  The drift method was recently developed to study queueing systems in
steady-state. It was successfully used to obtain bounds on the moments of the
scaled queue lengths, that are asymptotically tight in heavy-traffic, in a wide
variety of systems including generalized switches, input-queued switches,
bandwidth sharing networks, etc. In this paper we develop the use of transform
techniques for heavy-traffic analysis, with a special focus on the use of
moment generating functions. This approach simplifies the proofs of the drift
method, and provides a new perspective on the drift method. We present a
general framework and then use the MGF method to obtain the stationary
distribution of queue lengths in heavy-traffic in queueing systems that satisfy
the Complete Resource Pooling condition. In particular, we study load balancing
systems and generalized switches under general settings.
