We consider a switch with uniform traffic operating under the MaxWeight scheduling algorithm. This traffic pattern is interesting to study in the heavy-traffic regime since the queue lengths exhibit a multi-dimensional state-space collapse. 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 n − . Our result implies that the MaxWeight algorithm has optimal queue-length scaling behavior in the 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.
In a recent development, the case where all ports are uniformly saturated (thus, leading to the more difficult case of multi-dimensional state-space collapse) was studied in REF , where an exact expression for the heavy-traffic scaled queue length under the MaxWeight algorithm is derived.
Heavy-Traffic Behavior of the MaxWeight Algorithm in a Switch with Uniform Traffic
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Computer Science Mathematics