A normal copula model for the arrival process in a call center

We propose and examine a probabilistic model for the multivariate distribution of the number of calls in each period of the day (e.g., 15 or 30 minutes) in a call center, where the marginal distribution of the number of calls in any given period is arbitrary, and the dependence between the periods is modeled via a normal copula. Conditional on the number of calls in a period, their arrival times are independent and uniformly distributed over the period. This type of model has the advantage of being simple and reasonably flexible, and can match the correlations between the arrival counts in different periods much better than previously proposed models. For the situation where the number of periods is large, so the number of correlations to estimate can be excessive, we propose simple parametric forms for the correlations, defined as functions of the time lag between the periods. We test our proposed models on three data sets taken from real-life call centers and compare their goodness of fit to the best previously-proposed methods that we know. In the three cases, the new models provide a much better match of the correlations and of the coefficients of variation of the arrival counts in individual periods.