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]).
- 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 Scholar
- Massoulié, L. and Roberts, J. (2000). Bandwidth sharing and admission control for elastic traffic. Telecommunication Systems, 15 185--201.Google Scholar
Digital Library
- Williams, R. J. (1998). An invariance principle for semimartingale reflecting Brownian motions in an orthant. Queueing Systems, 30 5--25. Google Scholar
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Index Terms
Product form stationary distributions for diffusion approximations to a flow-level model operating under a proportional fair sharing policy
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