  This paper considers a parallel system of queues fed by independent arrival
streams, where the service rate of each queue depends on the number of
customers in all of the queues. Necessary and sufficient conditions for the
stability of the system are derived, based on stochastic monotonicity and
marginal drift properties of multiclass birth and death processes. These
conditions yield a sharp characterization of stability for systems, where the
service rate of each queue is decreasing in the number of customers in other
queues, and has uniform limits as the queue lengths tend to infinity. The
results are illustrated with applications where the stability region may be
nonconvex.
