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State space collapse and diffusion approximation for a network operating under a fair bandwidth sharing policy | | W. N. Kang
; F. P. Kelly
; N. H. Lee
; R. J. Williams
; | | Date: |
20 Oct 2009 | | Abstract: | We consider a connection-level model of Internet congestion control,
introduced by Massouli’{e} and Roberts [Telecommunication Systems 15 (2000)
185--201], that represents the randomly varying number of flows present in a
network. Here, bandwidth is shared fairly among elastic document transfers
according to a weighted $alpha$-fair bandwidth sharing policy introduced by Mo
and Walrand [IEEE/ACM Transactions on Networking 8 (2000) 556--567] [$alphain
(0,infty)$]. Assuming 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. A fluid model (or
functional law of large numbers approximation) for this stochastic model was
derived and analyzed in a prior work [Ann. Appl. Probab. 14 (2004) 1055--1083]
by two of the authors. Here, we use the long-time behavior of the solutions of
the fluid model established in that paper to derive a property called
multiplicative state space collapse, which, loosely speaking, shows that in
diffusion scale, the flow count process for the stochastic model can be
approximately recovered as a continuous lifting of the workload process. | | Source: | arXiv, 0910.3821 | | Services: | Forum | Review | PDF | Favorites | |
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