Many applications call for stochastic models that appropriately describe incoming traffic to a congested resource (e.g. popular websites, call centers, server farms, etc). In this talk, we discuss some of the limitations of conventional Poisson modeling, and point out what we call the “Poisson breakdown phenomenon”. In particular, real-world high volume traffic often exhibits medium time-scale (mesoscopic scale) correlations that are difficult to detect at the microscopic time scale of individual inter-arrivals. In view of this challenge, we discuss a class of Poisson autoregressive models intended to model traffic at such mesoscopic scales. These models are probabilistically very tractable and also lend themselves to straightforward calibration. This work is joint with Xiaowei Zhang.