This article proves that the stability region of a two-station,
five-class reentrant queueing network, operating under a
nonpreemptive static buffer priority service policy, depends on
the distributions of the interarrival and service times. In
particular, our result shows that conditions on the mean
interarrival and service times are not enough to determine the
stability of a queueing network under a particular policy. We
prove that when all distributions are exponential, the network is
unstable in the sense that, with probability 1, the total number
of jobs in the network goes to infinity with time. We show that
the same network with all interarrival and service times being
deterministic is stable. When all distributions are uniform with a
given range, our simulation studies show that the stability of the
network depends on the width of the uniform distribution. Finally,
we show that the same network, with deterministic interarrival and
service times, is unstable when it is operated under the
preemptive version of the static buffer priority service
policy. Thus, our examples also demonstrate that the stability
region depends on the preemption mechanism used.