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

January 2007

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.