A semiparametric Bayesian model for queueing arrival processes: An application to call centers

Nonhomogeneous Poisson process models have commonly been used to analyze and forecast arrivals. Such processes require specification of intensity (arrival rate) functions, which are typically defined in a parametric form. The accuracy of the parametric models is highly sensitive to the choice of the specific intensity function for the arrival process. We use a Bayesian framework by proposing a nonparametric form for the intensity function and introduce a robust semiparametric model. The model is suitable for analyzing both time of arrival data and interval censored count data and can capture both monotonic and non-monotonic arrival intensity. The intensity function in the model can be modulated to incorporate auxiliary information as well as seasonal and random effect components. We develop the Bayesian analysis of the proposed model and implement it on two real call center datasets with different characteristics. We also consider several extensions to our model and develop their Bayesian analyses. Our random effects extension model with cumulative baseline intensity changing on the days of the week and interday correlation with the Markov evolution extension model both provide high predictive accuracy. We also show that our proposed semiparametric model has robust performance for out-of-sample predictions. Accurate predictions of arrivals will assist managers in determining appropriate staffing levels and effective workforce scheduling, resulting in more efficient operations.