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

We study a single server FIFO queue that offers general service. Each of n customers enter the queue at random time epochs that are independent and identically distributed. We call this the random scattering traffic model, and the queueing model RS/G/1. We study the workload process associated with the queue in two different settings. First, we present Gaussian process approximations in a high intensity asymptotic scale and characterize the transient distribution of the approximation. Second, we study the rare event paths of the workload by proving a large deviations principle in the same high intensity regime. We also obtain exact asymptotics for the Gaussian approximations developed prior. This analysis significantly extends and simplifies recent work in [1] on uniform population acceleration asymptotics to the queue length and workload in the RS/G/1 queue.