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In this paper, flow models of networks without congestion control areconsidered. Users generate data transfers according to some Poisson processesand transmit corresponding packet at a fixed rate equal to their access rateuntil the entire document is received at the destination; some erasure codesare used to make the transmission robust to packet losses. We study thestability of the stochastic process representing the number of active flows intwo particular cases: linear networks and upstream trees. For the case oflinear networks, we notably use fluid limits and an interesting phenomenon of"time scale separation" occurs. Bounds on the stability region of linearnetworks are given. For the case of upstream trees, underlying monotonicproperties are used. Finally, the asymptotic stability of those processes isanalyzed when the access rate of the users decreases to 0. An appropriatescaling is introduced and used to prove that the stability region of thosenetworks is asymptotically maximized.

On the flow-level stability of data networks without congestion control: the case of linear networks and upstream trees