In this talk, we will discuss how the choice of traffic model manifests itself in the rare event behavior of a queueing system. Our specific focus is on rare events related to long waiting times in the single-server queue. We will discuss the behavior of such queues in heavy traffic in the presence of both short-range and long-range dependence, and will describe the associated rare event behavior in the heavy-traffic limit. For short-range dependent traffic, we will also characterize the point at which the event becomes sufficiently rare that heavy traffic theory (i.e. the invariance principle) no longer describes the rare event behavior and will discuss the approximations that hold beyond this point.