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In this paper, we characterize the network stability region (capacity region)of multi-queue multi-server (MQMS) queueing systems with stationary channeldistribution and stationary arrival processes. The stability region isspecified by a finite set of linear inequalities. We first show that thestability region is a polytope characterized by the finite set of its facetdefining hyperplanes. We explicitly determine the coefficients of the linearinequalities describing the facet defining hyperplanes of the stability regionpolytope. We further derive the necessary and sufficient conditions for thestability of the system for general arrival processes with finite first andsecond moments. For the case of stationary arrival processes, the derivedconditions characterize the system stability region. Furthermore, we obtain anupper bound for the average queueing delay of Maximum Weight (MW) serverallocation policy which has been shown in the literature to be a throughputoptimal policy for MQMS systems. Using a similar approach, we can characterizethe stability region for a fluid model MQMS system. However, the stabilityregion of the fluid model system is described by an infinite number of linearinequalities since in this case the stability region is a convex surface. Wepresent an example where we show that in some cases depending on the channeldistribution, the stability region can be characterized by a finite set ofnon-linear inequalities instead of an infinite number of linear inequalities.

Explicit Characterization of Stability Region for Stationary Multi-Queue Multi-Server Systems