Operational decision making in service systems often depends largely on the characterization of the random fluctuations involved. Exogenous arrivals (e.g., customers, orders, etc.) represent a primary source of uncertainty and their stochastic behavior needs to be modeled carefully. In this talk, we will present a new statistical finding regarding the random fluctuations of the arrival process in large service systems, and propose a tractable model accordingly. When a service system under the new arrival model is scaled up, its dynamics is fundamentally different from that typical queueing analysis stipulates, and leads to a new staffing rule for managing the servers. At last, we will demonstrate via data-driven simulation that our staffing rule improves the system performance substantially in general.