Abstract

This paper is a continuation on my revolutionary theory of solving the pointwise fluid flow approximation model for time-varying queues. Thus, the long-standing simulative approach has now been replaced by an exact solution by using a constant ratio 𝛽 (Ismail's ratio) , offering an exact analytical solution. The stability dynamics of the time-varying 𝑀/𝐸 𝑘 /1 queueing system are then examined numerically in relation to time, 𝛽, and the queueing parameters.