distributed file-sizes. The conjecture that the result holds for general file-size distributions has remained open, and is very relevant since heavy-tailed distributions are often the best models of Internet file sizes. In this paper, building on existing fluid models of the system, we use a partial differential equation to characterize the dynamics. The equation keeps track of residual file size and therefore is suitable for general file size distributions. For alpha fair bandwidth allocation, with any positive alpha parameter, a Lyapunov function is constructed with negative drift when the offered load is less than capacity. With this tool we answer the conjecture affirmatively in the fluid sense: we prove asymptotic convergence to zero of the fluid model for general file-size distributions of finite mean, and finite-time convergence for those of finite p>1 moment. In the stochastic sense, we build on recent work that relates fluid and stochastic stability subject to a certain light-tailed restriction. We further provide the supplementary fluid stability argument to establish the conjecture for this class that includes phase-type distributions. Results are supplemented by illustrative network simulations at the packet level.

Publication type

Journal article

Research centre

Swinburne University of Technology

Source

IEEE Transactions on Automatic Control, Vol. 57, no. 3 (Mar 2012), pp. 579-591

Publication year

2012

FOR Code(s)

0102 Applied Mathematics;  0906 Electrical and Electronic Engineering;  0913 Mechanical Engineering

Keyword(s)

Computer networks;  Lyapunov method;  Partial differential equations;  Stochastic processes

Publisher

IEEE

ISSN

0018-9286

Publisher URL

http://dx.doi.org/10.1109/tac.2011.2160013

Copyright

Copyright © 2011 IEEE. The accepted manuscript is reproduced in accordance with the copyright policy of the publisher. Personal use of this material is permitted. However, permission to reprint/republish this material for advertising or promotional purposes or for creating new collective works for resale or redistribution to servers or lists, or to reuse any copyrighted component of this work in other works must be obtained from the IEEE.

Research Projects

Efficient and fair traffic control for a multi-service internet, Australian Research Council grant number DP0985322
Increasing internet energy and cost efficiency by improving higher-layer protocols, Australian Research Council grant number FT0991594

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