  The Foster-Lyapunov theorem and its variants serve as the primary tools for
studying the stability of queueing systems. In addition, it is well known that
setting the drift of the Lyapunov function equal to zero in steady-state
provides bounds on the expected queue lengths. However, such bounds are often
very loose due to the fact that they fail to capture resource pooling effects.
The main contribution of this paper is to show that the approach of "setting
the drift of a Lyapunov function equal to zero" can be used to obtain bounds on
the steady-state queue lengths which are tight in the heavy-traffic limit. The
key is to establish an appropriate notion of state-space collapse in terms of
steady-state moments of weighted queue length differences, and use this
state-space collapse result when setting the Lyapunov drift equal to zero. As
an application of the methodology, we prove the steady-state equivalent of the
heavy-traffic optimality result of Stolyar for wireless networks operating
under the MaxWeight scheduling policy.
