Fluid limits for networks with bandwidth sharing and general document size distributions

H.C. Gromoll, R.J. Williams

Research output: Book/ReportReportAcademic

Abstract

We consider a stochastic model of Internet congestion control, introduced by Massoulie and Roberts [18], that represents the randomly varying number of flows in a network where bandwidth is shared amongst document transfers. In contrast to an earlier work by Kelly and Williams [12], the present paper allows inter arrival times and document sizes to be generally distributed, rather than exponentially distributed. Furthermore, we allow a fairly general class of bandwidth sharing policies that includes the weighted a-fair policies of Mo and Walrand [20], as well as certain other utility based scheduling policies. To describe the evolution of the system, measure valued processes are used to keep track of the residual document sizes of all flows through the network. We propose a uid model (or formal functional law of large numbers approximation) associated with the stochastic flow level model. Under mild conditions, we show that the appropriately rescaled measure valued processes corresponding to a sequence of such models (with fixed network structure) are tight, and that any weak limit point of the sequence is almost surely a fluid model solution. For the special case of weighted a-fair policies, we also characterize the invariant states of the fluid model.
Original languageEnglish
Place of PublicationEindhoven
PublisherEurandom
Number of pages46
Publication statusPublished - 2008

Publication series

NameReport Eurandom
Volume2008005
ISSN (Print)1389-2355

Fingerprint

Fluid Limits
Measure-valued Process
Sharing
Bandwidth
Fluid Model
Stochastic Flow
Weak Limit
Scheduling Policy
Law of large numbers
Arrival Time
Congestion Control
Limit Point
Network Structure
Stochastic Model
Model
Invariant
Approximation
Policy

Cite this

Gromoll, H. C., & Williams, R. J. (2008). Fluid limits for networks with bandwidth sharing and general document size distributions. (Report Eurandom; Vol. 2008005). Eindhoven: Eurandom.
Gromoll, H.C. ; Williams, R.J. / Fluid limits for networks with bandwidth sharing and general document size distributions. Eindhoven : Eurandom, 2008. 46 p. (Report Eurandom).
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Gromoll, HC & Williams, RJ 2008, Fluid limits for networks with bandwidth sharing and general document size distributions. Report Eurandom, vol. 2008005, Eurandom, Eindhoven.

Fluid limits for networks with bandwidth sharing and general document size distributions. / Gromoll, H.C.; Williams, R.J.

Eindhoven : Eurandom, 2008. 46 p. (Report Eurandom; Vol. 2008005).

Research output: Book/ReportReportAcademic

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Gromoll HC, Williams RJ. Fluid limits for networks with bandwidth sharing and general document size distributions. Eindhoven: Eurandom, 2008. 46 p. (Report Eurandom).