  In this paper, we consider queueing systems where the dynamics are
non-stationary and state-dependent. For performance analysis of these systems,
fluid and diffusion models have been typically used. Although they are proven
to be asymptotically exact, their effectiveness as approximations in the
non-asymptotic regime needs to be investigated. We find that existing fluid and
diffusion approximations might be either inaccurate under simplifying
assumptions or computationally intractable. To address this concern, this paper
focuses on developing a methodology based on adjusting the fluid model so that
it provides exact mean queue lengths. Further, we provide a computationally
tractable algorithm that exploits Gaussian density in order to obtain
performance measures of the system. We illustrate the accuracy of our algorithm
using a wide variety of numerical experiments.
