Stabilizing performance in a service system with time-varying arrivals and customer feedback

Analytical approximations are developed to determine the time-dependent offered load (effective demand) and appropriate staffing levels that stabilize performance at designated targets in a many-server queueing model with timevarying arrival rates, customer abandonment from queue and random feedback with additional delay after completing service. To provide a flexible model that can be readily fit to system data, the model has history-dependent Bernoulli routing, 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 finitecapacity queue, where the parameters may again depend on the visit number. 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. A many-server heavy-traffic FWLLN shows that the performance targets are achieved asymptotically as the scale increases.