Before revision:  We use a Lyapunov-type drift technique to characterize the heavy-traffic behavior of the expectation of the sum queue lengths in steady-state . 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:  We use a Lyapunov-type drift technique to characterize the heavy-traffic behavior of the expectation of the sum queue lengths in steady-state , 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.