Bayesian Forecasting of an Inhomogeneous Poisson Process with Applications to Call Center Data
Jonathan Weinberg, Lawrence D. Brown, Jonathan R. Stroud
The Wharton School, University of Pennsylvania
A call center is a centralized hub where customer and other telephone calls are dealt with by
an organization. In today's economy, they have become the primary point of contact between
customers and businesses. Accurate prediction of the call arrival rate is therefore
indispensable for call center practitioners to staff their call center efficiently and cost
effectively. This article proposes a multiplicative model for modeling and forecasting within-day
arrival rates to a US commercial bank's call center. Markov chain Monte Carlo sampling methods
are used to estimate both latent states and model parameters. One-day-ahead density forecasts
for the rates and counts are provided. The calibration of these predictive distributions
is evaluated by probability integral transforms. Furthermore, we provide one-day-ahead forecast
comparisons with classical statistical methods. Our predictions show significant improvements
of up to 25% over these standards. A sequential Monte Carlo algorithm is also proposed for
sequential estimation and forecasts of the model parameters and rates.
Keywords: Autoregressive models; Bayesian forecasting; call centers; cubic smoothing spline;
inhomogeneous Poisson process; Markov chain Monte Carlo; multiplicative models; sequential
Monte Carlo; state space models.
The manuscript is available in PDF format.