Before revision:  This settles the heavy-traffic version of an open conjecture  .
After revision:  This settles the heavy-traffic version of an open conjecture ; in fact, it is shown that the heavy-traffic queue length is at most within a factor of two from the optimal. We then consider certain asymptotic regimes where the load of the system scales simultaneously with the number of ports. We show that the MaxWeight algorithm has optimal queue length scaling behavior provided that the arrival rate approaches capacity sufficiently fast .