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• W2018654380 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." @default.
• W2018654380 created "2016-06-24" @default.
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• W2018654380 date "2009-10-01" @default.
• W2018654380 modified "2023-10-18" @default.
• W2018654380 title "State space collapse and diffusion approximation for a network operating under a fair bandwidth sharing policy" @default.
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• W2018654380 doi "https://doi.org/10.1214/08-aap591" @default.
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