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