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

Analytical offered-load and modified-offered-load (MOL) approximations are developed to determine staffing levels that stabilize performance at designated targets in a non-Markovian many-server queueing model with time-varying arrival rates, customer abandonment from queue and random feedback with additional feedback delay in an infinite-server or finite-server queue. To provide a flexible model that can be readily fit to system data, the model has Bernoulli routing, where the feedback probabilities, service-time, patience-time and feedback-delay distributions all are general and may depend on the visit number. Simulation experiments confirm that the new MOL approximations are effective. A many-server heavy-traffic FWLLN shows that the performance targets are achieved asymptotically as the scale increases.