ABSTRACT

We address the issue of stability for multi-class, non-acyclic, and
stochastic  queueing networks.  This has been an  exciting problem,
addressed by  the research  community  in over a decade,  where the
nature of the traffic  intensity condition  as being sufficient for
such  networks  to be  stable has  been debated  and questioned. We
argue that the concept of stability ought to be replaced by that of
stabilizability  and  that  this   property  is  intrinsic  to  the
network's topology. Under this  more generic setting, and resorting
to idling policies, we provide a distributed supervisory controller
that is able to  stabilize a large set  of networks, provided  that
the traffic intensity condition holds. Seidman's  example, [12], is
used to demonstrate such property.