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We study a single server FIFO queue that offers general service. Each of ncustomers enter the queue at random time epochs that are inde- pendent andidentically distributed. We call this the random scattering traffic model, andthe queueing model RS/G/1. We study the workload process associated with thequeue in two different settings. First, we present Gaussian processapproximations in a high intensity asymptotic scale and characterize thetransient distribution of the approximation. Second, we study the rare eventpaths of the workload by proving a large deviations principle in the same highintensity regime. We also obtain exact asymptotics for the Gaussianapproximations developed prior. This analysis significantly extends andsimplifies recent work in [1] on uniform population acceleration asymptotics tothe queue length and workload in the RS/G/1 queue.

On Gaussian Limits and Large Deviations for Queues Fed by High Intensity Randomly Scattered Traffic