Before revision:  Specifically, in the case of Bernoulli arrivals ,  we show that the heavy-traffic scaled queue length is \left({2n}}\right)\left( n-3{2}+1{2n} . Our result implies that the MaxWeight algorithm has optimal queue-length scaling behavior in the \right) heavy-traffic regime with respect to the size of a switch with a uniform traffic pattern. This settles the heavy-traffic version of an open conjecture  .
After revision:  Specifically, in the case of Bernoulli arrivals , we show that the heavy-traffic scaled queue length is \left({2n}}\right)\left( n-3{2}+1{2n} . Our result implies that the MaxWeight algorithm has optimal queue-length scaling behavior in the \right) heavy-traffic regime with respect to n, thus settling one version of an open conjecture .