Operational decision making in service systems often depends largely on the characterization of the random fluctuations involved. Exogenous arrivals represent a primary source of uncertainty and their stochastic behavior needs to be modeled carefully. In this talk, we will first argue that the conventional approach to arrival modeling which focuses on the microstructure, e.g., the distribution of the inter-arrival times, may be inadequate. Instead, as demonstrated via statistical experiments, the behavior of the arrival process over a longer time scale really matters for the system performance and operational decisions. Then, we will present a critical statistical feature 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.