On the modeling and forecasting of call center arrivals

We review and discuss the key issues in building statistical models for the call arrival process in telephone call centers, and then we survey and compare various types of models proposed so far. These models are used both for simulation and to forecast incoming call volumes to make staffing decisions and build (or update) work schedules for agents who answer those calls. Commercial software and call center managers usually base their decisions solely on point forecasts, given in the form of mathematical expectations (conditional on current information), but distributional forecasts, which come in the form of (conditional) probability distributions, are generally more useful, in particular in the context of simulation. Building realistic models is not simple, because arrival rates are themselves stochastic, time-dependent, dependent across time periods and across call types, and are often affected by external events. As an illustration, we evaluate the forecasting accuracy of selected models in an empirical study with real-life call center data.