  We study a single server FIFO queue that offers general service. Each of n
customers enter the queue at random time epochs that are inde- pendent 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.
