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Telephone call centers offer a convenient communication channel betweenbusinesses and their customers. Efficient management of call centers needsaccurate modeling of customer waiting behavior, which contains importantinformation about customer patience (how long a customer is willing to wait)and service quality (how long a customer needs to wait to get served). Hazardfunctions offer dynamic characterization of customer waiting behavior, andprovide critical inputs for agent scheduling. Motivated by this application, wedevelop a two-way functional hazards (tF-Hazards) model to study customerwaiting behavior as a function of two timescales, waiting duration and the timeof day that a customer calls in. The model stems from a two-way piecewiseconstant hazard function, and imposes low-rank structure and smoothness on thehazard rates to enhance interpretability. We exploit an alternating directionmethod of multipliers (ADMM) algorithm to optimize a penalized likelihoodfunction of the model. We carefully analyze the data from a US bank callcenter, and provide informative insights about customer patience and servicequality patterns along waiting time and across different times of a day. Thefindings provide primitive inputs for call center agent staffing andscheduling, as well as for call center practitioners to understand the effectof system protocols on customer waiting behavior.

To Wait or Not to Wait: Two-way Functional Hazards Model for Understanding Waiting in Call Centers