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Many-Server Fluid Queue

We determine the time-dependent performance of a deterministic fluid model that approximates the many-server Gt/GI/st + GI queueing model. The model has a time-varying arrival rate and service capacity, abandonment from queue, and non-exponential service and patience distributions. Our key assumptions are that (i) the system alternates between overloaded and underloaded intervals, and (ii) the model functions are suitably smooth. The results show the impact of the time-varying parameters and the model distributions on the performance. Simulations confirm that the approximation and the algorithm are effective.