# Sample path large deviations for marked point processes in the many sources asymptotic with small buffers: Heavily and lightly loaded systems

## TL;DR

This paper develops new large deviations results for queueing systems with many sources and small buffers, covering both heavily and lightly loaded regimes, and introduces a novel framework for analyzing various scalings.

## Contribution

It provides the first large deviations analysis for lightly loaded systems and introduces a new framework for exploring scalings in many sources queueing models.

## Key findings

- Established large deviations results for heavily loaded systems.
- Derived novel speed scalings for lightly loaded systems.
- Introduced a comprehensive framework for different scalings in many sources asymptotics.

## Abstract

Consider a queueing system fed by traffic from $N$ independent and identically distributed marked point processes. We establish several novel sample path large deviations results in the scaled uniform topology for such a system with a small buffer. This includes both the heavily loaded case (the load grows as $N\rightarrow\infty$) and the previously unexplored lightly loaded case (the load vanishes as $N\rightarrow\infty$); this latter case requires the introduction of novel speed scalings for such queueing systems. Alongside these sample path large deviations results, we introduce a new framework to explore the range of scalings in the many sources asymptotic for these systems.