The Poisson process has been an integral part of many models for the arrival process to a telephone call centers. However, several publications in recent years suggest the presence of a significant ‘‘overdisperson’’ relative to the Poisson process in real-life call center arrival data. In this paper, we study the overdispersion in the context of ‘‘heavy traffic’’ and identify a critical factor that characterizes the stochastic variability of the arrivals to their averages. We refer to such a factor as the scaling parameter and it potentially has a profound impact on the design of staffing rules. We propose an new model to capture the scaling parameter in this paper.