Stabilizing Customer Abandonment in Many-Server Queues with Time-Varying Arrivals

An algorithm is developed to determine time-dependent staffing levels to stabilize the time-dependent abandonment probabilities and expected delays at positive target values in the Mt/GI/st + GI many-server queueing model, which has a nonhomogeneous Poisson arrival process the Mt, has general service times the first GI, and allows customer abandonment according to a general patience distribution the +GI. New offered-load and modified-offered-load approximations involving infinite-server models are developed for that purpose. Simulations show that the approximations are effective. A many-server heavy-traffic limit in the efficiency-driven regime shows that i the proposed approximations achieve the goal asymptotically as the scale increases, and ii it is not possible to simultaneously stabilize the mean queue length in the same asymptotic regime.

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