Forecasting time series of inhomogeneous Poisson processes with application to call center workforce management

TL;DR

This paper introduces a novel method for forecasting inhomogeneous Poisson process rate profiles, specifically applied to call center call arrival rates, improving staffing efficiency through dynamic updates and distributional forecasts.

Contribution

The paper develops a new approach combining factor analysis and time series modeling for Poisson processes, with dynamic updating and distributional forecasting capabilities.

Findings

Improved accuracy in call center staffing predictions

Effective dynamic updating of Poisson rate forecasts

Validated methods through simulation and real data

Abstract

We consider forecasting the latent rate profiles of a time series of inhomogeneous Poisson processes. The work is motivated by operations management of queueing systems, in particular, telephone call centers, where accurate forecasting of call arrival rates is a crucial primitive for efficient staffing of such centers. Our forecasting approach utilizes dimension reduction through a factor analysis of Poisson variables, followed by time series modeling of factor score series. Time series forecasts of factor scores are combined with factor loadings to yield forecasts of future Poisson rate profiles. Penalized Poisson regressions on factor loadings guided by time series forecasts of factor scores are used to generate dynamic within-process rate updating. Methods are also developed to obtain distributional forecasts. Our methods are illustrated using simulation and real data. The empirical results demonstrate how forecasting and dynamic updating of call arrival rates can affect the accuracy of call center staffing.