  The model is a "generalized switch", serving multiple traffic flows in
discrete time. The switch uses MaxWeight algorithm to make a service decision
(scheduling choice) at each time step, which determines the probability
distribution of the amount of service that will be provided. We are primarily
motivated by the following question: in the heavy traffic regime, when the
switch load approaches critical level, will the service processes provided to
each flow remain "smooth" (i.e., without large gaps in service)? Addressing
this question reduces to the analysis of the asymptotic behavior of the
unscaled queue-differential process in heavy traffic. We prove that the
stationary regime of this process converges to that of a positive recurrent
Markov chain, whose structure we explicitly describe. This in turn implies
asymptotic "smoothness" of the service processes.
