We consider a stochastic fluid network with inputs which are
independent subordinators. We show that under some natural conditions the
distribution of the fluid content process converges in total variation to a
proper limit and that the limiting distribution has a positive mass at the
origin. As a consequence of the methodology used, we obtain upper and lower
bounds for the expected values of this limiting distribution. For the
two-dimensional case, under certain conditions, explicit formulas for the
means, variances and covariance of the steady-state fluid content are given.
Further, for the two-dimensional case, it is shown that, other than for trivial
setups, the limiting distribution cannot have product form.