skip to main content
research-article

Product form stationary distributions for diffusion approximations to a flow-level model operating under a proportional fair sharing policy

Authors Info & Claims
Published:01 September 2007Publication History
Skip Abstract Section

Abstract

We consider a flow-level model of Internet congestion control introduced by Massoulié and Roberts [2]. We assume that bandwidth is shared amongst elastic documents according to a weighted proportional fair bandwidth sharing policy. With Poisson arrivals and exponentially distributed document sizes, we focus on the heavy traffic regime in which the average load placed on each resource is approximately equal to its capacity. In [1], under a mild local traffic condition, we establish a diffusion approximation for the workload process (and hence for the flow count process) in this model. We first recall that result in this paper. We then state results showing that when all of the weights are equal (proportional fair sharing) the diffusion has a product form invariant distribution with a strikingly simple interpretation in terms of dual random variables, one for each of the resources of the network. This result can be extended to the case where document sizes are distributed as finite mixtures of exponentials, and to models that include multi-path routing (these extensions are not described here, but can be found in [1]).

References

  1. Kang, W. N., Kelly, F. P., Lee, N. H. and Williams, R. J. (2007). State space collapse and diffusion approximation for a network operating under a fair bandwidth sharing policy, preprint.Google ScholarGoogle Scholar
  2. Massoulié, L. and Roberts, J. (2000). Bandwidth sharing and admission control for elastic traffic. Telecommunication Systems, 15 185--201.Google ScholarGoogle ScholarDigital LibraryDigital Library
  3. Williams, R. J. (1998). An invariance principle for semimartingale reflecting Brownian motions in an orthant. Queueing Systems, 30 5--25. Google ScholarGoogle ScholarDigital LibraryDigital Library

Index Terms

  1. Product form stationary distributions for diffusion approximations to a flow-level model operating under a proportional fair sharing policy

              Recommendations

              Comments

              Login options

              Check if you have access through your login credentials or your institution to get full access on this article.

              Sign in

              Full Access

              • Published in

                cover image ACM SIGMETRICS Performance Evaluation Review
                ACM SIGMETRICS Performance Evaluation Review  Volume 35, Issue 2
                September 2007
                50 pages
                ISSN:0163-5999
                DOI:10.1145/1330555
                Issue’s Table of Contents

                Copyright © 2007 Authors

                Publisher

                Association for Computing Machinery

                New York, NY, United States

                Publication History

                • Published: 1 September 2007

                Check for updates

                Qualifiers

                • research-article

              PDF Format

              View or Download as a PDF file.

              PDF

              eReader

              View online with eReader.

              eReader
              About Cookies On This Site

              We use cookies to ensure that we give you the best experience on our website.

              Learn more

              Got it!