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

TL;DR

This paper analyzes a FIFO queue with high intensity randomly scattered arrivals, providing Gaussian approximations and large deviations principles for workload behavior, extending previous results with simplified methods.

Contribution

It introduces Gaussian process approximations and large deviations analysis for the RS/G/1 queue under high intensity, advancing understanding of workload fluctuations and rare events.

Findings

Gaussian process approximations for workload in high intensity regime

Large deviations principle for workload paths

Exact asymptotics for Gaussian approximations

Abstract

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.