Stabilizing Performance in Many-Server Queues with Time-Varying Arrivals and Customer Feedback

Analytical approximations are developed to determine staffing levels that stabilize performance at designated targets in a many-server queueing model with time-varying arrival rates, customer feedback and abandonment. To provide a flexible model that can be readily fit to system data, Markovian routing is not assumed. Instead, the model has Bernoulli routing, with at most finitely many feedbacks, where the feedback probabilities, service-time and patience distributions all may depend on the visit number. Before returning to receive a new service, the fed-back customers experience delays in an infinite-server or finite-capacity queue, where the parameters may again depend on the visit number. A many-server heavy-traffic FWLLN shows that the performance targets are achieved asymptotically as the scale increases. A new refined modified-offered-load approximation is developed to obtain good results with low waiting-time targets. Simulation experiments confirm that the approximations are effective