Effectively tailoring fluid and diffusion models for non-stationary state-dependent queueing systems

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.