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In this paper, we consider modeling time-dependent multi-server queues thatinclude abandonments and retrials. For the performance analysis of those, fluidand diffusion models called "strong approximations" have been widely used inthe literature. Although they are proven to be asymptotically exact, theireffectiveness as approximations in critically loaded regimes needs to beinvestigated. To that end, we find that existing fluid and diffusionapproximations might be either inaccurate under simplifying assumptions orcomputationally intractable. To address that concern, this paper focuses ondeveloping a methodology by adjusting the fluid and diffusion models so thatthey significantly improve the estimation accuracy. We illustrate the accuracyof our adjusted models by performing a number of numerical experiments.

Critically loaded multi-server queues with abandonments, retrials, and time-varying parameters