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.
After revision:  Specifically, in the case of Bernoulli arrivals , under the assumption that all ports are saturated and all queues receive non-zero traffic. Under these conditions, 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.