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For a long-standing solution via simulation, this study presents the first-ever analytic modelling for the Pointwise Stationary Fluid Flow Approximation (PSFFA) model of the non-stationary M/D/1 queueing system. This is accomplished by putting out the constant ratio 𝛽 (Ismail’s ratio), which provides a precise analytical answer and links the time-dependent mean arrival and mean service rates. We then do a numerical analysis of the stability dynamics of the time-varying M/D/1 queueing system with respect to time, 𝛽, and the queueing parameters. Applications of Pointwise Fluid Flow Approximation (PSFFA) to the Internet of Things are given. A summary and recommendations for further research round out the paper.
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