  We consider an input queued switch operating under the MaxWeight scheduling
algorithm. This system is interesting to study because it is a model for
Internet routers and data center networks. Recently, it was shown that the
MaxWeight algorithm has optimal heavy-traffic queue length scaling when all
ports are uniformly saturated. Here we consider the case when an arbitrary
number of ports are saturated (which we call the incompletely saturated case),
and each port is allowed to saturate at a different rate. We use a recently
developed drift technique to show that the heavy-traffic queue length under the
MaxWeight scheduling algorithm has optimal scaling with respect to the switch
size even in these cases.
