  A basic model of a dynamical distribution network is considered, modeled as a
directed graph with storage variables corresponding to every vertex and flow
inputs corresponding to every edge, subject to unknown but constant inflows and
outflows. We analyze the dynamics of the system in closed-loop with a
distributed proportional-integral controller structure, where the flow inputs
are constrained to take value in closed intervals. Results from our previous
work are extended to general flow constraint intervals, and conditions for
asymptotic load balancing are derived that rely on the structure of the graph
and its flow constraints.
