  We consider a system of processor-sharing queues with state-dependent service
rates. These are allocated according to balanced fairness within a polymatroid
capacity set. Balanced fairness is known to be both insensitive and
Pareto-efficient in such systems, which ensures that the performance metrics,
when computable, will provide robust insights into the real performance of the
system considered. We first show that these performance metrics can be
evaluated with a complexity that is polynomial in the system size if the system
is partitioned into a finite number of parts, so that queues are exchangeable
within each part and asymmetric across different parts. This in turn allows us
to derive stochastic bounds for a larger class of systems which satisfy less
restrictive symmetry assumptions. These results are applied to practical
examples of tree data networks, such as backhaul networks of Internet service
providers, and computer clusters.
