  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.
