  In this paper, we characterize the network stability region (capacity region)
of multi-queue multi-server (MQMS) queueing systems with stationary channel
distribution and stationary arrival processes. The stability region is
specified by a finite set of linear inequalities. We first show that the
stability region is a polytope characterized by the finite set of its facet
defining hyperplanes. We explicitly determine the coefficients of the linear
inequalities describing the facet defining hyperplanes of the stability region
polytope. We further derive the necessary and sufficient conditions for the
stability of the system for general arrival processes with finite first and
second moments. For the case of stationary arrival processes, the derived
conditions characterize the system stability region. Furthermore, we obtain an
upper bound for the average queueing delay of Maximum Weight (MW) server
allocation policy which has been shown in the literature to be a throughput
optimal policy for MQMS systems. Using a similar approach, we can characterize
the stability region for a fluid model MQMS system. However, the stability
region of the fluid model system is described by an infinite number of linear
inequalities since in this case the stability region is a convex surface. We
present an example where we show that in some cases depending on the channel
distribution, the stability region can be characterized by a finite set of
non-linear inequalities instead of an infinite number of linear inequalities.
