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The model is a "generalized switch", serving multiple traffic flows indiscrete time. The switch uses MaxWeight algorithm to make a service decision(scheduling choice) at each time step, which determines the probabilitydistribution of the amount of service that will be provided. We are primarilymotivated by the following question: in the heavy traffic regime, when theswitch load approaches critical level, will the service processes provided toeach flow remain "smooth" (i.e., without large gaps in service)? Addressingthis question reduces to the analysis of the asymptotic behavior of theunscaled queue-differential process in heavy traffic. We prove that thestationary regime of this process converges to that of a positive recurrentMarkov chain, whose structure we explicitly describe. This in turn impliesasymptotic "smoothness" of the service processes.

MaxWeight Scheduling: Asymptotic Behavior of Unscaled Queue-Differentials in Heavy Traffic