  Telephone call centers offer a convenient communication channel between
businesses and their customers. Efficient management of call centers needs
accurate modeling of customer waiting behavior, which contains important
information about customer patience (how long a customer is willing to wait)
and service quality (how long a customer needs to wait to get served). Hazard
functions offer dynamic characterization of customer waiting behavior, and
provide critical inputs for agent scheduling. Motivated by this application, we
develop a two-way functional hazards (tF-Hazards) model to study customer
waiting behavior as a function of two timescales, waiting duration and the time
of day that a customer calls in. The model stems from a two-way piecewise
constant hazard function, and imposes low-rank structure and smoothness on the
hazard rates to enhance interpretability. We exploit an alternating direction
method of multipliers (ADMM) algorithm to optimize a penalized likelihood
function of the model. We carefully analyze the data from a US bank call
center, and provide informative insights about customer patience and service
quality patterns along waiting time and across different times of a day. The
findings provide primitive inputs for call center agent staffing and
scheduling, as well as for call center practitioners to understand the effect
of system protocols on customer waiting behavior.
