Estimating customer patience-time density in large-scale call centers

We study the phenomenon of customer abandonment in a G/G/n + GI queue that serves as a building block to model large-scale call centers. In such a queue, customer patience times are assumed to be independent, identically distributed following a general distribution. The patience-time distribution has a huge impact on system performance. For a many-server queue that is heavily loaded with a small or moderate fraction of customer abandonment, theoretical and empirical evidences both suggest that the patience-time density at zero, rather than the entire distribution, often dictates the system performance. Using an asymptotic relationship established in [3], between abandonment processes and queue-length processes, we propose an estimator for the patience-time density at zero. We prove that the estimator is consistent in queues with time-nonhomogeneous arrival processes. We illustrate the effectiveness of this estimator in a realistic setting that allows for both time-varying arrival rates and time-varying staffing levels.