  In this paper, we present a condition to obtain instability for a class of
queueing networks where the arrival rates in each server are constant and the
departure rate in each server is a decreasing function of the queue lengths of
other servers. Under a stronger assumption, that the departure rates are
proportional to the queue length in each server, we obtain a characterization
of the stability region through a system of equations. We start by defining the
mathematical model and the queueing discipline we will study. We then obtain
irreducibility and monotonicity for the dynamics, which allow us to state our
two main results. We then use this result to obtain instability conditions for
two queueing networks for which stability is known: a medium access algorithm
and an interference queueing network.
